+<?xml version="1.0" encoding="UTF-8"?>

+

+<!--

+ *

+ * This help file was generated from arch_test.sci using help_from_sci().

+ *

+ -->

+

+<refentry version="5.0-subset Scilab" xml:id="arch_test" xml:lang="en"

+ xmlns="http://docbook.org/ns/docbook"

+ xmlns:xlink="http://www.w3.org/1999/xlink"

+ xmlns:svg="http://www.w3.org/2000/svg"

+ xmlns:ns3="http://www.w3.org/1999/xhtml"

+ xmlns:mml="http://www.w3.org/1998/Math/MathML"

+ xmlns:scilab="http://www.scilab.org"

+ xmlns:db="http://docbook.org/ns/docbook">

+

+ <refnamediv>

+ <refname>arch_test</refname>

+ <refpurpose>perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P)</refpurpose>

+ </refnamediv>

+

+

+<refsynopsisdiv>

+ <title>Calling Sequence</title>

+ <synopsis>

+ arch_test(Y,X,P)

+ PVAL = arch_test(Y,X,P)

+ [PVAL, LM]= arch_test(Y,X,P)

+ </synopsis>

+</refsynopsisdiv>

+

+<refsection>

+ <title>Parameters</title>

+ <variablelist>

+ <varlistentry><term>P:</term>

+ <listitem><para> Degrees of freedom</para></listitem></varlistentry>

+ <varlistentry><term>PVAL:</term>

+ <listitem><para>PVAL is the p-value (1 minus the CDF of this distribution at LM) of the test</para></listitem></varlistentry>

+ </variablelist>

+</refsection>

+

+<refsection>

+ <title>Description</title>

+ <para>

+perform a Lagrange Multiplier (LM) test of thenull hypothesis of no conditional heteroscedascity against the alternative of CH(P).

+ </para>

+ <para>

+I.e., the model is

+ </para>

+ <para>

+y(t) = b(1) * x(t,1) + ... + b(k) * x(t,k) + e(t),

+ </para>

+ <para>

+given Y up to t-1 and X up to t, e(t) is N(0, h(t)) with

+ </para>

+ <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.

+ </para>

+ <para>

+If the second argument is a scalar integer, k,perform the sametest in a linear autoregression model of orderk, i.e., with

+ </para>

+ <para>

+[1, y(t-1), ..., y(t-K)] as the t-th row of X.

+ </para>

+ <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.

+ </para>

+ <para>

+If no output argument is given, the p-value is displayed.

+</para>

+</refsection>

+</refentry>

+<?xml version="1.0" encoding="UTF-8"?>

+

+<!--

+ *

+ * This help file was generated from detrend1.sci using help_from_sci().

+ *

+ -->

+

+<refentry version="5.0-subset Scilab" xml:id="detrend1" xml:lang="en"

+ xmlns="http://docbook.org/ns/docbook"

+ xmlns:xlink="http://www.w3.org/1999/xlink"

+ xmlns:svg="http://www.w3.org/2000/svg"

+ xmlns:ns3="http://www.w3.org/1999/xhtml"

+ xmlns:mml="http://www.w3.org/1998/Math/MathML"

+ xmlns:scilab="http://www.scilab.org"

+ xmlns:db="http://docbook.org/ns/docbook">

+

+ <refnamediv>

+ <refname>detrend1</refname>

+ <refpurpose>This function removes the best fit of a polynomial of order P from the data X</refpurpose>

+ </refnamediv>

+

+

+<refsynopsisdiv>

+ <title>Calling Sequence</title>

+ <synopsis>

+ detrend1(X,P)

+ </synopsis>

+</refsynopsisdiv>

+

+<refsection>

+ <title>Parameters</title>

+ <variablelist>

+ <varlistentry><term>X:</term>

+ <listitem><para> Input vecor or matrix.</para></listitem></varlistentry>

+ <varlistentry><term>P:</term>

+ <listitem><para> The order of polnomial</para></listitem></varlistentry>

+ </variablelist>

+</refsection>

+

+<refsection>

+ <title>Description</title>

+ <para>

+If X is a vector, 'detrend1(X, P)' removes the best fit of apolynomial of order P from the data X.If X is a matrix, 'detrend1(X, P)' does the same for each column in X.

