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YULE‐WALKER ESTIMATES FOR CONTINUOUS‐TIME AUTOREGRESSIVE MODELS
Author(s) -
Hyndman Rob J.
Publication year - 1993
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1993.tb00145.x
Subject(s) - autocovariance , mathematics , estimator , autoregressive model , m estimator , extremum estimator , bootstrapping (finance) , statistics , asymptotic distribution , econometrics , mathematical analysis , fourier transform
. 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.