Matthew Kramer, William R. Bell, and Sergio Koreisha
KEYWORDS:ARIMA model, automatic model selection, differencing
ABSTRACT:Much research on time series model identification or selection assumes that model choice has important consequences for forecast accuracy. We empirically investigate this issue using a test data set of 40 Census Bureau seasonal time series. In previously reported work, ARIMA models were independently chosen for these series by three experienced modellers, and by a modification of the automatic selection scheme of Pukilla, Koreisha, and Kallinen (Biometrika 1990, 537--548). Out-of-sample evaluations showed the forecast accuracies of the different models chosen for a given series were nearly identical. In that investigation the models were constrained to differ only in regard to their nonseasonal autoregressive and moving average orders. The present paper extends consideration to other models, including a "naive" model, use of the popular "airline model" for all series, use of models with only seasonal differencing versus seasonal and nonseasonal differencing, and Harvey's (1989) ARIMA component (structural) models. We investigate which model differences, if any, affect forecast accuracy, and also investigate the empirical accuracy of the usual model-based estimates of expected forecast mean squared error.