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6 - Forecasting in cointegrated systems

Published online by Cambridge University Press:  02 November 2009

Michael Clements
Affiliation:
University of Warwick
David Hendry
Affiliation:
University of Oxford
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Summary

In chapter 4, we considered forecasting in univariate processes using simple time-series models. The properties of forecasts and prediction intervals derived from such models were found to depend crucially on the time-series properties of the variables. This chapter considers forecasting with systems of integrated variables. This is a non-trivial extension of the univariate analysis of forecasting with an integrated variable because of cointegration, whereby a linear combination of individually integrated variables may be non-integrated 1(0) variable, with potentially important consequences for forecasting. We first establish a number of representations of integrated-cointegrated systems, which highlight the relevant features of variables for forecasting. We then derive expressions for the asymptotic forecast-error variances or prediction intervals for multi-step forecasts. A particular form of model mis-specification is considered, that is, the implications for forecast accuracy of not imposing the restrictions implied by cointegration on the forecasting model. Antithetic variates establish conditions for unbiased forecasts. We then address the implications for forecast accuracy of small-sample parameter estimation uncertainty in a Monte Carlo, and compare the outcomes with those obtained using control variates.

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Publisher: Cambridge University Press
Print publication year: 1998

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