Characterizing Heteroscedasticity

The largest deviation from a simple random walk founds in the empirical time series is the volatility clustering, or heteroskedasticity. It is important to characterize at best the decay of the volatility lagged correlation because of its practical implications for the construction of processes. First, the volatility and correlation estimators most suited for this task are studied. Then, they are applied to a broad panel of financial time series. Finally, simple analytical shapes are estimated on the empirical lagged correlation. The best overall characterization is given by a logarithmic decay for increasing lags, whereas an exponential decay and power law decay can be eliminated. This shows that a multiscale structure should be used in the processes, capturing the observed long memory of the volatility clusters.