ARCHProcess

ARCHProcess[κ,{α1,,αq}]
represents an autoregressive conditionally heteroscedastic process of order q, driven by a standard white noise.

ARCHProcess[κ,{α1,,αq},init]
represents an ARCH process with initial data init.

DetailsDetails

  • ARCHProcess is a discrete-time and continuous-state random process.
  • A process is an ARCH 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 or a single path TemporalData object with time stamps understood as .
  • A scalar ARCH process can have non-negative coefficients and a positive coefficient κ.
  • ARCHProcess[q] represents an ARCH process of order q for use in EstimatedProcess and related functions.
  • ARCHProcess can be used with such functions as RandomFunction, CovarianceFunction, and TimeSeriesForecast.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Simulate an ARCHProcess:

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Unconditional mean and variance of a weakly stationary process:

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With fixed initial values:

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The observations are uncorrelated but dependent:

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The squared values of the data are correlated:

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Introduced in 2014
(10.0)