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<pre><span class="strong">/StataProgramFiles/Section 6.do <a href="../../StataProgramFiles/Section 6.do">open</a></span>
file:script:do</pre>
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<td class="colLast">Mon Jan 26 12:53:42 EST 2015</td>
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<span class="cmdcomment">********************************************************************************
// SECTION 6 Volatility
********************************************************************************</span>
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<pre class="wrap">********************************************************************************
// SECTION 6 Volatility
********************************************************************************</pre>
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<td class="colLast">********************************************************************************
// SECTION 6 Volatility
********************************************************************************</td>
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<span class="cmdcomment">// Exercise 1 {Modelling volatility in US yields}</span>
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<pre class="wrap">// Exercise 1 {Modelling volatility in US yields}</pre>
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<td class="colLast">// Exercise 1 {Modelling volatility in US yields}</td>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> **********************************************</div></td>
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10</a> <a onclick='toggle("cmd_-1979827800");' title="webuse">[+]</a>
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<span class="cmdcommand">webuse</span>
<span class="cmdparameters">"<a href="../files/_StataProgramFiles_Section 6.do.html#10">yields</a>.<a href="../tokens/d.html#dta">dta</a>"</span>
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webuse "yields.dta", clear</pre>
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<td class="colLast">"<a href="../files/_StataProgramFiles_Section 6.do.html#10">yields</a>.<a href="../tokens/d.html#dta">dta</a>"</td>
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12</a> <a onclick='toggle("cmd_-278238820");' title="tsset">[+]</a>
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<pre class="wrap">tsset obs , daily</pre>
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<pre class="wrap">replace obs = td(04oct1988)+_n-1</pre>
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<span class="cmdcomment">// 1. ARCH(2)
//See page 449, Brooks for testing ARCH models</span>
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<pre class="wrap">// 1. ARCH(2)
//See page 449, Brooks for testing ARCH models</pre>
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<td class="colLast">// 1. ARCH(2)
//See page 449, Brooks for testing ARCH models</td>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> * First regress the independent variable on a constant.</div></td>
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<span class="cmdcommand">reg</span>
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<pre class="wrap">* First regress the independent variable on a constant.
qui reg dr3m</pre>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> * Next implement the ARCH test.</div></td>
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<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
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<pre class="wrap">* Next implement the ARCH test.
estat archlm, lags(2)</pre>
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24</a> <a onclick='toggle("cmd_-175304630");' title="estat">[+]</a>
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<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
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<pre class="wrap">estat archlm, lags(2)</pre>
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<span class="cmdcommand">reg</span>
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<a name="27" title="estat"><!-- -->
27</a> <a onclick='toggle("cmd_698983132");' title="estat">[+]</a>
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<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags(</a>2)</span>
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33</a> <a onclick='toggle("cmd_1816783112");' title="estat">[+]</a>
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35</a> <a onclick='toggle("cmd_-501524902");' title="reg">[+]</a>
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<a name="36" title="estat"><!-- -->
36</a> <a onclick='toggle("cmd_876113539");' title="estat">[+]</a>
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<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
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<td class="colFirst">command</td>
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37</a> <a onclick='toggle("cmd_-1830627170");' title="comment">[+]</a>
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<span class="cmdcomment">* All the chi2 statistics and p-values are the same as those given in Table 3.
* The results suggest that there is autocorrelation (in the second lag) for all these time series.</span>
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<pre class="wrap">* All the chi2 statistics and p-values are the same as those given in Table 3.
* The results suggest that there is autocorrelation (in the second lag) for all these time series.</pre>
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<td class="colFirst">comment</td>
<td class="colLast">* All the chi2 statistics and p-values are the same as those given in Table 3.
* The results suggest that there is autocorrelation (in the second lag) for all these time series.</td>
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<br>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 2. GARCH(1,1)</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="41" title="arch"><!-- -->
41</a> <a onclick='toggle("cmd_910709659");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">arch</span>
<span class="cmdparameters"> <a href="../tokens/d.html#dr3m">dr3m</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1) // <a href="../files/_StataProgramFiles_Section 6.do.html#41">Refer</a> <a href="../tokens/t.html#to">to</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">slide</a> 15 <a href="../tokens/o.html#of">of</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">lecture</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">handout</a>.</span>
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<pre class="wrap">// 2. GARCH(1,1)
qui arch dr3m, arch(1) garch(1) // Refer to slide 15 of lecture handout.</pre>
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<td class="colFirst">command</td>
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<td class="colFirst">indent</td>
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<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1) // <a href="../files/_StataProgramFiles_Section 6.do.html#41">Refer</a> <a href="../tokens/t.html#to">to</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">slide</a> 15 <a href="../tokens/o.html#of">of</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">lecture</a> <a href="../files/_StataProgramFiles_Section 6.do.html#41">handout</a>.</td>
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<td class="colFirst">parameters</td>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // -arch (1)- corresponds to q // -garch(1)- corresponds to p</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="44" title="est"><!-- -->
44</a> <a onclick='toggle("cmd_621960720");' title="est">[+]</a>
</td>
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<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dr3m">dr3m</a></span>
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<pre class="wrap"> // -arch (1)- corresponds to q
// -garch(1)- corresponds to p
est store dr3m</pre>
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<td class="colFirst">command</td>
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<td class="colFirst">indent</td>
<td class="colLast">0</td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="45" title="arch"><!-- -->
45</a> <a onclick='toggle("cmd_-1355145154");' title="arch">[+]</a>
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46</a> <a onclick='toggle("cmd_1094615193");' title="est">[+]</a>
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<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dr1y">dr1y</a></span>
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47</a> <a onclick='toggle("cmd_-1105929142");' title="arch">[+]</a>
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, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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48</a> <a onclick='toggle("cmd_1114356453");' title="est">[+]</a>
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<span class="cmdcommand">est</span>
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<td class="colLast">0</td>
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<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dr3y">dr3y</a></td>
