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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_fit</span>
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<div class="refnamediv"><h1 class="refname">arch_fit</h1>
<p class="refpurpose">This functions fits an ARCH regression model to the time series Y using the scoring algorithm in Engle's original ARCH paper.</p></div>
<div class="refsynopsisdiv"><h3 class="title">Calling Sequence</h3>
<div class="synopsis"><pre><span class="default">[</span><span class="default">A</span><span class="default">, </span><span class="default">B</span><span class="default">] = </span><span class="functionid">arch_fit</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">ITER</span><span class="default">, </span><span class="default">GAMMA</span><span class="default">, </span><span class="default">A0</span><span class="default">, </span><span class="default">B0</span><span class="default">)</span></pre></div></div>
<div class="refsection"><h3 class="title">Parameters</h3>
<dl></dl></div>
<div class="refsection"><h3 class="title">Description</h3>
<p class="para">Fit an ARCH regression model to the time series Y using the scoring algorithm in Engle's original ARCH paper.</p>
<p class="para">The model is</p>
<p class="para">y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),
h(t) = a(1) + a(2) * e(t-1)^2 + ... + a(p+1) * e(t-p)^2</p>
<p class="para">in which e(t) is N(0, h(t)), given a time-series vector Y up to time t-1 and a matrix of (ordinary) regressors X up to t. The order of the regression of the residual variance is specified by P.</p>
<p class="para">If invoked as 'arch_fit (Y, K, P)' with a positive integer K, fit an ARCH(K, P) process, i.e., do the above with the t-th row of X given by</p>
<p class="para">[1, y(t-1), ..., y(t-k)]</p>
<p class="para">Optionally, one can specify the number of iterations ITER, the updating factor GAMMA, and initial values a0 and b0 for the scoring algorithm.</p></div>
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