Quasi Maximum Likelihood Estimation For A Class Of Continuous Time Long Memory Processes

Quasi-Maximum Likelihood Estimation for a Class of Continuous-Time Long-Memory Processes

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.

Long-Memory Processes

Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.

Statistica Sinica