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<a name="49" title="arch"><!-- -->
49</a> <a onclick='toggle("cmd_-1073268236");' title="arch">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
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, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<a name="50" title="est"><!-- -->
50</a> <a onclick='toggle("cmd_-1772832272");' title="est">[+]</a>
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<span class="cmdcommand">est</span>
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<a name="51" title="arch"><!-- -->
51</a> <a onclick='toggle("cmd_1890477322");' title="arch">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">arch</span>
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, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<a name="52" title="est"><!-- -->
52</a> <a onclick='toggle("cmd_599738868");' title="est">[+]</a>
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<span class="cmdcommand">est</span>
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<a name="53" title="arch"><!-- -->
53</a> <a onclick='toggle("cmd_2142065469");' title="arch">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">arch</span>
<span class="cmdparameters"> <a href="../tokens/d.html#dr10y">dr10y</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<a name="54" title="est"><!-- -->
54</a> <a onclick='toggle("cmd_-2064536303");' title="est">[+]</a>
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<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dr10y">dr10y</a></span>
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<td class="colFirst">command</td>
<td class="colLast">est</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dr10y">dr10y</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="56" title="est"><!-- -->
56</a> <a onclick='toggle("cmd_1852279519");' title="est">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/t.html#table">table</a> <a href="../tokens/d.html#dr3m">dr3m</a> <a href="../tokens/d.html#dr1y">dr1y</a> <a href="../tokens/d.html#dr3y">dr3y</a> <a href="../tokens/d.html#dr5y">dr5y</a> <a href="../tokens/d.html#dr7y">dr7y</a> <a href="../tokens/d.html#dr10y">dr10y</a></span>
, <span class="cmdoptions"> t <a href="../tokens/t.html#title">title</a> ("<a href="../files/_StataProgramFiles_Section 6.do.html#56">Garch(</a>1,1)")</span>
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<pre class="wrap">est table dr3m dr1y dr3y dr5y dr7y dr10y, t title ("Garch(1,1)")</pre>
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<td class="colLast"> t <a href="../tokens/t.html#title">title</a> ("<a href="../files/_StataProgramFiles_Section 6.do.html#56">Garch(</a>1,1)")</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/t.html#table">table</a> <a href="../tokens/d.html#dr3m">dr3m</a> <a href="../tokens/d.html#dr1y">dr1y</a> <a href="../tokens/d.html#dr3y">dr3y</a> <a href="../tokens/d.html#dr5y">dr5y</a> <a href="../tokens/d.html#dr7y">dr7y</a> <a href="../tokens/d.html#dr10y">dr10y</a></td>
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<a name="57" title="comment"><!-- -->
57</a> <a onclick='toggle("cmd_1057786492");' title="comment">[+]</a>
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<span class="cmdcomment">* "arch L1." gives the estimate for alpha_1
* "garch L1." gives the estimate for beta_1
* The constant in the ARCH section is alpha_0
* The other constant is gamma_0</span>
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<pre class="wrap">* "arch L1." gives the estimate for alpha_1
* "garch L1." gives the estimate for beta_1
* The constant in the ARCH section is alpha_0
* The other constant is gamma_0</pre>
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<td class="colFirst">comment</td>
<td class="colLast">* "arch L1." gives the estimate for alpha_1
* "garch L1." gives the estimate for beta_1
* The constant in the ARCH section is alpha_0
* The other constant is gamma_0</td>
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<a name="62" title="comment"><!-- -->
62</a> <a onclick='toggle("cmd_1103388262");' title="comment">[+]</a>
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<span class="cmdcomment">* The results for dr3y, dr5y, dr7y and dr10y are almost identical to those in Table 4.
* The estimates for constant terms for dr3m and dr1y are different (decimals in different places) but t-stats are the same.</span>
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<pre class="wrap">* The results for dr3y, dr5y, dr7y and dr10y are almost identical to those in Table 4.
* The estimates for constant terms for dr3m and dr1y are different (decimals in different places) but t-stats are the same.</pre>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">* The results for dr3y, dr5y, dr7y and dr10y are almost identical to those in Table 4.
* The estimates for constant terms for dr3m and dr1y are different (decimals in different places) but t-stats are the same.</td>
</tr>
</tbody>
</table>
<br>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 3. GARCH-M // Not covered in lectures, but steps can be found at http://www.stata.com/manuals13/tsarch.pdf</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="68" title="arch"><!-- -->
68</a> <a onclick='toggle("cmd_474956191");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/d.html#dr3m">dr3m</a></span>
, <span class="cmdoptions"> <a href="../files/_StataProgramFiles_Section 6.do.html#68">archm</a> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1) <a href="../files/_StataProgramFiles_Section 6.do.html#68">archmexp(</a><a href="../files/_StataProgramFiles_Section 6.do.html#68">sqrt(X</a>))</span>
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<pre class="wrap">// 3. GARCH-M
// Not covered in lectures, but steps can be found at http://www.stata.com/manuals13/tsarch.pdf
arch dr3m, archm arch(1) garch(1) archmexp(sqrt(X))</pre>
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<td class="colLast">arch</td>
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<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/d.html#dr3m">dr3m</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="69" title="est"><!-- -->
69</a> <a onclick='toggle("cmd_940146644");' title="est">[+]</a>
</td>
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<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../files/_StataProgramFiles_Section 6.do.html#69">garchm</a></span>
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<td class="colFirst">command</td>
<td class="colLast">est</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
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<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../files/_StataProgramFiles_Section 6.do.html#69">garchm</a></td>
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<a name="72" title="comment"><!-- -->
72</a> <a onclick='toggle("cmd_1244832881");' title="comment">[+]</a>
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<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">**********************************************</span>
<div id="cmd_1244832881" style="display:none">
<ul class="blockList">
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<pre class="wrap">**********************************************</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">**********************************************</td>
</tr>
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<a name="75" title="comment"><!-- -->
75</a> <a onclick='toggle("cmd_88877329");' title="comment">[+]</a>
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<span class="cmdcomment">// Exercise 2 {Foreign Exchange Market Volatility}</span>
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<pre class="wrap">// Exercise 2 {Foreign Exchange Market Volatility}</pre>
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<td class="colFirst">comment</td>
<td class="colLast">// Exercise 2 {Foreign Exchange Market Volatility}</td>
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<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> **********************************************</div></td>
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<a name="79" title="webuse"><!-- -->
79</a> <a onclick='toggle("cmd_1076953685");' title="webuse">[+]</a>
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<span class="cmdcommand">webuse</span>
<span class="cmdparameters">"<a href="../tokens/h.html#hours">hours</a>.<a href="../tokens/d.html#dta">dta</a>"</span>
, <span class="cmdoptions"> <a href="../tokens/c.html#clear">clear</a></span>
<div id="cmd_1076953685" style="display:none">
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<pre class="wrap">**********************************************
webuse "hours.dta", clear</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">webuse</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/c.html#clear">clear</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast">"<a href="../tokens/h.html#hours">hours</a>.<a href="../tokens/d.html#dta">dta</a>"</td>
</tr>
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<br>
</br>
</div>
</td>
