Financial Mathematics, Volatility and Covariance Modelling

12Covariance estimation and quasi-likelihood analysis

Yuta Koike and Nakahiro Yoshida

1 Nonparametric covariance estimation from high-frequency data

For a semi-martingale, the quadratic covariation is a natural quantity to measure its covariance structure. This motivates researchers to develop statistical inference for the quadratic covariation of a semi-martingale based on high-frequency observation data. Starting with the pioneering work in financial econometrics of Foster and Nelson[34], Andersen and Bollerslev [6] and Barndorff-Nielsen and Shephard [11], a number of articles have been devoted to this subject in the past two decades. In this section we give a brief review on this topic.

1.1 Realized covariance

Let X = (X_t)_t∈[0,T], $X_t=$