The Annals of Statistics

An efficient estimator for locally stationary Gaussian long-memory processes

Wilfredo Palma and Ricardo Olea

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This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying parametric formulation of these models is introduced and a Whittle likelihood technique is proposed for estimating the parameters involved. Large sample properties of these Whittle estimates such as consistency, normality and efficiency are established in this work. Furthermore, the finite sample behavior of the estimators is investigated through Monte Carlo experiments. As a result from these simulations, we show that the estimates behave well even for relatively small sample sizes.

Article information

Ann. Statist. Volume 38, Number 5 (2010), 2958-2997.

First available in Project Euclid: 20 August 2010

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Mathematical Reviews number (MathSciNet)

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60G15: Gaussian processes

Nonstationarity local stationarity long-range dependence Whittle estimation consistency asymptotic normality efficiency


Palma, Wilfredo; Olea, Ricardo. An efficient estimator for locally stationary Gaussian long-memory processes. Ann. Statist. 38 (2010), no. 5, 2958--2997. doi:10.1214/10-AOS812.

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