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<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 1. Compute returns</div></td>
</tr>
<tr class="cmd_systemcmd rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="82" title="tsset"><!-- -->
82</a> <a onclick='toggle("cmd_-159932900");' title="tsset">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">tsset</span>
<span class="cmdparameters"><a href="../tokens/o.html#obs">obs</a></span>
, <span class="cmdoptions"> <a href="../tokens/d.html#daily">daily</a></span>
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<pre class="wrap">// 1. Compute returns
tsset obs, daily</pre>
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<td class="colFirst">command</td>
<td class="colLast">tsset</td>
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<tr class="altColor">
<td class="colFirst">indent</td>
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<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/d.html#daily">daily</a></td>
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<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/o.html#obs">obs</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="83" title="g"><!-- -->
83</a> <a onclick='toggle("cmd_-918029191");' title="g">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">g</span>
<span class="cmdparameters"><a href="../tokens/r.html#retbp">retbp</a> = <a href="../tokens/l.html#log">log(</a><a href="../files/_StataProgramFiles_Section 6.do.html#83">bp</a>)-<a href="../tokens/l.html#log">log(</a><a href="../tokens/l.html#L1">L1</a>.<a href="../files/_StataProgramFiles_Section 6.do.html#83">bp</a>)</span>
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<pre class="wrap">g retbp = log(bp)-log(L1.bp)</pre>
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<th class="colFirst" scope="col">key</th>
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<td class="colFirst">command</td>
<td class="colLast">g</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retbp">retbp</a> = <a href="../tokens/l.html#log">log(</a><a href="../files/_StataProgramFiles_Section 6.do.html#83">bp</a>)-<a href="../tokens/l.html#log">log(</a><a href="../tokens/l.html#L1">L1</a>.<a href="../files/_StataProgramFiles_Section 6.do.html#83">bp</a>)</td>
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</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="84" title="g"><!-- -->
84</a> <a onclick='toggle("cmd_-70308238");' title="g">[+]</a>
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<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">g</span>
<span class="cmdparameters"><a href="../tokens/r.html#retdm">retdm</a> = <a href="../tokens/l.html#log">log(</a><a href="../tokens/d.html#dm">dm</a>)-<a href="../tokens/l.html#log">log(</a><a href="../tokens/l.html#L1">L1</a>.<a href="../tokens/d.html#dm">dm</a>)</span>
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<pre class="wrap">g retdm = log(dm)-log(L1.dm)</pre>
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<td class="colFirst">command</td>
<td class="colLast">g</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retdm">retdm</a> = <a href="../tokens/l.html#log">log(</a><a href="../tokens/d.html#dm">dm</a>)-<a href="../tokens/l.html#log">log(</a><a href="../tokens/l.html#L1">L1</a>.<a href="../tokens/d.html#dm">dm</a>)</td>
</tr>
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</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 2. Test for ARCH(1) and ARCH(2)</div></td>
</tr>
<tr class="cmd_estcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="87" title="reg"><!-- -->
87</a> <a onclick='toggle("cmd_650770961");' title="reg">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">reg</span>
<span class="cmdparameters"> <a href="../tokens/r.html#retbp">retbp</a></span>
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<pre class="wrap">// 2. Test for ARCH(1) and ARCH(2)
qui reg retbp</pre>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">reg</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"> <a href="../tokens/r.html#retbp">retbp</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">prefix</td>
<td class="colLast"><a href="../tokens/q.html#qui">qui</a></td>
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</br>
</div>
</td>
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<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="88" title="estat"><!-- -->
88</a> <a onclick='toggle("cmd_412213488");' title="estat">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags(</a>1 2)</span>
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<pre class="wrap">estat archlm, lags(1 2)</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">estat</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/l.html#lags">lags(</a>1 2)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/a.html#archlm">archlm</a></td>
</tr>
</tbody>
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<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_estcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="90" title="reg"><!-- -->
90</a> <a onclick='toggle("cmd_1353815101");' title="reg">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">reg</span>
<span class="cmdparameters"> <a href="../tokens/r.html#retdm">retdm</a></span>
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<pre class="wrap">qui reg retdm</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">reg</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"> <a href="../tokens/r.html#retdm">retdm</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">prefix</td>
<td class="colLast"><a href="../tokens/q.html#qui">qui</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="91" title="estat"><!-- -->
91</a> <a onclick='toggle("cmd_-183645794");' title="estat">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags</a> (1 2)</span>
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<pre class="wrap">estat archlm, lags (1 2)</pre>
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<th class="colLast" scope="col">content</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">estat</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/l.html#lags">lags</a> (1 2)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/a.html#archlm">archlm</a></td>
</tr>
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</br>
</div>
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<tr class="cmd_comment altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="92" title="comment"><!-- -->
92</a> <a onclick='toggle("cmd_-188583435");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">* P-value = 0.0000
* There are ARCH(1) and ARCH(2) effects in the BP and DM exchange rates</span>
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<pre class="wrap">* P-value = 0.0000
* There are ARCH(1) and ARCH(2) effects in the BP and DM exchange rates</pre>
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<td class="colFirst">comment</td>
<td class="colLast">* P-value = 0.0000
* There are ARCH(1) and ARCH(2) effects in the BP and DM exchange rates</td>
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</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 3.(a)</div></td>
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<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="96" title="arch"><!-- -->
96</a> <a onclick='toggle("cmd_-163888713");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/r.html#retbp">retbp</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<pre class="wrap">// 3.(a)
arch retbp , arch(1) garch(1)</pre>
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<th class="colLast" scope="col">content</th>
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<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retbp">retbp</a></td>
</tr>
</tbody>
</table>
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</div>
</td>
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<tr class="cmd_manipulate altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="97" title="predict"><!-- -->
97</a> <a onclick='toggle("cmd_413742072");' title="predict">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">predict</span>
<span class="cmdparameters"><a href="../tokens/h.html#hbp">hbp</a></span>
, <span class="cmdoptions"> <a href="../tokens/v.html#variance">variance</a> // <a href="../tokens/f.html#For">For</a> <a href="../tokens/q.html#question">question</a> 4.</span>
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<pre class="wrap">predict hbp, variance // For question 4.</pre>
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<th class="colLast" scope="col">content</th>
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<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">predict</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/v.html#variance">variance</a> // <a href="../tokens/f.html#For">For</a> <a href="../tokens/q.html#question">question</a> 4.</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/h.html#hbp">hbp</a></td>
</tr>
</tbody>
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</div>
</td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="98" title="arch"><!-- -->
