<?xml-stylesheet type="text/xsl" href="../styles/pmathml.xsl"?>
<!-- saved from url=(0014)about:internet -->
<html xmlns="http://www.w3.org/1999/xhtml" xmlns:dsi="http://www.w3.org/1999/xlink" xmlns:m="http://www.w3.org/1998/Math/MathML" xml:space="preserve"><head><meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"/><title>G13 Chapter Contents : NAG Library Manual, Mark 22</title><link rel="stylesheet" href="../styles/libdoc.css" type="text/css"/></head><body><hr/><div><a class="chap" href="../../pdf/G13/g13conts.pdf">G13 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="g13intro.xml">G13 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div><hr/><h1 class="libdoc">NAG Library Chapter Contents<br/><br/>G13 &#8211; Time Series Analysis</h1>
<h3 class="standard"><a class="chapint" href="../G13/g13intro.xml">G13 Chapter Introduction</a></h3>
<div class="left-tablediv"><table class="contents"><tbody>
<tr>
<td class="contents" valign="top" align="left"><b>Routine<br/>Name</b></td>
<td class="contents" valign="top" align="center"><b>Mark of<br/>Introduction</b></td>
<td class="contents" valign="top" align="left"><br/><b>Purpose</b></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13aaf.xml">G13AAF</a>
<br/><a class="tocexample" href="../../examples/source/g13aafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13aafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, seasonal and non-seasonal differencing</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13abf.xml">G13ABF</a>
<br/><a class="tocexample" href="../../examples/source/g13abfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13abfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, sample autocorrelation function</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13acf.xml">G13ACF</a>
<br/><a class="tocexample" href="../../examples/source/g13acfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13acfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, partial autocorrelations from autocorrelations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13adf.xml">G13ADF</a>
<br/><a class="tocexample" href="../../examples/source/g13adfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13adfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, preliminary estimation, seasonal ARIMA model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13aef.xml">G13AEF</a>
<br/><a class="tocexample" href="../../examples/source/g13aefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13aefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, estimation, seasonal ARIMA model (comprehensive)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13aff.xml">G13AFF</a>
<br/><a class="tocexample" href="../../examples/source/g13affe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13affe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, estimation, seasonal ARIMA model (easy-to-use)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13agf.xml">G13AGF</a>
<br/><a class="tocexample" href="../../examples/source/g13agfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13agfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, update state set for forecasting</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13ahf.xml">G13AHF</a>
<br/><a class="tocexample" href="../../examples/source/g13ahfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13ahfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">9</td>
<td class="contentsdoc" valign="top">Univariate time series, forecasting from state set</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13ajf.xml">G13AJF</a>
<br/><a class="tocexample" href="../../examples/source/g13ajfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13ajfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Univariate time series, state set and forecasts, from fully specified seasonal ARIMA model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13amf.xml">G13AMF</a>
<br/><a class="tocexample" href="../../examples/source/g13amfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13amfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">22</td>
<td class="contentsdoc" valign="top">Univariate time series, exponential smoothing</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13asf.xml">G13ASF</a>
<br/><a class="tocexample" href="../../examples/source/g13asfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13asfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Univariate time series, diagnostic checking of residuals, following <a class="rout" href="../G13/g13aef.xml">G13AEF</a> or <a class="rout" href="../G13/g13aff.xml">G13AFF</a></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13auf.xml">G13AUF</a>
<br/><a class="tocexample" href="../../examples/source/g13aufe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13aufe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">14</td>
<td class="contentsdoc" valign="top">Computes quantities needed for range-mean or standard deviation-mean plot</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13baf.xml">G13BAF</a>
<br/><a class="tocexample" href="../../examples/source/g13bafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, filtering (pre-whitening) by an ARIMA model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bbf.xml">G13BBF</a>
<br/><a class="tocexample" href="../../examples/source/g13bbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, filtering by a transfer function model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bcf.xml">G13BCF</a>
<br/><a class="tocexample" href="../../examples/source/g13bcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, cross-correlations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bdf.xml">G13BDF</a>
<br/><a class="tocexample" href="../../examples/source/g13bdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, preliminary estimation of transfer function model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bef.xml">G13BEF</a>
<br/><a class="tocexample" href="../../examples/source/g13befe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13befe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, estimation of multi-input model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bgf.xml">G13BGF</a>
<br/><a class="tocexample" href="../../examples/source/g13bgfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bgfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, update state set for forecasting from multi-input model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bhf.xml">G13BHF</a>
<br/><a class="tocexample" href="../../examples/source/g13bhfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bhfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, forecasting from state set of multi-input model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13bjf.xml">G13BJF</a>
<br/><a class="tocexample" href="../../examples/source/g13bjfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13bjfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, state set and forecasts from fully specified multi-input model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13caf.xml">G13CAF</a>
<br/><a class="tocexample" href="../../examples/source/g13cafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Univariate time series, smoothed sample spectrum using rectangular, Bartlett, Tukey or Parzen lag window</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13cbf.xml">G13CBF</a>
<br/><a class="tocexample" href="../../examples/source/g13cbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Univariate time series, smoothed sample spectrum using spectral smoothing by the trapezium frequency (Daniell) window</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13ccf.xml">G13CCF</a>
<br/><a class="tocexample" href="../../examples/source/g13ccfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13ccfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, smoothed sample cross spectrum using rectangular, Bartlett, Tukey or Parzen lag window</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13cdf.xml">G13CDF</a>
<br/><a class="tocexample" href="../../examples/source/g13cdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, smoothed sample cross spectrum using spectral smoothing by the trapezium frequency (Daniell) window</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13cef.xml">G13CEF</a>
