Quasi‐Maximum Likelihood Estimation for a Class of Continuous‐time Long‐memory Processes

Henghsiu Tsai () and K. S. Chan

Journal of Time Series Analysis, 2005, vol. 26, issue 5, 691-713

Abstract: Tsai and Chan (2003) has recently introduced the Continuous‐time Auto‐Regressive Fractionally Integrated Moving‐Average (CARFIMA) models useful for studying long‐memory data. We consider the estimation of the CARFIMA models with discrete‐time data by maximizing the Whittle likelihood. We show that the quasi‐maximum likelihood estimator is asymptotically normal and efficient. Finite‐sample properties of the quasi‐maximum likelihood estimator and those of the exact maximum likelihood estimator are compared by simulations. Simulations suggest that for finite samples, the quasi‐maximum likelihood estimator of the Hurst parameter is less biased but more variable than the exact maximum likelihood estimator. We illustrate the method with a real application.

Date: 2005
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