Time-series forecast jointly allowing the unit-root detection and the Box-Cox transformation

An information-criterion-based model-selection method is presented for forecasting that allows for the unit-root detection and the Box-Cox transformation simultaneously. In this method, a battery of alternative models with and without unit root is considered changing the order of autoregressive process and the Box Cox parameter, and the best model is selected using information criteria. Simulation results suggest that the Bayesian information criterion (BIC) outperforms the bias-corrected Akaike information criterion (AICc) and that the augmented Dickey-Fuller test performs worse in the case of incorrect data transformation. The results of forecasting quarterly time series of industrial production indicate that the BIC-based method outperforms the other conventional methods.