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Properties of Forecast Errors and Estimates of Misspecified RegARIMA and Intermediate Memory Models and the Optimality of GLS for One-Step-Ahead Forecasting

David F. Findley

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ABSTRACT

We consider the modeling of time series that have an asymptotically stationary autocovariance structure and a mean function of linear regression form in which the regression vector satisfies a weakened version of Grenander's conditions, one that allows transitory regression variables of the sort used for outlier and intervention effect modeling. Neither the model's regression vector sequence nor its parametric family of invertible, short/intermediate-memory autocovariances need be correct. Convergence of both likelihood maximizing and squared-forecast-error minimizing parameter estimates are established as a consequence of uniform strong laws for sample second moments of forecast errors. Both OLS and GLS estimates of the mean function are considered. We show that GLS has an optimal one-step-ahead forecasting property relative to OLS when the model omits a regression variable of the true mean function that is asymptotically correlated with a modeled regression variable. Some inherent ambiguity in the concept of bias for regression coefficient estimators in this situation is discussed.

CITATION:

Source: U.S. Census Bureau, Statistical Research Division

Created: 26-SEP-2003


Source: U.S. Census Bureau | Statistical Research Division | (301) 763-3215 (or chad.eric.russell@census.gov) |   Last Revised: October 08, 2010