The Annals of Statistics

State space modeling of long-memory processes

Ngai Hang Chan and Wilfredo Palma

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This paper develops a state space modeling for long-range dependent data. Although a long-range dependent process has an infinite-dimensional state space representation, it is shown that by using the Kalman filter, the exact likelihood function can be computed recursively in a finite number of steps. Furthermore, an approximation to the likelihood function based on the truncated state space equation is considered. Asymptotic properties of these approximate maximum likelihood estimates are established for a class of long-range dependent models, namely, the fractional autoregressive moving average models. Simulation studies show rapid converging properties of the approximate maximum likelihood approach.

Article information

Ann. Statist., Volume 26, Number 2 (1998), 719-740.

First available in Project Euclid: 31 July 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62E20: Asymptotic distribution theory
Secondary: 60F17: Functional limit theorems; invariance principles

ARFIMA asymptotic normality consistency efficiency long-memory MLE truncated state space


Chan, Ngai Hang; Palma, Wilfredo. State space modeling of long-memory processes. Ann. Statist. 26 (1998), no. 2, 719--740. doi:10.1214/aos/1028144856.

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