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Inference for Multi‐dimensional High‐frequency Data with an Application to Conditional Independence Testing
Author(s) -
Bibinger Markus,
Mykland Per A.
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12230
Subject(s) - mathematics , estimator , smoothing , conditional independence , asymptotic distribution , inference , statistical inference , kernel (algebra) , kernel density estimation , econometrics , statistics , discrete mathematics , artificial intelligence , computer science
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 and endogenous. 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. The theory leads to multi‐dimensional stable central limit theorems and feasible versions. Hence, they allow to draw statistical inference for a broad class of multivariate models, which 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 construct a test for investigating hypotheses that correlated assets are independent conditional on a common factor.