Fitting EXPAR Models Through the Extended Kalman Filter

Abstract

Exponential autoregressive (EXPAR) family of parametric nonlinear time-series models, which is a discrete-time approximation of continuous-time nonlinear stochastic dynamical system, is considered. A heartening feature of this model is that it is capable of describing those data sets that depict cyclical variations. The estimation procedure for EXPAR models is developed using extended Kalman filter (EKF). Through simulation studies, it is shown that EKF is very efficient for fitting EXPAR models. Formulae for optimal one-step and two-step ahead out-of-sample forecasts are derived analytically by recursive use of conditional expectation. Conditions for the existence of limit cycle behaviour for EXPAR models are also established. Superiority of EKF method vis-a-vis Genetic algorithms (GA) method for fitting EXPAR models is shown through simulation studies. As an illustration, EXPAR models are employed for modelling and forecasting Oil sardine, Mackerel and Bombay duck time-series landings data in India. It is shown that all the three fitted models exhibit the desirable feature of existence of limit cycle behaviour. It is concluded that the EXPAR model performs better than ARIMA methodology for both modelling and forecasting purposes for the data sets under consideration.