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Zbl 1156.62055
Beran, Jan
On parameter estimation for locally stationary long-memory processes. (English)
[J] J. Stat. Plann. Inference 139, No. 3, 900-915 (2009). ISSN 0378-3758

Summary: We consider parameter estimation for time-dependent locally stationary long-mem\-ory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth, are obtained. In spite of long memory, the optimal bandwidth turns out to be of the order $n^{-1/5}$ and inversely proportional to the square of the second derivative of $d$. In this sense, local estimation of $d$ is comparable to regression smoothing with iid residuals.

MSC 2000:: *62M10 Time series, etc. (statistics)
62F10 Point estimation
62E20 Asymptotic distribution theory in statistics
62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators

Keywords: long memory; fractional ARIMA process; local stationarity; bandwidth selection

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Zentralblatt MATH Berlin [Germany]