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Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes

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  • Faÿ, Gilles
  • Moulines, Eric
  • Soulier, Philippe

Abstract

The validity of the Edgeworth expansion for densities of linear statistics of linear processes is proved. In contrast with previous works on Edgeworth expansions for dependent processes, this result is valid under long-range dependence.

Suggested Citation

  • Faÿ, Gilles & Moulines, Eric & Soulier, Philippe, 2004. "Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 275-288, February.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:3:p:275-288
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    References listed on IDEAS

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    1. Hall, Peter, 1992. "Convergence rates in the central limit theorem for means of autoregressive and moving average sequences," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 115-131, November.
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    Cited by:

    1. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2012. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 8/12, Monash University, Department of Econometrics and Business Statistics.
    2. Faÿ, Gilles, 2010. "Moment bounds for non-linear functionals of the periodogram," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 983-1009, June.
    3. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
    4. 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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