Generalized and Subset Integrated Autoregressive Moving Average Bilinear Time Series Models

Abstract

Generalized integrated autoregressive moving average bilinear model which is capable of achieving stationary for all non linear series is proposed and compared with subset generalized integrated autoregressive moving average bilinear model using the residual variance to see which perform better. The parameters of the proposed models are estimated using Newton-Raphson iterative method and Marquardt algorithm and the statistical properties of the derived estimates were investigated. An algorithm was proposed to eliminate redundant parameters from the full order generalized integrated autoregressive moving average bilinear models. To determine the order of the models, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were adopted. Generalized integrated autoregressive moving average bilinear models are fitted to Wolfer sunspot numbers and stationary conditions are satisfied. Generalized integrated autoregressive moving average bilinear model performed better than subset generalized integrated autoregressive bilinear model.

Keywords: Stationary, Newton-Raphson, Residual Variance, Marquardt Algorithm and Parameters.