On specication, stationarity and estimation of parameters of

mixed one-dimensional seasonal autoregressive integrated moving

average bilinear time series models

J.F. Ojoaand L.O. Adekolab

Department of Statistics, University of Ibadan, Ibadan, Nigeria; bDepartment of Physical

Sciences, Bells University of Technology, Ota, Nigeria

Abstract. 

In practice, many time series processes exhibit both the seasonal and non-seasonal behaviour

coupled with their nonlinear nature. Hence, this study considers the Specication, Stationarity and Esti-

mation of the parameters of the full one-dimensional Mixed Seasonal Autoregressive Integrated Moving

Average Bilinear Models (MSARIMABL) which are capable of achieving stationarity for all nonlinear

seasonal time series. The stationarity and convergence conditions for these models are established. The

nonlinear least squares method of minimizing errors and the Newton-Raphson iterative procedure are

employed in the estimation of the parameters.

Keywords: mixed, one-dimensional, integrated, seasonal bilinear time series model, least square method, Newton-Raphson iterative procedure.