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<span class="path"><a href="index.html">FOSSEE Signal Processing Toolbox</a> >> <a href="section_e54aa8aac34aa55341e8b4b782fe1a74.html">FOSSEE Signal Processing Toolbox</a> > arch_test</span>
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<div class="refnamediv"><h1 class="refname">arch_test</h1>
<p class="refpurpose">perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P)</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="functionid">arch_test</span><span class="default">(</span><span class="default">Y</span><span class="default">,</span><span class="default">X</span><span class="default">,</span><span class="default">P</span><span class="default">)</span>
<span class="default">PVAL</span><span class="default"> = </span><span class="functionid">arch_test</span><span class="default">(</span><span class="default">Y</span><span class="default">,</span><span class="default">X</span><span class="default">,</span><span class="default">P</span><span class="default">)</span>
<span class="default">[</span><span class="default">PVAL</span><span class="default">, </span><span class="default">LM</span><span class="default">]= </span><span class="functionid">arch_test</span><span class="default">(</span><span class="default">Y</span><span class="default">,</span><span class="default">X</span><span class="default">,</span><span class="default">P</span><span class="default">)</span></pre></div></div>
<div class="refsection"><h3 class="title">Parameters</h3>
<dl><dt><span class="term">P:</span>
<dd><p class="para">Degrees of freedom</p></dd></dt>
<dt><span class="term">PVAL:</span>
<dd><p class="para">PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test</p></dd></dt></dl></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P).</p>
<p class="para">I.e., the model is</p>
<p class="para">y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),</p>
<p class="para">given Y up to t-1 and X up to t, e(t) is N(0, h(t)) with</p>
<p class="para">h(t) = v + a(1) * e(t-1)^2 + ... + a(p) *e(t-p)^2, and the null is a(1) == ... == a(p) == 0.</p>
<p class="para">If the second argument is a scalar integer, k,perform the sametest in a linear autoregression model of orderk, i.e., with</p>
<p class="para">[1, y(t-1), ..., y(t-K)] as the t-th row of X.</p>
<p class="para">Under the null, LM approximatel has a chisquare distribution with P degrees of freedom and PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test.</p>
<p class="para">If no output argument is given, the p-value is displayed.</p></div>
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