The Time Series Module is a tool for constructing ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models. Additional explanatory variables (predictors) may also be present, in which case the model is called MGARCH (Multivariate GARCH). The autoregressive model assumes that the variance of the particular error term is functionally dependent on the past variances. Precisely speaking, if is the error term (white noise) then variance series may be modelled by ARCH(q) process according to the formula

with the constraints and

for

. In case of GARCH(p,q) process, the variance terms are modelled as

with the constraints ,

and

for

. Model estimator is obtained by non-linear maximization of log-likelihood functions. In case of MGARCH(p,q) model, automatic variable selection is available, analogously to other statistical models in AdvancedMiner (see Variable Selection section).