VoseTimeMultiGARCH | Vose Software

# VoseTimeMultiGARCH

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.