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Inference for continuous-time long memory randomly sampled processes

Author

Listed:
  • Mohamedou Ould Haye

    (Carleton University)

  • Anne Philippe

    (Nantes Université)

  • Caroline Robet

    (Nantes Université)

Abstract

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn using a renewal sampling process. We establish the existence of the spectral density of the sampled process, and we give its expression in terms of that of the initial process. We also investigate different aspects of the statistical inference on the sampled process. In particular, we obtain asymptotic results for the periodogram, the local Whittle estimator of the memory parameter and the long run variance of partial sums. We mainly focus on Gaussian continuous-time process. The challenge being that the randomly sampled process will no longer be jointly Gaussian.

Suggested Citation

  • Mohamedou Ould Haye & Anne Philippe & Caroline Robet, 2024. "Inference for continuous-time long memory randomly sampled processes," Statistical Papers, Springer, vol. 65(5), pages 3111-3134, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01515-z
    DOI: 10.1007/s00362-023-01515-z
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    References listed on IDEAS

    as
    1. Anne Philippe & Caroline Robet & Marie-Claude Viano, 2021. "Random discretization of stationary continuous time processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 375-400, April.
    2. Chambers, Marcus J., 1996. "The Estimation of Continuous Parameter Long-Memory Time Series Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 374-390, June.
    3. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 215-218, December.
    4. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, March.
    5. Jean‐Marc Bardet & Pierre R. Bertrand, 2010. "A Non‐Parametric Estimator of the Spectral Density of a Continuous‐Time Gaussian Process Observed at Random Times," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 458-476, September.
    6. F. Comte, 1996. "Simulation And Estimation Of Long Memory Continuous Time Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(1), pages 19-36, January.
    7. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    8. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    9. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series 497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    Full references (including those not matched with items on IDEAS)

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