The FEXP estimator for potentially non-stationary linear time series

Clifford Hurvich, Eric Moulines and Philippe Soulier

Stochastic Processes and their Applications, 2002, vol. 97, issue 2, 307-340

Abstract: We consider semiparametric fractional exponential (FEXP) estimators of the memory parameter d for a potentially non-stationary linear long-memory time series with additive polynomial trend. We use differencing to annihilate the polynomial trend, followed by tapering to handle the potential non-invertibility of the differenced series. We propose a method of pooling the tapered periodogram which leads to more efficient estimators of d than existing pooled, tapered estimators. We establish asymptotic normality of the tapered FEXP estimator in the Gaussian case with or without pooling. We establish asymptotic normality of the estimator in the linear case if pooling is used. Finally, we consider minimax rate-optimality and feasible nearly rate-optimal estimators in the Gaussian case.

Keywords: Long memory Fractional exponential models Periodogram; Semiparametric estimation; Tapering; Bartlett decomposition; Minimax rate-optimality (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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