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Keywords:

  • quadratic variation;
  • realized correlation;
  • realized volatility

This paper constructs estimates of daily stock index volatilities and correlation using high-frequency (one-minute) intraday stock indices. The key feature of these ‘realized’ volatilities and correlations is that they are not only model-free but also approximately measurement-error-free. In fact, they can be treated as observed rather than latent, so that direct modeling and forecasting of the realized volatilities can be performed using conventional time series approaches. Some interesting results appear in the analysis. Despite the fact that the unstandardized returns are skewed to the right and have fatter tails than normal, the distributions of the raw returns scaled by the realized standard deviations appear to be approximately Gaussian. The unconditional distributions of the realized variances and covariances are leptokurtic as well as highly right-skewed, but the realized correlation tends to be approximately normally distributed. There is no evidence in support of asymmetric volatility effects commonly found in previous findings. However, we find strong evidence to support the fact that there exists high contemporaneous correlation between realized volatilities and high comovement between realized correlation and volatilities.