10.18452/4446
Bibinger, Markus
Mykland, Per A.
Inference for Multi-Dimensional High-Frequency Data
Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing
Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
2013
high-frequency data
microstructure noise
asymptotic distribution theory
asynchronous observations
conditional independence
multivariate limit theorems
310 Sammlungen allgemeiner Statistiken
330 Wirtschaft
Humboldt-Universität zu Berlin
Humboldt-Universität zu Berlin
2017-06-16
2017-06-16
2013-01-28
2013-01-15
2013-01-15
1860-5664
http://edoc.hu-berlin.de/18452/5098
urn:nbn:de:kobv:11-100206991
2195055-6
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.