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Generalized integrated autoregressive bilinear model which is capable of achieving stationary for all non linear series is proposed and compared with subset generalized integrated autoregressive 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 bilinear models. To determine the order of the models, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were adopted. Generalized integrated autoregressive bilinear models are fitted to Wolfer sunspot numbers and stationary conditions are satisfied. Generalized integrated autoregressive bilinear model performed better than subset generalized integrated autoregressive bilinear model.

Generalized and subset integrated autoregressive bilinear time series models with applications