VoseTimeARCH

See also: Time series in ModelRisk; Fitting in ModelRisk;Univariate Time Series Fit

VoseTimeARCH(Mu, Omega, A, R0, Log Return, Initial Value)

Array function that models an autoregressive conditional heteroskedasticity time series of order 1.

Mu - mean log return;
Omega - the constant coefficient of the variance equation;
A - autoregressive parameter;
R0 - the log return at period 0;
Log Return - an optional parameter. Function generates log returns if set to TRUE, or variable values if set to FALSE or omitted;
Initial Value - starting value (at time zero). The generated time series values will continue on from this value. Should only be provided if the Log Return parameter is set to FALSE or omitted.

As the Vose Time Series functions typically take a lot of parameters, we recommend for these in particular to use the Time Series window for these.

Equations

where:

- a sample from a Normal(0,1)

- if is the value of the variable at time t, then is the log return defined as

- log return mean

- log return standard deviation

- log return variance constant

a - sigma autoregressive factor

VoseFunctions for this time series

VoseTimeARCH - generates an array of random values from this time series.

VoseTimeARCHFit - generates an array of random values from this time series fitted to data.

VoseTimeARCHFitP - returns the parameters of this time series fitted to data.

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