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David Findley, US Census Bureau Print
Friday, 09 September 2011, 14:00 - 15:00

David Findley, US Census Bureau

Selection Between Non-Nested, Incorrect ARIMA Models via h-Step-Ahead Forecasting

Abstract : We develop and show applications of two new test statistics for deciding if one incorrect ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their asymptotic mean square forecast errors. Both models are assumed to have the correct differencing operator but to be incorrect in other ways. The test statistics differ in the consistent variance estimates used for normalization. One estimate accounts for parameter estimation, the other assumes fixed parameters, and their limiting variances differ when h>1. The h=1 results yield likelihood-ratio-tests for non-nested comparisons. The forecast comparison tests offer improvements to what are known as tests of Diebold and Mariano (1995) type. These often-used tests treat parameters as fixed and utilize variance estimates that are generally inconsistent. For the new test-statistics and the Diebold-Mariano statistic, size and power simulation results will be presented and also an empirical study involving time series modeled in widely used textbooks.

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