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On the Asymptotic Properties of a Feasible Estimator of the Continuous Time Long Memory Parameter

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  • Joanne S. Ercolani

Abstract

This paper considers a fractional noise model in continuous time and examines the asymptotic properties of a feasible frequency domain maximum likelihood estimator of the long memory parameter. The feasible estimator is one that maximises an approximation to the likelihood function (the approximation arises from the fact that the spectral density function involves the finite truncatin of an infinite summation). It is of interest therefore to explore the conditions required of this approximation to ensure the consistency and asymptotic normality of this estimator. It is shown that the truncation parameter has to be a function of the sample size and that the optimal rate is different for stocks and flows and is a function of the long memory parameter itself. The results of a simulation exercise are provided to assess the small sample properties of the estimator.

Suggested Citation

  • Joanne S. Ercolani, 2010. "On the Asymptotic Properties of a Feasible Estimator of the Continuous Time Long Memory Parameter," Discussion Papers 10-09, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:10-09
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    References listed on IDEAS

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    1. Chambers, Marcus J. & McGarry, Joanne S., 2002. "Modeling Cyclical Behavior With Differential-Difference Equations In An Unobserved Components Framework," Econometric Theory, Cambridge University Press, vol. 18(2), pages 387-419, 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. Ercolani, Joanne S. & Chambers, Marcus J., 2006. "Estimation Of Differential-Difference Equation Systems With Unknown Lag Parameters," Econometric Theory, Cambridge University Press, vol. 22(3), pages 483-498, June.
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    More about this item

    Keywords

    Continuous time models; long memory processes;

    JEL classification:

    • 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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