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The Bias of Forecasts from a First-OrderAutoregression

Published online by Cambridge University Press:  11 February 2009

Jan R. Magnus  and
Bahram Pesaran
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Abstract

The exact finite sample behavior is investigated on thebias of multiperiod leastsquares forecasts in thenormal autoregressive modelyt =α +βyt–1+ ut.Necessary and sufficient conditions are given forthe existence of the bias and an expression ispresented which we use to obtain exact numericalresults for finite samples. The unit root and nearunit root behavior is studied in detail and somepopular preconceptions about the behavior of thebias are shown to be false.

Information

Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 2 , June 1991 , pp. 222 - 235
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1. Cryer, J.D., Nankervis, J.C. & Savin, N.E.. Forecast error symmetry in ARIMA models. The University of Iowa typescript, 1989.CrossRefGoogle Scholar
2. Fuller, W.A. & Hasza, D.P.. Predictors for the first-order autoregressive process. Journal of Econometrics 13 (1980): 139–157.10.1016/0304-4076(80)90012-3CrossRefGoogle Scholar
3. Hoque, A., Magnus, J.R. & Pesaran, B.. The exact multi-period mean-square forecast error for the first-order autoregressive model. Journal of Econometrics 39 (1988): 327–346.10.1016/0304-4076(88)90062-0CrossRefGoogle Scholar
4. Lahiri, K. Multiperiod predictions in dynamic models. International Economic Review 16 (1975): 699–711.10.2307/2526004CrossRefGoogle Scholar
5. Magnus, J.R. On certain moments relating to ratios of quadratic forms in normal variables: further results. Sankhyā, Series B (Part 1) 52 (1991): 1–13.Google Scholar
6. Magnus, J.R. & Pesaran, B.. The exact multi-period mean-square forecast error for the firstorder autoregressive model with an intercept. Journal of Econometrics 42 (1989): 157–179.10.1016/0304-4076(89)90001-8CrossRefGoogle Scholar
7. Magnus, J.R. & Rothenberg, T.J.. Least-squares autoregression with near-unit root. LSE other, 1988.Google Scholar
8. Malinvaud, E. Statistical Methods of Econometrics, 2nd Ed. Amsterdam: North-Holland, 1970.Google Scholar
9.Numerical Algorithms Group. NAG Fortran Library Manual, Mark 11. Oxford: NAGLIB, 1984.Google Scholar