A Shrinked Forecast in Stationary Processes Favouring Percentage Error

In stationary time-series forecasting, the commonly used criterion for selecting a proper forecast is the mean square error (MSE), which is minimized by the conditional expectation of future observation given the entire past known as a minimum MSE forecast. In this paper, mean square percentage error (MSPE) instead of is used to forecast autoregressive moving average (ARMA)(p,q) series. The suggested forecast takes the form of 1 - cv2 t+1 or (1 + CV2 t+1)-1 (CV t+1 is the coefficient of variation for one step ahead) times the minimum MSE forecast, which performs better not only in MSPE, but also in mean absolute percentage error (MAPE) than the ordinary MSE forecast in simulation studies. A real data example also supported this result. We conclude that, if percentage error is a prime concern, this shrinked version of MSE forecast performs better than the ordinary forecast in the stationary ARMA(p,q) model