Obtaining and Predicting the Bounds of Realized Correlations

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 1- and 10-step forecasts even in volatile periods.