THEORY OF GENERALIZED INTEGRATED AUTOREGRESSIVE BILINEAR TIME SERIES MODELLING

*¹Ojo J.F. and D. K. Shangodoyin²

¹ Department of Statistics, University of Ibadan, Nigeria

²Department of Statistics, University of Botswana, Botswana

E-mail:jfunminiyiojo@yahoo.co.uk

ABSTRACT

The theory of generalized integrated autoregressive bilinear time series models which are capable of achieving stationary for all nonlinear series are proposed in this paper. These models are denoted by GBL (p, d, 0, r, s). The sufficient conditions for stationary of this bilinear time series models are derived. An algorithm for selecting the best order of the model is proposed. The parameters of the proposed models are estimated using robust nonlinear least squares method and statistical properties of the derived estimates are investigated. The bilinear models are fitted to Wolfer sunspot numbers and stationary conditions are satisfied.

Keywords: Non-linear Least Squares, Parameters, Wolfer sunspot numbers, Algorithm and Stationary