ARIMA, Forecasting, Frequency Domain, Nonstationary, Signal Extraction.
We study the fitting of time series models via minimization of a multi-step ahead forecast error criterion that is based on the asymptotic average of squared forecast errors. Our objective function uses frequency domain concepts, but is formulated in the time domain, and allows estimation of all linear processes (e.g., ARIMA and component ARIMA). By using an asymptotic form of the forecast mean squared error, we obtain a well-defined nonlinear function of the parameters that is provably minimized at the true parameter vector when the model is correctly specified. We derive the statistical properties of the parameter estimates, and study the asymptotic impact of model misspecification on multi-step ahead forecasting. The method is illustrated through a forecasting exercise applied to several time series.
Tucker McElroy and Marc Wilidi. (2012). Multi-Step Ahead Estimation of Time Series Models. Center for Statistical Research & Methodology, Research and Methodology Directorate Research Report Series (Statistics #2012-11). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2012-11.pdf>.
[PDF] or denotes a file in Adobe’s Portable Document Format. To view the file, you will need the Adobe® Reader®
available free from Adobe.
This symbol indicates a link to a non-government web site. Our linking to these sites does not constitute an endorsement of any products, services or the information found on them. Once you link to another site you are subject to the policies of the new site.