YULE‐WALKER ESTIMATES FOR CONTINUOUS‐TIME AUTOREGRESSIVE MODELS

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Abstract

Abstract. I consider continuous‐time autoregressive processes of order p and develop estimators of the model parameters based on Yule‐Walker type equations. For continuously recorded data, it is shown that these estimators are least squares estimators and have the same asymptotic distribution as maximum likelihood estimators. In practice, though, data can only be observed discretely. For discrete data, I consider approximations to the continuous‐time estimators. It is shown that some of these discrete‐time estimators are asymptotically biased. Alternative estimators based on the autocovariance function are suggested. These are asymptotically unbiased and are a fast alternative to the maximum likelihood estimators described by Jones. They may also be used as starting values for maximum likelihood estimation.

Original languageEnglish
Pages (from-to)281-296
Number of pages16
JournalJournal of Time Series Analysis
Volume14
Issue number3
DOIs
Publication statusPublished - 1 Jan 1993
Externally publishedYes

Keywords

  • continuously recorded time series
  • Continuous‐time autoregression
  • unequally spaced time series
  • Yule‐Walker estimates

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