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

In the actual world, many time series are not stationary. The purpose of this research is to use the Box and Cox family of transformations to convert a nonstationary time series to a stationary time series in order to determine the influence of a transformation on the data. This is accomplished by setting particular values for the transformation parameter. The sample autocorrelation function (SACF) and the sample partial autocorrelation function (SPACF) were used to test for stationarity of the Box and Cox parameters. 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 EWMA is selected among the competing models using some evaluation 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 EWMA using the RMSE and MAE. Our findings are that the transformed k-th EWMA models outperformed the classical ARIMA on the set of given data.