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State space modeling of long-memory processes. (English) Zbl 0929.62091
Summary: 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.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62M20 Inference from stochastic processes and prediction
60F17 Functional limit theorems; invariance principles
Software:
longmemo
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