Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T18:19:51.952Z Has data issue: false hasContentIssue false
  • English
  • Français

The Bias of Forecasts from a First-Order Autoregression

Published online by Cambridge University Press:  11 February 2009

Jan R. Magnus  and
Bahram Pesaran
Get access Rights & Permissions [Opens in a new window]

Abstract

The exact finite sample behavior is investigated on the bias of multiperiod leastsquares forecasts in the normal autoregressive model yt = α + βyt–1 + ut. Necessary and sufficient conditions are given for the existence of the bias and an expression is presented which we use to obtain exact numerical results for finite samples. The unit root and near unit root behavior is studied in detail and some popular preconceptions about the behavior of the bias are shown to be false.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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