A multivariate generalized arch model for time series analysis

In conventional Time series models, the variance of the error term is assumed to be constant. Under certain situations the assumption of constant variance is inappropriate. The residuals derived from an Autoregression or an Autoregressive Moving Average (ARMA) model or standard regression model with conditional variance of study variable in the time series analysis provides an usual Autoregressive Conditional Heteroscedastic (ARCH) model. Eollersler (1986) extended ARCH model by developing a technique that allows the conditional variance to be an ARMA model. The Generalized ARCH (p,q) or GARCH (p,q) model allows for both autoregressive and moving average components in the heteroscedastic variance. The application of GARCH (p,q) model often enhances parsimony, because compared with a pure ARCH model, less parameters are needed for the description of the data.