A practice that has become widespread is that of comparing forecasts of financial return variability obtained from discrete time models against high frequency estimates based on continuous time theory. In explanatory financial return variability modelling this raises several methodological and...

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when...

A critique that has been directed towards the log-GARCH model is that its log-volatility specification does not exist in the presence of zero returns. A common ``remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders Quasi Maximum Likelihood...

Estimation of log-GARCH models via the ARMA representation is attractive because it enables a vast amount of already established results in the ARMA literature. We propose an exponential Chi-squared QMLE for log-GARCH models via the ARMA representation. The advantage of the estimator is that it...

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when...

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) are of special interest, since they enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in...

A critique that has been directed towards the log-GARCH model is that its log-volatility specification does not exist in the presence of zero returns. A common ``remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders estimation asymptotically...

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) are of special interest, since they enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in...

We propose and study simple but flexible methods for density selection of skewed versions of the two most popular density classes in finance, the exponential power distribution and the t distribution. For the first type of method, which simply consists of selecting a density by means of an...

Estimation of large financial volatility models is plagued by the curse of dimensionality: As the dimension grows, joint estimation of the parameters becomes infeasible in practice. This problem is compounded if covariates or conditioning variables (``X") are added to each volatility equation....