Optimal Identification of Subclass of Autoregressive Integrated Moving Average Models Using Sum of Square Deviation Forecasts Criterion.

Identification of appropriate subclass of ARIMA models to be fitted to a set of sampled data has ranged from graphical methods to estimation methods. This study is based on the optimal identification of subclass of ARIMA models using Sum of Square Deviation Forecasts Criterion (SSDFC). The algorithm was applied to a known nonstationary series and the result shows that ARIMA (2, 1, 1) is the best fitted model among all subclass of ARIMA models. The Marquardt algorithm and Newton-Raphson iterative algorithm were adopted to estimate the parameters of the model. The SSDFC can compete more favourably than Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in detecting overfitting and identifying the best fitted model to any given time series.