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The FEXP estimator for potentially non-stationary linear time series

Author

Listed:
  • Hurvich, Clifford M.
  • Moulines, Eric
  • Soulier, Philippe

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.

Suggested Citation

  • Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
  • Handle: RePEc:eee:spapps:v:97:y:2002:i:2:p:307-340
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    References listed on IDEAS

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    1. Soulier, Philippe, 2001. "Moment bounds and central limit theorem for functions of Gaussian vectors," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 193-203, September.
    2. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February.
    3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
    4. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(01), pages 44-79, February.
    5. Fay, Gilles & Soulier, Philippe, 2001. "The periodogram of an i.i.d. sequence," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 315-343, April.
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    Citations

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    Cited by:

    1. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
    2. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA.
    3. Chen, Willa W. & Hurvich, Clifford M., 2003. "Estimating fractional cointegration in the presence of polynomial trends," Journal of Econometrics, Elsevier, vol. 117(1), pages 95-121, November.
    4. Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, EconWPA.
    5. Faÿ, Gilles & Moulines, Eric & Roueff, François & Taqqu, Murad S., 2009. "Estimators of long-memory: Fourier versus wavelets," Journal of Econometrics, Elsevier, vol. 151(2), pages 159-177, August.

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