<br/><a class="tocexample" href="../../examples/source/g13cefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, cross amplitude spectrum, squared coherency, bounds, univariate and bivariate (cross) spectra</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13cff.xml">G13CFF</a>
<br/><a class="tocexample" href="../../examples/source/g13cffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, gain, phase, bounds, univariate and bivariate (cross) spectra</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13cgf.xml">G13CGF</a>
<br/><a class="tocexample" href="../../examples/source/g13cgfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13cgfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">10</td>
<td class="contentsdoc" valign="top">Multivariate time series, noise spectrum, bounds, impulse response function and its standard error</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dbf.xml">G13DBF</a>
<br/><a class="tocexample" href="../../examples/source/g13dbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Multivariate time series, multiple squared partial autocorrelations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dcf.xml">G13DCF</a>
<br/><a class="tocexample" href="../../examples/source/g13dcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">12</td>
<td class="contentsdoc" valign="top">Multivariate time series, estimation of VARMA model<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 24, see <a class="sec" href="../GENINT/replace.xml#G13DCF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13ddf.xml">G13DDF</a>
<br/><a class="tocexample" href="../../examples/source/g13ddfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13ddfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">22</td>
<td class="contentsdoc" valign="top">Multivariate time series, estimation of VARMA model</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13djf.xml">G13DJF</a>
<br/><a class="tocexample" href="../../examples/source/g13djfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13djfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Multivariate time series, forecasts and their standard errors</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dkf.xml">G13DKF</a>
<br/><a class="tocexample" href="../../examples/source/g13dkfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dkfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Multivariate time series, updates forecasts and their standard errors</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dlf.xml">G13DLF</a>
<br/><a class="tocexample" href="../../examples/source/g13dlfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dlfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Multivariate time series, differences and/or transforms</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dmf.xml">G13DMF</a>
<br/><a class="tocexample" href="../../examples/source/g13dmfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dmfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Multivariate time series, sample cross-correlation or cross-covariance matrices</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dnf.xml">G13DNF</a>
<br/><a class="tocexample" href="../../examples/source/g13dnfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dnfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Multivariate time series, sample partial lag correlation matrices, <m:math><m:msup><m:mi>&#967;</m:mi><m:mn>2</m:mn></m:msup></m:math>&#160;statistics and significance levels</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dpf.xml">G13DPF</a>
<br/><a class="tocexample" href="../../examples/source/g13dpfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dpfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">16</td>
<td class="contentsdoc" valign="top">Multivariate time series, partial autoregression matrices</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dsf.xml">G13DSF</a>
<br/><a class="tocexample" href="../../examples/source/g13dsfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dsfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Multivariate time series, diagnostic checking of residuals, following <a class="rout" href="../G13/g13ddf.xml">G13DDF</a></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13dxf.xml">G13DXF</a>
<br/><a class="tocexample" href="../../examples/source/g13dxfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13dxfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Calculates the zeros of a vector autoregressive (or moving average) operator</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13eaf.xml">G13EAF</a>
<br/><a class="tocexample" href="../../examples/source/g13eafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13eafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13ebf.xml">G13EBF</a>
<br/><a class="tocexample" href="../../examples/source/g13ebfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/g13ebfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13faf.xml">G13FAF</a>
<br/><a class="tocexample" href="../../examples/source/g13fafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, parameter estimation for either a symmetric GARCH process or a GARCH process with asymmetry of the form <m:math><m:msup><m:mfenced separators=""><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub><m:mo>+</m:mo><m:mi>&#947;</m:mi></m:mfenced><m:mn>2</m:mn></m:msup></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fbf.xml">G13FBF</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, forecast function for either a symmetric GARCH process or a GARCH process with asymmetry of the form <m:math><m:msup><m:mfenced separators=""><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub><m:mo>+</m:mo><m:mi>&#947;</m:mi></m:mfenced><m:mn>2</m:mn></m:msup></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fcf.xml">G13FCF</a>
<br/><a class="tocexample" href="../../examples/source/g13fcfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, parameter estimation for a GARCH process with asymmetry of the form <m:math><m:msup><m:mfenced separators=""><m:mfenced open="|" close="|" separators=""><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub></m:mfenced><m:mo>+</m:mo><m:mi>&#947;</m:mi><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub></m:mfenced><m:mn>2</m:mn></m:msup></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fdf.xml">G13FDF</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, forecast function for a GARCH process with asymmetry of the form <m:math><m:msup><m:mfenced separators=""><m:mfenced open="|" close="|" separators=""><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub></m:mfenced><m:mo>+</m:mo><m:mi>&#947;</m:mi><m:msub><m:mi>&#949;</m:mi><m:mrow><m:mi>t</m:mi><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow></m:msub></m:mfenced><m:mn>2</m:mn></m:msup></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fef.xml">G13FEF</a>
<br/><a class="tocexample" href="../../examples/source/g13fefe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, parameter estimation for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fff.xml">G13FFF</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, forecast function for an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fgf.xml">G13FGF</a>
<br/><a class="tocexample" href="../../examples/source/g13fgfe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, parameter estimation for an exponential GARCH (EGARCH) process</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../G13/g13fhf.xml">G13FHF</a></td>
<td class="contentsdoc" valign="top" align="center">20</td>
<td class="contentsdoc" valign="top">Univariate time series, forecast function for an exponential GARCH (EGARCH) process</td>
</tr>
</tbody>
</table></div><hr/><div><a class="chap" href="../../pdf/G13/g13conts.pdf">G13 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="g13intro.xml">G13 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div>
<div><hr/><a class="genint" href="../FRONTMATTER/copyright.xml">&#169; The Numerical Algorithms Group Ltd, Oxford, UK. 2009</a></div></body></html>
