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Asymptotic Theory for Estimating the Persistent Parameter in the Fractional Vasicek Model

Author

Listed:
  • Xiao, Weilin

    (Zhejiang University)

  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

This paper develops the asymptotic theory for the least squares (LS) estimator of the persistent parameter in the fractional Vasicek model when a continuous record of observations is available. The fractional Vasicek model is assumed to be driven by the fractional Brownian motion with a known Hurst parameter greater than or equal to one half. It is shown that the asymptotic properties depend on the sign of the persistent parameter, corresponding to the stationary case, the explosive case and the null recurrent case. The strong consistency and the asymptotic distribution are obtained in all three cases.

Suggested Citation

  • Xiao, Weilin & Yu, Jun, 2016. "Asymptotic Theory for Estimating the Persistent Parameter in the Fractional Vasicek Model," Economics and Statistics Working Papers 13-2016, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2016_013
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    More about this item

    Keywords

    Least squares estimation; Fractional Vasicek model; Stationary process; Explosive process; Consistency; Asymptotic distribution;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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