Econometric reduction theory provides a comprehensive probabilistic framework for the analysis and classification of the reductions (simplifications) associated with empirical econometric models. However, the available approaches to econometric reduction theory are unable to satisfactory...

An EGARCH model in which the conditional distribution is heavy-tailed and skewed is proposed. The properties of the model, including unconditional moments, autocorrelations and the asymptotic distribution of the maximum likelihood estimator, are set out. Evidence for skewness in a conditional...

The general-to-specific (GETS) methodology is widely employed in the modelling of economic series, but less so in financial volatility modelling, due to its computational complexity when many explanatory variables are involved. This study proposes a simple way of avoiding this problem when the...

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...