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Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing

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  • Markus Bibinger
  • Per A. Mykland
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    Abstract

    We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous. The central limit theorem is shown to have a feasible version. In the process, we show that the classes of multi-scale and kernel estimators for smoothing noise perturbation are asymptotically equivalent in the sense of having the same asymptotic distribution for corresponding kernel and weight functions. We also include the analysis for the Hayashi-Yoshida estimator in absence of microstructure. The theory leads to multi-dimensional stable central limit theorems for respective estimators and hence allows to draw statistical inference for a broad class of multivariate models and linear functions of the recorded components. This paves the way to tests and confidence intervals in risk measurement for arbitrary portfolios composed of high-frequently observed assets. As an application, we enhance the approach to cover more complex functions and in order to construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2013-006.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2013-006.

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    Length: 37 pages
    Date of creation: Jan 2013
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    Handle: RePEc:hum:wpaper:sfb649dp2013-006

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    Keywords: asymptotic distribution theory; asynchronous observations; conditional independence; high-frequency data; microstructure noise; multivariate limit theorems;

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    References

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