This paper introduces the concept of risk parameter in conditional volatility models of the form $\epsilon_t=\sigma_t(\theta_0)\eta_t$ and develops statistical procedures to estimate this parameter. For a given risk measure $r$, the risk parameter is expressed as a function of the volatility...

A new approach is proposed to estimate a large class of multivariate volatility models. The method is based on estimating equation-by-equation the volatility parameters of the individual returns by quasi-maximum likelihood in a first step, and estimating the correlations based on...

This paper studies the probabilistic properties and the estimation of the asymmetric log-GARCH($p,q$) model. In this model, the log-volatility is written as a linear function of past values of the log-squared observations, with coefficients depending on the sign of the observations, and past...

Regularity conditions are given for the consistency of the Poisson quasi-maximum likelihood estimator of the conditional mean parameter of a count time series. The asymptotic distribution of the estimator is studied when the parameter belongs to the interior of the parameter space and when it...

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...

We establish the strong consistency and the asymptotic normality of the variance-targeting estimator (VTE) of the parameters of the multivariate CCC-GARCH($p,q$) processes. This method alleviates the numerical difficulties encountered in the maximization of the quasi likelihood by using an...

A two-step approach for conditional Value at Risk (VaR) estimation is considered. In the first step, a generalized-quasi-maximum likelihood estimator (gQMLE) is employed to estimate the volatility parameter, and in the second step the empirical quantile of the residuals serves to estimate the...

We consider estimation for general power GARCH models under stable--Paretian innovations. Exploiting the simple structure of the conditional characteristic function of the observations driven by these models we propose minimum distance estimation based on the empirical characteristic function of...

This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1,1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic...

The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive...