| By: |
Markus Bibinger;
Per A. Mykland;
;
|
| 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. |
| Keywords: |
asymptotic distribution theory, asynchronous observations, conditional independence, high-frequency data, microstructure noise, multivariate limit theorems |
| JEL: |
C14 C32 C58 G10 |
| Date: |
2013–01 |
| URL: |
http://d.repec.org/n?u=RePEc:hum:wpaper:sfb649dp2013-006&r=ets |