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BOUNDEDNESS OF M-ESTIMATORS FOR LINEAR REGRESSION IN TIME SERIES

Published online by Cambridge University Press:  04 September 2018

Søren Johansen  and
Bent Nielsen
Søren Johansen
Affiliation:
University of Copenhagen, and CREATES Aarhus University
Bent Nielsen*
Affiliation:
University of Oxford
*
*Address correspondence to Bent Nielsen, Nuffield College & Department of Economics, University of Oxford & Programme for Economic Modelling Nuffield College, Oxford, OX1 1NF, UK; e-mail: [email protected].
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Abstract

We show boundedness in probability uniformly in sample size of a general M-estimator for multiple linear regression in time series. The positive criterion function for the M-estimator is assumed lower semicontinuous and sufficiently large for large argument. Particular cases are the Huber-skip and quantile regression. Boundedness requires an assumption on the frequency of small regressors. We show that this is satisfied for a variety of deterministic and stochastic regressors, including stationary and random walks regressors. The results are obtained using a detailed analysis of the condition on the regressors combined with some recent martingale results.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 3 , June 2019 , pp. 653 - 683
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

The first author is grateful to CREATES - Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, and to Steffen Lauritzen for useful comments.

References

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