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On existence of moment of mean reversion estimator in linear diffusion models

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  • Bao, Yong
  • Ullah, Aman
  • Zinde-Walsh, Victoria

Abstract

In this note it is shown that the expectation of the usual MLE estimator of the mean-reversion parameter in linear diffusion models does not exist. However, the moment does exist conditionally on the estimator of the autoregressive parameter in the discretized model being positive.

Suggested Citation

  • Bao, Yong & Ullah, Aman & Zinde-Walsh, Victoria, 2013. "On existence of moment of mean reversion estimator in linear diffusion models," Economics Letters, Elsevier, vol. 120(2), pages 146-148.
    • Handle: RePEc:eee:ecolet:v:120:y:2013:i:2:p:146-148
    DOI: 10.1016/j.econlet.2013.04.024
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    References listed on IDEAS

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    1. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
    2. Roberts, Leigh A., 1995. "On the Existence of Moments of Ratios of Quadratic Forms," Econometric Theory, Cambridge University Press, vol. 11(4), pages 750-774, August.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
    5. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Chen, Ye & Yu, Jun, 2015. "Optimal jackknife for unit root models," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 135-142.

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    More about this item

    Keywords

    Expectation; Mean-reversion parameter; MLE;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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