+ </para>

+ <para>

+The second argument P is optional. If it is not specified, a value of 1 is assumed. This corresponds to removing a linear trend.

+The order of the polynomial can also be given as a string, in which case P must be either "constant" (corresponds to 'P=0') or "linear"(corresponds to 'P=1')

+</para>

+</refsection>

+</refentry>

+<!ENTITY a1495e32bc54c2e2975785e8e2e4521bd SYSTEM "/home/abhinav/Documents/IITB/Repos/FOSSEE-Signal-Processing-Toolbox/help/en_US/arch_test.xml">

+<!ENTITY aead61bf67b6895372794be69a80b5ab9 SYSTEM "/home/abhinav/Documents/IITB/Repos/FOSSEE-Signal-Processing-Toolbox/help/en_US/detrend1.xml">

+&a1495e32bc54c2e2975785e8e2e4521bd;

+&aead61bf67b6895372794be69a80b5ab9;

+ <refpurpose>Return the periodogram (Power Spectral Density) of X</refpurpose>

+

+<refsynopsisdiv>

+ <title>Calling Sequence</title>

+ <synopsis>

+ [PXX, W] = periodogram (X)

+ [PXX, W] = periodogram (X, WIN)

+ [PXX, W] = periodogram (X, WIN, NFFT)

+ [PXX, W] = periodogram (X, WIN, NFFT, FS)

+ [PXX, W] = periodogram (..., "RANGE")

+ </synopsis>

+</refsynopsisdiv>

+

+<refsection>

+ <title>Parameters</title>

+ <variablelist>

+ <varlistentry><term>X:</term>

+ <listitem><para>data vector. If X is real-valued a one-sided spectrum is estimated. If X is complex-valued, or "RANGE" specifies "twosided", the full spectrum is estimated.</para></listitem></varlistentry>

+ <varlistentry><term>WIN:</term>

+ <listitem><para> window weight data. If window is empty or unspecified a default rectangular window is used. Otherwise, the window is applied to the signal ('X .* WIN') before computing th periodogram. The window data must be a vector of the same length as X.</para></listitem></varlistentry>

+ <varlistentry><term>NFFT:</term>

+ <listitem><para>number of frequency bins. The default is 256 or the next higher power of 2 greater than the length of X ('max (256,2.^nextpow2 (length (x)))'). If NFFT is greater than the length of the input then X will be zero-padded to the length of NFFT.</para></listitem></varlistentry>

+ <varlistentry><term>FS:</term>

+ <listitem><para>sampling rate. The default is 1.</para></listitem></varlistentry>

+ <varlistentry><term>RANGE:</term>

+ <listitem><para>range of spectrum. "onesided" computes spectrum from [0..nfft/2+1]."twosided" computes spectrum from [0..nfft-1].</para></listitem></varlistentry>

+ </variablelist>

+</refsection>

+

+<refsection>

+ <title>Description</title>

+ <para>

+The optional second output W are the normalized angular frequencies. For a one-sided calculation W is in the range [0, pi]. If NFFT is even and [0, pi) if NFFT is odd. Similarly, for a two-sided calculation W is in the range [0, 2*pi] or [0, 2*pi)depending on NFFT.

+ </para>

+ <para>

+If a sampling frequency is specified, FS, then the output frequencies F will be in the range [0, FS/2] or [0, FS/2) for one-sided calculations. For two-sided calculations the range will be [0, FS).

+ </para>

+ <para>

+When called with no outputs the periodogram is immediately plotted in the current figure window.

+</para>

+</refsection>

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