Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-01T13:59:26.840Z Has data issue: false hasContentIssue false
  • English
  • Français

(WHEN) DO LONG AUTOREGRESSIONS ACCOUNT FOR NEGLECTED CHANGES IN PARAMETERS?

Published online by Cambridge University Press:  13 July 2015

Matei Demetrescu  and
Uwe Hassler
Matei Demetrescu*
Affiliation:
Christian-Albrechts-University of Kiel
Uwe Hassler
Affiliation:
Goethe University Frankfurt
*
*Address correspondence to Matei Demetrescu, Institute for Statistics and Econometrics, Christian-Albrechts-University of Kiel, Olshausenstr. 40-60, D-24118 Kiel, Germany; e-mail: mdeme@stat-econ.uni-kiel.de.
Get access Rights & Permissions [Opens in a new window]

Abstract

To construct forecasts for time series exhibiting breaks, the paper examines long autoregressions, where the number of lags is growing with T, and possible breaks are simply ignored. The paper shows that the OLS estimators are still elementwise consistent for the true autoregressive coefficients when neglecting a break in mean, but the sum of the estimators converges to unity. Thanks to this unit-root like behavior of the fitted model, the resulting conditional forecasts are consistent for the true values. As long as the dynamic structure is invariant, the robustness property of the forecasts holds a) under data-dependent lag length selection, b) for a piecewise smoothly varying mean function, and c) under general autoregressive dynamics of possibly infinite order including stationary long memory. Under breaks in the dynamic structure, however, estimators are asymptotically biased, and the forecasts from long autoregressions are biased themselves even in the limit.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 6 , December 2016 , pp. 1317 - 1348
Copyright
Copyright © Cambridge University Press 2015 

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

Akaike, H. (1969) Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics 21(1), 243–247.CrossRefGoogle Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2(3), 489–502.CrossRefGoogle Scholar
Bhansali, R. (1978) Linear prediction by autoregressive model fitting in the time domain. The Annals of Statistics 6(1), 224–231.CrossRefGoogle Scholar
Brockwell, P.J. & Davis, R.A. (1991) Time Series: Theory and Methods. Springer.CrossRefGoogle Scholar
Clements, M.P. & Hendry, D.F. (2006) Forecasting with breaks. In Elliott, G., Granger, C.W.J., & Timmermann, A. (eds.), Handbook of Economic Forecasting, vol. 1, pp. 605–657. Elsevier.CrossRefGoogle Scholar
Clements, M.P. & Hendry, D.F. (2011) Forecasting from misspecified models in the presence of unanticipated location shifts. In Clements, M.P. & Hendry, D.F. (eds.), Oxford Handbook of Economic Forecasting, pp. 271–313. Oxford University Press.CrossRefGoogle Scholar
Demetrescu, M. (2009) Panel unit root testing with nonlinear instruments for infinite-order autoregressive processes. Journal of Time Series Econometrics 1(2), Article 3.CrossRefGoogle Scholar
Durbin, J. (1960) The fitting of time-series models. Revue de l’Institut International de Statistique 28(3), 233–244.CrossRefGoogle Scholar
Giraitis, L., Kapetanios, G., & Price, S. (2013) Adaptive forecasting in the presence of recent and ongoing structural change. Journal of Econometrics 177(2), 153–170.CrossRefGoogle Scholar
Gonçalves, S. & Kilian, L. (2007) Asymptotic and bootstrap inference for ar (infinity) processes with conditional heteroskedasticity. Econometric Reviews 26(6), 609–641.CrossRefGoogle Scholar
Hassler, U. & Kokoszka, P. (2010) Impulse responses of fractionally integrated processes with long memory. Econometric Theory 26, 1855–1861.CrossRefGoogle Scholar
Heinen, F., Sibbertsen, P., & Kruse, R. (2009) Forecasting Long Memory Time Series Under a Break in Persistence. CREATES Research Paper 2009–53.Google Scholar
Lewis, R. & Reinsel, G.C. (1985) Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16(3), 393–411.CrossRefGoogle Scholar
Lütkepohl, H. (1996) Handbook of Matrices. Wiley.Google Scholar
Pesaran, M.H. & Timmermann, A. (2007) Selection of estimation window in the presence of breaks. Journal of Econometrics 137(1), 134–161.CrossRefGoogle Scholar
Phillips, P.C.B. (1996) Econometric model determination. Econometrica 64(4), 763–812.CrossRefGoogle Scholar
Poskitt, D.S. (2007) Autoregressive approximation in nonstandard situations: The fractionally integrated and non-invertible cases. Annals of the Institute of Statistical Mathematics 59(4), 697–725.CrossRefGoogle Scholar
Poskitt, D.S. (2008) Properties of the sieve bootstrap for fractionally integrated and non-invertible processes. Journal of Time Series Analysis 29(2), 224–250.CrossRefGoogle Scholar
Rossi, B. (2013) Advances in forecasting under instability. In Elliott, G. & Timmermann, A. (eds.), Handbook of Economic Forecasting, vol. 2, pp. 1203–1324. Elsevier.Google Scholar
Timmermann, A. & van Dijk, H.K. (2013) Dynamic econometric modelisng and forecasting in the presence of instability. Journal of Econometrics 177(2), 131–133.CrossRefGoogle Scholar
Wang, C.S.-H., Bauwens, L., & Hsiao, C. (2013) Forecasting a long memory process subject to structural breaks. Journal of Econometrics 177(2), 171–184.CrossRefGoogle Scholar