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
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: Suggested Citation
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