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(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.
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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 

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