Comparing Maximum Likelihood Estimation with Generalized Prediction Problem Mean-Square Minimization Estimation on Time Series Data

• Activity Number: 24
• Type: Topic Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Kevin Tolliver*+ and Tucker S. McElroy
• Companies: U.S. Census Bureau and U.S. Census Bureau
• Keywords: Revision Variance ; Signal Extraction ; Time Series ; generalized prediction problem ; multi-step ahead ; forecasting

Abstract

Revising data is an inevitable consequence of seasonal adjustment. Still, for statistical agencies publishing periodic data it is desirable to have the smallest revisions possible. Because model specification plays an enormous role in determining the multi-step ahead forecasts that are implicitly present in seasonal adjustments, both model selection and model fitting are extremely important for keeping revisions small. Both model fitting and selection are typically treated from a one-step ahead in-sample forecast error, via maximum likelihood estimation (MLE) and the generalized likelihood ratio test. In this paper we address the fitting of seasonal ARIMA models with the generalized prediction problem (GPP) - that minimizes in-sample asymptotic signal extraction revision error. When the model is mis-specified, the GPP estimates can differ substantially from MLEs, and produce smaller asymptotic revisions. We defer the GPP model selection problem, and focus on comparisons of the performance of GPP to MLE using varying data sub-spans and SARIMA models. Empirical results show there is some measurable benefit to the GPP method when the models are not well-specified.