On the Theory of Bilinear Time Series Models

Abstract

SUMMARY The theory of bilinear time series models is considered in this paper. The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained. The conditions for the invertibility of the model are also included. The estimation of the parameters of the scalar bilinear time series model is considered. The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion. The forecasting of sunspot numbers is also considered.