Working Paper

Multi-step ahead forecasting of vector time series

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, developing the forecast filters and the forecast error filters explicitly, and also provide formulas for forecasting from a finite-sample of data. This latter application can be accomplished by the use of large matrices, which remains practicable when the total sample size is moderate. Expressions for Mean Square Error of forecasts are also derived, and can be implemented readily. Three diverse data applications illustrate the flexibility and generality of these formulas: forecasting Euro Area macroeconomic aggregates; backcasting fertility rates by racial category; and forecasting regional housing starts using a seasonally co-integrated model.

https://doi.org/10.20955/wp.2012.060

Bibliographic Information

Provider: Federal Reserve Bank of St. Louis

Part of Series: Working Papers

Publication Date: 2012

Number: 2012-060