98</a> <a onclick='toggle("cmd_-969179390");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/r.html#retdm">retdm</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<pre class="wrap">arch retdm, arch(1) garch(1)</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retdm">retdm</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_manipulate altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="99" title="predict"><!-- -->
99</a> <a onclick='toggle("cmd_619059825");' title="predict">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">predict</span>
<span class="cmdparameters"><a href="../tokens/h.html#hdm">hdm</a></span>
, <span class="cmdoptions"> <a href="../tokens/v.html#variance">variance</a> // <a href="../tokens/f.html#For">For</a> <a href="../tokens/q.html#question">question</a> 4.</span>
<div id="cmd_619059825" style="display:none">
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<pre class="wrap">predict hdm, variance // For question 4.</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">predict</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/v.html#variance">variance</a> // <a href="../tokens/f.html#For">For</a> <a href="../tokens/q.html#question">question</a> 4.</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/h.html#hdm">hdm</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_comment rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="100" title="comment"><!-- -->
100</a> <a onclick='toggle("cmd_757155129");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">// (b) and (c) not covered in lecture</span>
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<pre class="wrap">// (b) and (c) not covered in lecture</pre>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
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<tbody>
<tr class="altColor">
<td class="colFirst">comment</td>
<td class="colLast">// (b) and (c) not covered in lecture</td>
</tr>
</tbody>
</table>
<br>
</br>
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</td>
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<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 4. Plot conditional variance against actual squared returns // Generate the squared returns</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="104" title="g"><!-- -->
104</a> <a onclick='toggle("cmd_457886398");' title="g">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">g</span>
<span class="cmdparameters"><a href="../tokens/r.html#retbp2">retbp2</a> = <a href="../tokens/r.html#retbp">retbp</a>^2</span>
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<pre class="wrap">// 4. Plot conditional variance against actual squared returns
// Generate the squared returns
g retbp2 = retbp^2</pre>
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<th class="colFirst" scope="col">key</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">g</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retbp2">retbp2</a> = <a href="../tokens/r.html#retbp">retbp</a>^2</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="105" title="g"><!-- -->
105</a> <a onclick='toggle("cmd_214641931");' title="g">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">g</span>
<span class="cmdparameters"><a href="../tokens/r.html#retdm2">retdm2</a> = <a href="../tokens/r.html#retdm">retdm</a>^2</span>
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<pre class="wrap">g retdm2 = retdm^2</pre>
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<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">g</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/r.html#retdm2">retdm2</a> = <a href="../tokens/r.html#retdm">retdm</a>^2</td>
</tr>
</tbody>
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<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // Plot the graphs (and combine, if you wish)</div></td>
</tr>
<tr class="cmd_statcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="107" title="twoway"><!-- -->
107</a> <a onclick='toggle("cmd_-1027532924");' title="twoway">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">twoway</span>
<span class="cmdparameters">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/r.html#retbp2">retbp2</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hbp">hbp</a>)</span>
, <span class="cmdoptions"> <a href="../tokens/n.html#name">name(</a><a href="../tokens/p.html#pl_bp">pl_bp</a>)</span>
<div id="cmd_-1027532924" style="display:none">
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<pre class="wrap">// Plot the graphs (and combine, if you wish)
twoway (tsline retbp2) (tsline hbp), name(pl_bp)</pre>
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<th class="colFirst" scope="col">key</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">twoway</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/n.html#name">name(</a><a href="../tokens/p.html#pl_bp">pl_bp</a>)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/r.html#retbp2">retbp2</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hbp">hbp</a>)</td>
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<br>
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</div>
</td>
</tr>
<tr class="cmd_statcmd rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="108" title="twoway"><!-- -->
108</a> <a onclick='toggle("cmd_1891971895");' title="twoway">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">twoway</span>
<span class="cmdparameters">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/r.html#retdm2">retdm2</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hdm">hdm</a>)</span>
, <span class="cmdoptions"> <a href="../tokens/n.html#name">name(</a><a href="../tokens/p.html#pl_dm">pl_dm</a>)</span>
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<pre class="wrap">twoway (tsline retdm2) (tsline hdm), name(pl_dm)</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
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<th class="colFirst" scope="col">key</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">twoway</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/n.html#name">name(</a><a href="../tokens/p.html#pl_dm">pl_dm</a>)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/r.html#retdm2">retdm2</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hdm">hdm</a>)</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_statcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="109" title="graph combine"><!-- -->
109</a> <a onclick='toggle("cmd_-1766523534");' title="graph combine">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">graph combine</span>
<span class="cmdparameters"><a href="../tokens/p.html#pl_bp">pl_bp</a> <a href="../tokens/p.html#pl_dm">pl_dm</a></span>
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<pre class="wrap">graph combine pl_bp pl_dm</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">graph combine</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/p.html#pl_bp">pl_bp</a> <a href="../tokens/p.html#pl_dm">pl_dm</a></td>
</tr>
</tbody>
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<br>
</br>
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</td>
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<tr class="cmd_comment rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="112" title="comment"><!-- -->
112</a> <a onclick='toggle("cmd_830224962");' title="comment">[+]</a>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">comment</td>
<td class="colLast">**********************************************</td>
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</br>
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<a name="115" title="comment"><!-- -->
115</a> <a onclick='toggle("cmd_689338887");' title="comment">[+]</a>
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<span class="cmdcomment">// Exercise 3 {Modelling Volatility of the S&P Index}</span>
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<pre class="wrap">// Exercise 3 {Modelling Volatility of the S&P Index}</pre>
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<th class="colLast" scope="col">content</th>
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<td class="colFirst">comment</td>
<td class="colLast">// Exercise 3 {Modelling Volatility of the S&P Index}</td>
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<a name="118" title="comment"><!-- -->
118</a> <a onclick='toggle("cmd_923549797");' title="comment">[+]</a>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
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<a name="123" title="comment"><!-- -->
123</a> <a onclick='toggle("cmd_397431965");' title="comment">[+]</a>
</td>
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<span class="cmdcomment">// Exercise 4 {Time varying risk in the Australian term structure}</span>
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<pre class="wrap">// Exercise 4 {Time varying risk in the Australian term structure}</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">// Exercise 4 {Time varying risk in the Australian term structure}</td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="126" title="comment"><!-- -->
126</a> <a onclick='toggle("cmd_-649210921");' title="comment">[+]</a>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
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<td class="colFirst">comment</td>
