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Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading

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  • Hounyo, Ulrich

Abstract

We propose a bootstrap method for estimating the distribution (and functionals of it such as the variance) of various integrated covariance matrix estimators. In particular, we first adapt the wild blocks of blocks bootstrap method suggested for the pre-averaged realized volatility estimator to a general class of estimators of integrated covolatility. We then show the first-order asymptotic validity of this method in the multivariate context with a potential presence of jumps, dependent microstructure noise, irregularly spaced and non-synchronous data. Our results justify using the bootstrap to estimate the covariance matrix of a broad class of covolatility estimators. The bootstrap variance estimator is positive semi-definite by construction, an appealing feature that is not always shared by existing variance estimators of the integrated covariance estimator. As an application of our results, we also consider the bootstrap for regression coefficients. We show that the wild blocks of blocks bootstrap, appropriately centered, is able to mimic both the dependence and heterogeneity of the scores. We provide a proof of construction of bootstrap percentile and percentile-t intervals as well as variance estimates in this context. This contrasts the traditional pairs bootstrap which is not able to mimic the score heterogeneity even in the simple case where no microstructure noise is present. Our Monte Carlo simulations show that the wild blocks of blocks bootstrap improve the finite sample properties of the alternative approach based on the Gaussian approximation. We illustrate its practical use on high-frequency equity data.

Suggested Citation

  • Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
  • Handle: RePEc:eee:econom:v:197:y:2017:i:1:p:130-152
    DOI: 10.1016/j.jeconom.2016.11.002
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    Cited by:

    1. repec:oup:biomet:v:104:y:2017:i:2:p:481-488. is not listed on IDEAS
    2. repec:eee:econom:v:202:y:2018:i:2:p:178-195 is not listed on IDEAS
    3. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.

    More about this item

    Keywords

    High-frequency data; Market microstructure noise; Non-synchronous data; Jumps; Realized measures; Integrated covariance; Wild bootstrap; Block bootstrap;

    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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