Obtaining and Predicting the Bounds of Realized Correlations

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