Yule-Walker estimates for continuous-time autoregressive models


Rob J Hyndman


16 July 1993

Publication details

Journal of Time Series Analysis 14, 281-296




I consider continuous time autoregressive (CAR) 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 (1981). They may also be used as starting values for maximum likelihood estimation.