Inference for linear models with dependent errors

Zhou Zhou, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review


The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M-estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M-estimators. Methodologically, we extend the recently proposed self-normalized approach of Shao from stationary time series to the regression set-up, where the sequence of response variables is typically non-stationary in mean. Since the limiting distribution of the self-normalized statistic depends on the design matrix and its corresponding critical values are case dependent, we develop a simulation-based approach to approximate the critical values consistently. Through a simulation study, we demonstrate favourable finite sample performance of our method in comparison with a block-bootstrap-based approach. Empirical illustrations using two real data sets are also provided.

Original languageEnglish (US)
Pages (from-to)323-343
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - Mar 2013


  • M-estimation
  • Non-linear time series
  • Quantile regression
  • Self-normalization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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