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Estimating the mean under strong persistence

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  • Hassler, Uwe
  • Hosseinkouchack, Mehdi

Abstract

We study a maximum likelihood [ML] type estimator for the mean of strongly persistent processes. Its limiting Gaussian distribution is obtained and compared with that of the arithmetic sample mean. The rates of convergence turn out to be equal. Two special cases of strong persistence are discussed: Fractional integration [FI] and harmonic weighting [HW]. Notwithstanding equal rates, efficiency gains relative to the arithmetic mean are available under FI, while for HW processes the relative efficiency turns out to be one asymptotically. For applied work, where the true model is not known, we suggest to use the estimator building on HW as a general purpose device, since it does not require the estimation of any parameter.

Suggested Citation

  • Hassler, Uwe & Hosseinkouchack, Mehdi, 2020. "Estimating the mean under strong persistence," Economics Letters, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:ecolet:v:188:y:2020:i:c:s0165176520300069
    DOI: 10.1016/j.econlet.2020.108950
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    References listed on IDEAS

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    1. Johansen, Søren & Nielsen, Morten Ørregaard, 2016. "The Role Of Initial Values In Conditional Sum-Of-Squares Estimation Of Nonstationary Fractional Time Series Models," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1095-1139, October.
    2. Uwe Hassler & Mehdi Hosseinkouchack, 2020. "Harmonically Weighted Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 41-66, January.
    3. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    4. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas & Koul, Hira L., 2014. "Asymptotic Normality For Weighted Sums Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 30(1), pages 252-284, February.
    5. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.
    6. Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, vol. 178(P2), pages 331-341.
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    More about this item

    Keywords

    Limiting normality; Long memory; Fractional integration; Harmonic weighting; Efficiency;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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