Estimation of stochastic volatility models with diagnostics

Efficient method of moments (EMM) is used to fit the standard stochastic volatility model of various extensions to several daily financial time series. EMM matches to the score of the model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are ‘semiparametric ARCH’ and ‘nonlinear nonparametric’. With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient.