Identification of Optimal Models in Higher Order Integrated Autoregressive Models and Autoregressive Integrated Moving Average Models in the Presence of 2^k-1 Subsets

Significant efforts have been made in the study of the theory of integrated autoregressive models and autoregressive integrated moving average models, but less concerted effort has been made in the identification of optimal models which are of great importance in the forecasting of future values. Little attention has been focused on higher order integrated autoregressive models and autoregressive integrated moving average models which are always characterized by many parameters and the use of subsetting that eliminate redundant parameters in these higher order models. This study therefore focuses on identification of optimal models in higher order integrated autoregressive models and autoregressive integrated moving average models in the presence of 2k-1 subsets. The parameters of these models were estimated using Marquardt algorithm and Newton-Raphson iterative method and the statistical properties of the derived estimates were investigated. An algorithm was proposed to eliminate redundant parameters from the full order integrated autoregressive models and autoregressive integrated moving average models. To control the parameters of integrated autoregressive models and autoregressive integrated moving average models in the estimation procedure, the elements of 2k-1 subsets (when k=3) was used. To determine optimal models, residual variance, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were adopted.