Method of regression and time-varying autoregression

A regression and time-varying autoregression (RTVAR) model and a generalized regression and time-varying autoregression (GRTVAR) model are presented. They extend the regression and autoregression model with the covariance stationary error series to that with the generalized time-varying error series. The parameter estimation of RTVAR and GRTVAR models and the GRTVAR prediction formulas are also established. By combining regression and time-varying autoregression, the models can enhance the precision of analysis and forecast in automatic control, fault diagnosis, economic forecast and other fields.