VoseTimeMultiGARCH

See also: Time series in ModelRisk, Vose Multivariate Time Series window; Fitting in ModelRisk;Multivariate Time Series Fit

VoseTimeMultiGARCH({Means}, {Autoregressive factors}, {Moving average factors}, {CovMatrix}, {E0}, {H0}, Log Return, {Initial Values}, Data_in_rows)

 

 

 

Multivariate generalized autoregressive conditional heteroskedaticity time series model.

  • {Means} - array of mean log returns per period for each variable.

  • {Autoregressive factors} - autoregressive parameters matrix.

  • {Moving average factors} - moving average parameters matrix.

  • {CovMatrix} - covariance matrix of log returns.

  • {E0} - vector white noise process at period 0

  • {H0} - conditional covariance matrix 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 Values} - array of starting values (at time zero) for each variable.

  • Data_in_rows - optional parameter that specifies if the data is in rows (TRUE) or columns (FALSE, default).

Equations

where:

- k x k conditional covariance matrix

k - number of variables

- k x 1 random vector, if   is the value of the variable at time t, then is the log return defined as

- k x 1 vector of means

 A - k x k autoregressive coefficient matrix

 B - k x k moving average coefficient matrix

 C - k x k covariance matrix

  - k x 1 vector of uncorrelated random variables, which is defined as follows:

VoseFunctions for this time series

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

VoseTimeMultiGARCHObject - creates an Object for this time series.

VoseTimeMultiGARCHFit - generates an array with random values from this time series fitted to data.

VoseTimeMultiGARCHFitObject - creates an Object for this time series fitted to data.

 

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