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131</a> <a onclick='toggle("cmd_1081708535");' title="comment">[+]</a>
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<span class="cmdcomment">// Exercise 5 {Leverage effects in Equity Markets}</span>
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<pre class="wrap">// Exercise 5 {Leverage effects in Equity Markets}</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">// Exercise 5 {Leverage effects in Equity Markets}</td>
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</div>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="134" title="comment"><!-- -->
134</a> <a onclick='toggle("cmd_1127664204");' title="comment">[+]</a>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
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<tbody>
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<td class="colFirst">comment</td>
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</tbody>
</table>
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</br>
</div>
</td>
</tr>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="139" title="comment"><!-- -->
139</a> <a onclick='toggle("cmd_471642110");' title="comment">[+]</a>
</td>
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<span class="cmdcomment">// Exercise 6 {Equity returns}</span>
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<pre class="wrap">// Exercise 6 {Equity returns}</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">// Exercise 6 {Equity returns}</td>
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</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> **********************************************</div></td>
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<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="143" title="webuse"><!-- -->
143</a> <a onclick='toggle("cmd_1735880068");' title="webuse">[+]</a>
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<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">webuse</span>
<span class="cmdparameters">"<a href="../files/_StataProgramFiles_Section 6.do.html#143">equity</a>.<a href="../tokens/d.html#dta">dta</a>"</span>
, <span class="cmdoptions"> <a href="../tokens/c.html#clear">clear</a></span>
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webuse "equity.dta", clear</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">webuse</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/c.html#clear">clear</a></td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast">"<a href="../files/_StataProgramFiles_Section 6.do.html#143">equity</a>.<a href="../tokens/d.html#dta">dta</a>"</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> * Note there are 4952 observations, not 4953 as stated in the question. * Note also that the variables appear to be the percentage returns, not the actual stock index values.</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="146" title="tsset"><!-- -->
146</a> <a onclick='toggle("cmd_1971346310");' title="tsset">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">tsset</span>
<span class="cmdparameters"><a href="../files/_StataProgramFiles_Section 6.do.html#146">datevec</a></span>
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<pre class="wrap">* Note there are 4952 observations, not 4953 as stated in the question.
* Note also that the variables appear to be the percentage returns, not the actual stock index values.
tsset datevec</pre>
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<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">tsset</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../files/_StataProgramFiles_Section 6.do.html#146">datevec</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
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<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 1. Estimate unconditional distribution</div></td>
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<span class="cmdcommand">kdensity</span>
<span class="cmdparameters"><a href="../tokens/f.html#ftse">ftse</a></span>
, <span class="cmdoptions"> <a href="../tokens/n.html#normal">normal</a> <a href="../tokens/t.html#title">title</a> ("<a href="../tokens/k.html#Kernel">Kernel</a> <a href="../tokens/d.html#Density">Density</a> - <a href="../files/_StataProgramFiles_Section 6.do.html#149">FTSE</a>")</span>
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<pre class="wrap">// 1. Estimate unconditional distribution
kdensity ftse, normal title ("Kernel Density - FTSE")</pre>
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<td class="colLast"> <a href="../tokens/n.html#normal">normal</a> <a href="../tokens/t.html#title">title</a> ("<a href="../tokens/k.html#Kernel">Kernel</a> <a href="../tokens/d.html#Density">Density</a> - <a href="../files/_StataProgramFiles_Section 6.do.html#149">FTSE</a>")</td>
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<a name="150" title="kdensity"><!-- -->
150</a> <a onclick='toggle("cmd_170487709");' title="kdensity">[+]</a>
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<span class="cmdcommand">kdensity</span>
<span class="cmdparameters"><a href="../tokens/d.html#dow">dow</a></span>
, <span class="cmdoptions"> <a href="../tokens/n.html#normal">normal</a> <a href="../tokens/t.html#title">title</a> ("<a href="../tokens/k.html#Kernel">Kernel</a> <a href="../tokens/d.html#Density">Density</a> - <a href="../files/_StataProgramFiles_Section 6.do.html#150">Dow</a>")</span>
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<pre class="wrap">kdensity dow, normal title ("Kernel Density - Dow")</pre>
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<td class="colFirst">command</td>
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<a name="151" title="kdensity"><!-- -->
151</a> <a onclick='toggle("cmd_223621260");' title="kdensity">[+]</a>
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<span class="cmdcommand">kdensity</span>
<span class="cmdparameters"><a href="../tokens/n.html#nk">nk</a></span>
, <span class="cmdoptions"> <a href="../tokens/n.html#normal">normal</a> <a href="../tokens/t.html#title">title</a> ("<a href="../tokens/k.html#Kernel">Kernel</a> <a href="../tokens/d.html#Density">Density</a> - <a href="../files/_StataProgramFiles_Section 6.do.html#151">Nikkei</a>")</span>
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<td class="colFirst">command</td>
<td class="colLast">kdensity</td>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 2. Compute daily percentage returns and test for ARCH</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="154" title="reg"><!-- -->
154</a> <a onclick='toggle("cmd_1242928487");' title="reg">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">reg</span>
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<pre class="wrap">// 2. Compute daily percentage returns and test for ARCH
qui reg ftse</pre>
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<td class="colLast">reg</td>
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<a name="155" title="estat"><!-- -->
155</a> <a onclick='toggle("cmd_-1428288965");' title="estat">[+]</a>
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<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</span>
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<td class="colLast">estat</td>
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<td class="colLast"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</td>
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<td class="colLast"><a href="../tokens/a.html#archlm">archlm</a></td>
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<a name="156" title="reg"><!-- -->
156</a> <a onclick='toggle("cmd_-451775995");' title="reg">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
<span class="cmdcommand">reg</span>
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<pre class="wrap">qui reg dow</pre>
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<td class="colFirst">command</td>
<td class="colLast">reg</td>
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<td class="colLast">0</td>
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<a name="157" title="estat"><!-- -->
157</a> <a onclick='toggle("cmd_-173889297");' title="estat">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</span>
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<pre class="wrap">estat archlm, lags(1 2 3)</pre>
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<td class="colFirst">command</td>
<td class="colLast">estat</td>
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<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</td>
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<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/a.html#archlm">archlm</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="158" title="reg"><!-- -->
158</a> <a onclick='toggle("cmd_1200642355");' title="reg">[+]</a>
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<span class="cmdprefix"><a href="../tokens/q.html#qui">qui</a></span>
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<pre class="wrap">qui reg nk</pre>
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<td class="colFirst">command</td>
<td class="colLast">reg</td>
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<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
