Abstract
This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for entries of the precision matrix. To accomplish this purpose, we establish an abstract asymptotic theory for the weighted graphical Lasso and its de-biased version without specifying the form of the initial covariance estimator. We also extend the scope of the theory to the case that a known factor structure is present in the data. The developed theory is applied to the concrete situation where we can use the realized covariance matrix as the initial covariance estimator, and we obtain a feasible asymptotic distribution theory to construct (simultaneous) confidence intervals and (multiple) testing procedures for entries of the precision matrix.
Highlights
In high-frequency financial econometrics, covariance matrix estimation of asset returns has been extensively studied in the past two decades
This paper is novel in the respect that we develop an asymptotic distribution theory in a high-dimensional setting
We have developed a generic asymptotic theory to estimate the high-dimensional precision matrix of high-frequency data using the weighted graphical Lasso
Summary
In high-frequency financial econometrics, covariance matrix estimation of asset returns has been extensively studied in the past two decades. Since the 2000s, great progress has been made in high-dimensional covariance estimation from i.i.d. data, so researchers are naturally led to apply the techniques developed therein to the context of high-frequency data. To estimating the covariance matrix of high-frequency data which are asynchronously observed with noise. See [4,5,6,7] for further developments in this approach. In the meantime, it is well-recognized that the factor structure is an important ingredient both theoretically and empirically for financial data
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