Testing volatility autocorrelation in the constant elasticity of variance stochastic volatility model

The sample autocovariance of the suitably scaled squared returns of a given stock is shown here to be a consistent and asymptotically normal estimator of the theoretical autocovariance of the mean variance, when the data is generated by the Constant Elasticity of Variance stochastic volatility (CEV SV) process. By computing explicitly the asymptotic variance of the estimator, confidence bands are obtained for the theoretical autocovariance. For each one of the stock indexes S&P500, CAC40, FTSE, DAX and SMI the estimated confidence bands are compared with the theoretical autocovariances computed for several values of the model parameters. The results suggest that the CEV SV model is able to capture the empirical autocovariance detected on the observed data. Analogous results are derived for the theoretical autocorrelation function.