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...