Boundedness of M-estimators for linear regression in time series

Søren Johansen, Bent Nielsen*

*Corresponding author for this work

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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.

Original languageEnglish
JournalEconometric Theory
Volume35
Issue3
Pages (from-to)653-683
Number of pages31
ISSN0266-4666
DOIs
Publication statusPublished - Jun 2019

Keywords

  • CONSISTENCY
  • LIMIT THEORY
  • MARTINGALES
  • SQUARES

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