Multiplicative Error Models: 20 years on

The issue of combining low– and high–frequency components of volatility is addressed within the class of Multiplicative Error Models both in the univariate and multivariate cases. Inference based on the Generalized Method of Moments is suggested, which has the advantage of not requiring a parametric choice for the error distribution. The application relates to several volatility market indices (US, Europe and East Asia, with interde- pendencies in the short–run components of absolute returns, realized kernel volatility and option–based implied volatility indices): a set of diagnostic tools is used to evaluate the evidence of a relevant low–frequency component across markets, also from a forecasting comparison perspective. The results show that the slow–moving component in the dynamics achieves a better fit to the data and allows for an interpretation of what moves the local average level of volatility.