Goodness of fit and model selection criteria for time series models

Abstract

Time series is an important part of decision making and several results are constructed on estimates of forthcoming events. In the Time series process, since, for the coming actions include probability; the predictions are frequently not perfect. The objectives of the Time series are to decrease the prediction error; to create predictions that are rarely improper and that have minor prediction mistakes. In selecting a suitable Time series model, the researcher wants to be responsive that numerous altered models may have comparable properties. A good model will fit the data well. The goodness of fit recovers as additional limits are involved in the model. This arises a problem with the ARMA (p, q) models, because p and q take low values. It should be noted that the best model fit need not imply to provide best forecasts. There exists several model selection criteria that trade off a decrease in the sum of squares of the errors for a more sparing model. A goodness of fit criterion for ARMA (p, q) model and modified selection criteria for Time series models have been suggested in the present study.