Multi-Step Ahead Forecasting of Vector Time Series

FRB of St. Louis Working Paper No. 2012-060B

29 Pages Posted: 8 Dec 2012 Last revised: 26 Sep 2014

See all articles by Tucker McElroy

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology

Michael W. McCracken

Federal Reserve Banks - Federal Reserve Bank of St. Louis

Date Written: September 1, 2014

Abstract

This paper develops the theory of multi-step ahead forecasting for vector time series that exhibit temporal nonstationarity and co-integration. We treat the case of a semi-infinite past by developing the forecast filters and the forecast error filters explicitly. We also provide formulas for forecasting from a finite data sample. This latter application can be accomplished by using large matrices, which remains practicable when the total sample size is moderate. Expressions for the mean square error of forecasts are also derived and can be implemented readily. The flexibility and generality of these formulas are illustrated by four diverse applications: forecasting euro area macroeconomic aggregates; backcasting fertility rates by racial category; forecasting long memory inflation data; and forecasting regional housing starts using a seasonally co-integrated model.

Keywords: Euro Area, Fertility Rates, Frequency Domain, Housing Starts, Multivariate Time Series, VAR Models

JEL Classification: C53, C12, C52

Suggested Citation

McElroy, Tucker and McCracken, Michael W., Multi-Step Ahead Forecasting of Vector Time Series (September 1, 2014). FRB of St. Louis Working Paper No. 2012-060B, Available at SSRN: https://ssrn.com/abstract=2186235 or http://dx.doi.org/10.2139/ssrn.2186235

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology ( email )

4600 Silver Hill Road
Washington, DC 20233-9100
United States

Michael W. McCracken (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of St. Louis ( email )

411 Locust St
Saint Louis, MO 63011
United States