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<td class="colLast"> <a href="../tokens/n.html#nk">nk</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="159" title="estat"><!-- -->
159</a> <a onclick='toggle("cmd_-941264524");' title="estat">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">estat</span>
<span class="cmdparameters"><a href="../tokens/a.html#archlm">archlm</a></span>
, <span class="cmdoptions"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</span>
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<pre class="wrap">estat archlm, lags(1 2 3)</pre>
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<td class="colFirst">command</td>
<td class="colLast">estat</td>
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<td class="colFirst">indent</td>
<td class="colLast">0</td>
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<td class="colLast"> <a href="../tokens/l.html#lags">lags(</a>1 2 3)</td>
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<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/a.html#archlm">archlm</a></td>
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<a name="160" title="comment"><!-- -->
160</a> <a onclick='toggle("cmd_-274077451");' title="comment">[+]</a>
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<span class="cmdcomment">* All three indices exhibit ARCH(1), ARCH(2) and ARCH(3).</span>
<div id="cmd_-274077451" style="display:none">
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<pre class="wrap">* All three indices exhibit ARCH(1), ARCH(2) and ARCH(3).</pre>
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<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">* All three indices exhibit ARCH(1), ARCH(2) and ARCH(3).</td>
</tr>
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</br>
</div>
</td>
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<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 3. Estimate GARCH(1,1)</div></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="163" title="arch"><!-- -->
163</a> <a onclick='toggle("cmd_-1608570044");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/f.html#ftse">ftse</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<pre class="wrap">// 3. Estimate GARCH(1,1)
arch ftse, arch(1) garch(1)</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/f.html#ftse">ftse</a></td>
</tr>
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</br>
</div>
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<tr class="cmd_other altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="164" title="est"><!-- -->
164</a> <a onclick='toggle("cmd_1178781545");' title="est">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/f.html#ftse">ftse</a></span>
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<pre class="wrap">est store ftse</pre>
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<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">est</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../tokens/f.html#ftse">ftse</a></td>
</tr>
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</br>
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<tr class="cmd_manipulate rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="165" title="predict"><!-- -->
165</a> <a onclick='toggle("cmd_1516577089");' title="predict">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">predict</span>
<span class="cmdparameters"><a href="../tokens/h.html#hftse">hftse</a></span>
, <span class="cmdoptions"> <a href="../tokens/v.html#variance">variance</a></span>
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<pre class="wrap">predict hftse, variance</pre>
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<th class="colLast" scope="col">content</th>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">predict</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/v.html#variance">variance</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/h.html#hftse">hftse</a></td>
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<td class="colFirst" style="width:30px;text-align:right;">
<a name="167" title="arch"><!-- -->
167</a> <a onclick='toggle("cmd_-1412344800");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/d.html#dow">dow</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
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<pre class="wrap">arch dow, arch(1) garch(1)</pre>
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<th class="colLast" scope="col">content</th>
</tr>
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<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/d.html#dow">dow</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="168" title="est"><!-- -->
168</a> <a onclick='toggle("cmd_-1026048436");' title="est">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dow">dow</a></span>
<div id="cmd_-1026048436" style="display:none">
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<pre class="wrap">est store dow</pre>
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<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">est</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../tokens/d.html#dow">dow</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_manipulate altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="169" title="predict"><!-- -->
169</a> <a onclick='toggle("cmd_-1490384559");' title="predict">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">predict</span>
<span class="cmdparameters"><a href="../tokens/h.html#hdow">hdow</a></span>
, <span class="cmdoptions"> <a href="../tokens/v.html#variance">variance</a></span>
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<pre class="wrap">predict hdow, variance</pre>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">predict</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/v.html#variance">variance</a></td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/h.html#hdow">hdow</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="171" title="arch"><!-- -->
171</a> <a onclick='toggle("cmd_-126384452");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../tokens/n.html#nk">nk</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
<div id="cmd_-126384452" style="display:none">
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<pre class="wrap">arch nk, arch(1) garch(1)</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/n.html#nk">nk</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="172" title="est"><!-- -->
172</a> <a onclick='toggle("cmd_-1867470388");' title="est">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">est</span>
<span class="cmdparameters"><a href="../tokens/s.html#store">store</a> <a href="../tokens/n.html#nk">nk</a></span>
<div id="cmd_-1867470388" style="display:none">
<ul class="blockList">
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<pre class="wrap">est store nk</pre>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">est</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/s.html#store">store</a> <a href="../tokens/n.html#nk">nk</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_manipulate rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="173" title="predict"><!-- -->
173</a> <a onclick='toggle("cmd_-1735002026");' title="predict">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">predict</span>
<span class="cmdparameters"><a href="../tokens/h.html#hnk">hnk</a></span>
, <span class="cmdoptions"> <a href="../tokens/v.html#variance">variance</a></span>
<div id="cmd_-1735002026" style="display:none">
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<pre class="wrap">predict hnk, variance</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">predict</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/v.html#variance">variance</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/h.html#hnk">hnk</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // Plot conditional variances</div></td>
</tr>
<tr class="cmd_statcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="176" title="twoway"><!-- -->
176</a> <a onclick='toggle("cmd_-1289925210");' title="twoway">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">twoway</span>
<span class="cmdparameters">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hftse">hftse</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hdow">hdow</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hnk">hnk</a>)</span>
<div id="cmd_-1289925210" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">// Plot conditional variances
twoway (tsline hftse) (tsline hdow) (tsline hnk)</pre>
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</ul>
<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">twoway</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast">(<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hftse">hftse</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hdow">hdow</a>) (<a href="../tokens/t.html#tsline">tsline</a> <a href="../tokens/h.html#hnk">hnk</a>)</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_comment rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="178" title="comment"><!-- -->
178</a> <a onclick='toggle("cmd_-34819646");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">// 4.
