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Estimation of longrun variance of continuous time stochastic process using discrete sample

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  • Lu, Ye
  • Park, Joon Y.

Abstract

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longrun variance of continuous time process, but also how to choose bandwidth optimally with data dependent procedures, using discrete samples. Our framework is also useful to analyze the high frequency behaviors of usual longrun variance estimators for discrete time series. In particular, we show that they all diverge to infinity as the sampling frequency increases. The relevance and usefulness of our continuous time framework and asymptotic theory are demonstrated by illustration and simulation.

Suggested Citation

  • Lu, Ye & Park, Joon Y., 2019. "Estimation of longrun variance of continuous time stochastic process using discrete sample," Journal of Econometrics, Elsevier, vol. 210(2), pages 236-267.
  • Handle: RePEc:eee:econom:v:210:y:2019:i:2:p:236-267
    DOI: 10.1016/j.jeconom.2018.04.006
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    References listed on IDEAS

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    2. Jiang, Bibo & Lu, Ye & Park, Joon Y., 2020. "Testing for Stationarity at High Frequency," Journal of Econometrics, Elsevier, vol. 215(2), pages 341-374.

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    More about this item

    Keywords

    Continuous time model; Longrun variance estimator; Kernel estimation; Bandwidth selection;
    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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