Control variate method for stationary processes

Tomoyuki Amano, Masanobu Taniguchi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The sample mean is one of the most natural estimators of the population mean based on independent identically distributed sample. However, if some control variate is available, it is known that the control variate method reduces the variance of the sample mean. The control variate method often assumes that the variable of interest and the control variable are i.i.d. Here we assume that these variables are stationary processes with spectral density matrices, i.e. dependent. Then we propose an estimator of the mean of the stationary process of interest by using control variate method based on nonparametric spectral estimator. It is shown that this estimator improves the sample mean in the sense of mean square error. Also this analysis is extended to the case when the mean dynamics is of the form of regression. Then we propose a control variate estimator for the regression coefficients which improves the least squares estimator (LSE). Numerical studies will be given to see how our estimator improves the LSE.

Original languageEnglish
Pages (from-to)20-29
Number of pages10
JournalJournal of Econometrics
Issue number1
Publication statusPublished - 2011 Nov 3
Externally publishedYes


  • Control variate method
  • Nonparametric spectral estimator
  • Spectral density matrix
  • Stationary processes

ASJC Scopus subject areas

  • Economics and Econometrics


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