// Not covered in lecture</span>
<div id="cmd_-34819646" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">// 4.
// Not covered in lecture</pre>
</li>
</ul>
<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">comment</td>
<td class="colLast">// 4.
// Not covered in lecture</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_comment altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="182" title="comment"><!-- -->
182</a> <a onclick='toggle("cmd_1188174258");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">**********************************************</span>
<div id="cmd_1188174258" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">**********************************************</pre>
</li>
</ul>
<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">**********************************************</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_comment rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="185" title="comment"><!-- -->
185</a> <a onclick='toggle("cmd_-1141204842");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">// Exercise 7 {Bond spreads}</span>
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<pre class="wrap">// Exercise 7 {Bond spreads}</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">comment</td>
<td class="colLast">// Exercise 7 {Bond spreads}</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_comment altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="188" title="comment"><!-- -->
188</a> <a onclick='toggle("cmd_-103841680");' title="comment">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcomment">**********************************************
// The .dta file is not on the server. Find it in the folder or ask for it.</span>
<div id="cmd_-103841680" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">**********************************************
// The .dta file is not on the server. Find it in the folder or ask for it.</pre>
</li>
</ul>
<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">comment</td>
<td class="colLast">**********************************************
// The .dta file is not on the server. Find it in the folder or ask for it.</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // Generate a time variable</div></td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="192" title="g"><!-- -->
192</a> <a onclick='toggle("cmd_1650263564");' title="g">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">g</span>
<span class="cmdparameters"><a href="../tokens/o.html#obs">obs</a> = 1+<a href="../tokens/_.html#_n">_n</a>-1</span>
<div id="cmd_1650263564" style="display:none">
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<pre class="wrap">// Generate a time variable
g obs = 1+_n-1</pre>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">g</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/o.html#obs">obs</a> = 1+<a href="../tokens/_.html#_n">_n</a>-1</td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_systemcmd altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="193" title="tsset"><!-- -->
193</a> <a onclick='toggle("cmd_-140359742");' title="tsset">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">tsset</span>
<span class="cmdparameters"><a href="../tokens/o.html#obs">obs</a></span>
, <span class="cmdoptions"> <a href="../tokens/d.html#daily">daily</a></span>
<div id="cmd_-140359742" style="display:none">
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<pre class="wrap">tsset obs, daily</pre>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">tsset</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/d.html#daily">daily</a></td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../tokens/o.html#obs">obs</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 1. Plot</div></td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="195" title="tsline"><!-- -->
195</a> <a onclick='toggle("cmd_-721573730");' title="tsline">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">tsline</span>
<span class="cmdparameters"><a href="../variables/spread.html">spread</a></span>
<div id="cmd_-721573730" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">// 1. Plot
tsline spread</pre>
</li>
</ul>
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<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">tsline</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../variables/spread.html">spread</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_other altColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="196" title="tsline"><!-- -->
196</a> <a onclick='toggle("cmd_670952983");' title="tsline">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">tsline</span>
<span class="cmdparameters"><a href="../variables/rets.html">rets</a></span>
<div id="cmd_670952983" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">tsline rets</pre>
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<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="altColor">
<td class="colFirst">command</td>
<td class="colLast">tsline</td>
</tr>
<tr class="rowColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../variables/rets.html">rets</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr>
<td class="colFirst" style="width:30px"></td>
<td class="colLast" style="padding-left:0em"><div class="cmd_comment"> // 2. Estimate GARCH(1,1)</div></td>
</tr>
<tr class="cmd_other rowColor">
<td class="colFirst" style="width:30px;text-align:right;">
<a name="199" title="arch"><!-- -->
199</a> <a onclick='toggle("cmd_-1929833310");' title="arch">[+]</a>
</td>
<td class="colLast" style="padding-left:0em">
<span class="cmdcommand">arch</span>
<span class="cmdparameters"><a href="../variables/rets.html">rets</a></span>
, <span class="cmdoptions"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</span>
<div id="cmd_-1929833310" style="display:none">
<ul class="blockList">
<li class="blockList">
<pre class="wrap">// 2. Estimate GARCH(1,1)
arch rets, arch(1) garch(1)</pre>
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</ul>
<table class="packageSummary" border="0" cellpadding="3" cellspacing="0" summary="Properties">
<caption><span><a name="properties"><!-- --></a>All properties</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colFirst" scope="col">key</th>
<th class="colLast" scope="col">content</th>
</tr>
<tbody>
<tr class="rowColor">
<td class="colFirst">command</td>
<td class="colLast">arch</td>
</tr>
<tr class="altColor">
<td class="colFirst">indent</td>
<td class="colLast">0</td>
</tr>
<tr class="rowColor">
<td class="colFirst">options</td>
<td class="colLast"> <a href="../tokens/a.html#arch">arch(</a>1) <a href="../tokens/g.html#garch">garch(</a>1)</td>
</tr>
<tr class="altColor">
<td class="colFirst">parameters</td>
<td class="colLast"><a href="../variables/rets.html">rets</a></td>
</tr>
</tbody>
</table>
<br>
</br>
</div>
</td>
</tr>
<tr class="cmd_manipulate altColor">
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********************************************************************************
// SECTION 6 Volatility
********************************************************************************
// Exercise 1 {Modelling volatility in US yields}
**********************************************
webuse "yields.dta", clear
tsset obs , daily
replace obs = td(04oct1988)+_n-1
// 1. ARCH(2)
//See page 449, Brooks for testing ARCH models
* First regress the independent variable on a constant.
