Abstract
The problem of estimation of realized correlation, which is analogous to realized covariance, is compounded by effects of market microstructure, noise, and asynchronous trading. Various methods have been proposed to decrease the biases, but they require assumptions to be made that may be unrealistic. This paper argues that the inherent data problems make precise point identification of realized correlation difficult, but identification bounds in the spirit of Manski (1995) can be derived. These identification bounds allow for a more robust approach to inference, especially when the realized correlation is used for estimating other risk measures. We forecast the identification bounds using the HAR model of Corsi (2003) using data during the year of onset of the credit crisis, and find that the bounds provide good predictive coverage of the realized correlation for both one step and ten step forecasts, even in volatile periods.
Highlights
Given the plethora of bias correction methods for the estimation of realized covariance and correlation that only work well under certain conditions, this paper proposes a different approach to the problem
We interpret this spike to be the degree of deviation from the true latent efficient process and take the upper bound of noise levels l to be 12%, in recognition that the percentage noise computed here may not be precise due to assumptions involved in obtaining the bias term
For multistep forecasting, the worsening in terms of predictive mean square error (PMSE) as compared to the 1-step forecast is less severe for the bounds than RCorr and ssRCorr
Summary
Given the plethora of bias correction methods for the estimation of realized covariance and correlation that only work well under certain conditions, this paper proposes a different approach to the problem. The paper is organised as follows: Section 2 gives the mathematical description of the previous tick realized covariance and correlation as well as the subsampled estimator of Zhang, Mykland, and Aït-Sahalia (2005); Section 3 describes the idea of partial identification, how we apply such identification analysis to estimate bounds of the realized covariance and correlation when the problems of asynchronicity and microstructure noise are present in the data, some practical issues involved in the bounds estimation, and the forecasting of the bounds; Section 4 gives the results of a simulation exercise to study the efficacy of these bounds and their sensitivity to the tuning parameters; Section 5 gives an empirical application using two stocks, first describing the dataset and the results of the bounds estimation and forecasting efficacy.
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