Selection Between Models Through Multi-Step-Ahead Forecasting
نویسندگان
چکیده
We develop and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their mean square forecast error. The two statistics differ in the variance estimates used for normalization. Both variance estimates are consistent even when the models considered are incorrect. Our main variance estimate is further distinguished by accounting for parameter estimation. The simpler variance estimate, which ignores estimation uncertainty, can be rather straightforwardly calculated for any pair of ARIMA models with the same differencing operator, and its broad consistency property offers improvement to what are known as tests of Diebold and Mariano (1995) type. 1 Statistical Research Division, U.S. Census Bureau, 4600 Silver Hill Road, Washington, D.C. 20233-9100 ∗ Corresponding author. E-mail address: [email protected]
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