qui reg dr3m
* Next implement the ARCH test.
estat archlm, lags(2)
qui reg dr1y
estat archlm, lags(2)
qui reg dr3y
estat archlm, lags(2)
qui reg dr5y
estat archlm, lags(2)
qui reg dr7y
estat archlm, lags(2)
qui reg dr10y
estat archlm, lags(2)
* All the chi2 statistics and p-values are the same as those given in Table 3.
* The results suggest that there is autocorrelation (in the second lag) for all these time series.
// 2. GARCH(1,1)
qui arch dr3m, arch(1) garch(1) // Refer to slide 15 of lecture handout.
// -arch (1)- corresponds to q
// -garch(1)- corresponds to p
est store dr3m
qui arch dr1y, arch(1) garch(1)
est store dr1y
qui arch dr3y, arch(1) garch(1)
est store dr3y
qui arch dr5y, arch(1) garch(1)
est store dr5y
qui arch dr7y, arch(1) garch(1)
est store dr7y
qui arch dr10y, arch(1) garch(1)
est store dr10y
est table dr3m dr1y dr3y dr5y dr7y dr10y, t title ("Garch(1,1)")
* "arch L1." gives the estimate for alpha_1
* "garch L1." gives the estimate for beta_1
* The constant in the ARCH section is alpha_0
* The other constant is gamma_0
* The results for dr3y, dr5y, dr7y and dr10y are almost identical to those in Table 4.
* The estimates for constant terms for dr3m and dr1y are different (decimals in different places) but t-stats are the same.
// 3. GARCH-M
// Not covered in lectures, but steps can be found at http://www.stata.com/manuals13/tsarch.pdf
arch dr3m, archm arch(1) garch(1) archmexp(sqrt(X))
est store garchm
**********************************************
// Exercise 2 {Foreign Exchange Market Volatility}
**********************************************
webuse "hours.dta", clear
// 1. Compute returns
tsset obs, daily
g retbp = log(bp)-log(L1.bp)
g retdm = log(dm)-log(L1.dm)
// 2. Test for ARCH(1) and ARCH(2)
qui reg retbp
estat archlm, lags(1 2)
qui reg retdm
estat archlm, lags (1 2)
* P-value = 0.0000
* There are ARCH(1) and ARCH(2) effects in the BP and DM exchange rates
// 3.(a)
arch retbp , arch(1) garch(1)
predict hbp, variance // For question 4.
arch retdm, arch(1) garch(1)
predict hdm, variance // For question 4.
// (b) and (c) not covered in lecture
// 4. Plot conditional variance against actual squared returns
// Generate the squared returns
g retbp2 = retbp^2
g retdm2 = retdm^2
// Plot the graphs (and combine, if you wish)
twoway (tsline retbp2) (tsline hbp), name(pl_bp)
twoway (tsline retdm2) (tsline hdm), name(pl_dm)
graph combine pl_bp pl_dm
**********************************************
// Exercise 3 {Modelling Volatility of the S&P Index}
**********************************************
// Data file not available
**********************************************
// Exercise 4 {Time varying risk in the Australian term structure}
**********************************************
// Data file not available
**********************************************
// Exercise 5 {Leverage effects in Equity Markets}
**********************************************
// Data file not available
**********************************************
// Exercise 6 {Equity returns}
**********************************************
webuse "equity.dta", clear
* Note there are 4952 observations, not 4953 as stated in the question.
* Note also that the variables appear to be the percentage returns, not the actual stock index values.
tsset datevec
// 1. Estimate unconditional distribution
kdensity ftse, normal title ("Kernel Density - FTSE")
kdensity dow, normal title ("Kernel Density - Dow")
kdensity nk, normal title ("Kernel Density - Nikkei")
// 2. Compute daily percentage returns and test for ARCH
qui reg ftse
estat archlm, lags(1 2 3)
qui reg dow
estat archlm, lags(1 2 3)
qui reg nk
estat archlm, lags(1 2 3)
* All three indices exhibit ARCH(1), ARCH(2) and ARCH(3).
// 3. Estimate GARCH(1,1)
arch ftse, arch(1) garch(1)
est store ftse
predict hftse, variance
arch dow, arch(1) garch(1)
est store dow
predict hdow, variance
arch nk, arch(1) garch(1)
est store nk
predict hnk, variance
// Plot conditional variances
twoway (tsline hftse) (tsline hdow) (tsline hnk)
// 4.
// Not covered in lecture
**********************************************
// Exercise 7 {Bond spreads}
**********************************************
// The .dta file is not on the server. Find it in the folder or ask for it.
// Generate a time variable
g obs = 1+_n-1
tsset obs, daily
// 1. Plot
tsline spread
tsline rets
// 2. Estimate GARCH(1,1)
arch rets, arch(1) garch(1)
predict hrets, variance
tsline hrets
// 3.
// Not covered in lecture
// 4.
// Not covered in lecture
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