Effect of Box-Cox Transformation on a k-th Weighted Moving Average Processes for Time Series

Abstract

In this paper, we examine, if the effect of transformation leads to improvement of model performance in time series modeling. The class of transformations that was considered is the Box-Cox family of transformation on the k-th weighted moving average (k-th WMA) model and autoregressive integrated moving average (ARIMA) model from a given nonstationary economic realization time series data. A real nonstationary economic time series data was used to demonstrate this procedure. The nonstationary time series data can be transformed to stationary data using the process of differencing alongside with Box-Cox transformation. The ARIMA model is fitted to the transformed data using the techniques of Box-Jenkins, where the best ARIMA is selected among the competing ARIMA models using Akaike information corrected criterian (AICc) while the best k-th WMA is selected among the competing models using some eval_uation metrics such as root mean square error (RMSE) and mean absolute error (MAE).  Finally, the optimal model is selected between ARIMA model and k-th WMA using the RMSE and MAE. Our findings are that the transformed k-th WMA models outperformed the classical ARIMA models for the set of Box-Cox transformation parameters considered for the data used.