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Asymptotic Theory For Maximum Likelihood Estimation Of The Memory Parameter In Stationary Gaussian Processes

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  • Lieberman, Offer
  • Rosemarin, Roy
  • Rousseau, Judith

Abstract

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

Suggested Citation

  • Lieberman, Offer & Rosemarin, Roy & Rousseau, Judith, 2012. "Asymptotic Theory For Maximum Likelihood Estimation Of The Memory Parameter In Stationary Gaussian Processes," Econometric Theory, Cambridge University Press, vol. 28(2), pages 457-470, April.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:457-470_00
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    Cited by:

    1. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    2. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    3. Shi, Shuping & Yu, Jun & Zhang, Chen, 2024. "On the spectral density of fractional Ornstein–Uhlenbeck processes," Journal of Econometrics, Elsevier, vol. 245(1).
    4. Hongchang Hu & Weifu Hu & Xinxin Yu, 2021. "Pseudo-maximum likelihood estimators in linear regression models with fractional time series," Statistical Papers, Springer, vol. 62(2), pages 639-659, April.
    5. Xiaohu Wang & Weilin Xiao & Jun Yu & Chen Zhang, 2025. "Maximum Likelihood Estimation of Fractional Ornstein-Uhlenbeck Process with Discretely Sampled Data," Working Papers 202527, University of Macau, Faculty of Business Administration.

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