# GARCHProcess

GARCHProcess[κ,{α1,,αq},{β1,,βp}]

represents a generalized autoregressive conditionally heteroscedastic process of orders p and q, driven by a standard white noise.

GARCHProcess[κ,{α1,,αq},{β1,,βp},init]

represents a GARCH process with initial data init.

# Details • GARCHProcess is a discrete-time and continuous-state random process.
• A process x[t] is a GARCH process if the conditional mean Expectation[x[t]{x[t-1],}]=0 and the conditional variance given by Expectation[x[t]2{x[t-1],}] satisfies the equation .
• The initial data init can be given as a list {,y[-2],y[-1]} or a single-path TemporalData object with time stamps understood as {,-2,-1}.
• A scalar GARCHProcess should have non-negative coefficients αi and βj and a positive coefficient κ.
• GARCHProcess[q,p] represents a GARCH process of orders q and p for use in EstimatedProcess and related functions.
• GARCHProcess can be used with such functions as RandomFunction, CovarianceFunction, and TimeSeriesForecast.

# Examples

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## Basic Examples(3)

Simulate a GARCHProcess:

 In:= Out= In:= Out= In:= Out= Unconditional mean and variance of a weakly stationary process:

 In:= Out= In:= Out= With fixed initial values:

 In:= Out= In:= Out= The observations are uncorrelated but dependent:

 In:= In:= Out= The squared values of the data are correlated:

 In:= In:= Out= ## Properties & Relations(3)

Introduced in 2014
(10.0)