This article addresses estimating parametric marginal densities of stationary time series in the absence of precise information on the dynamics of the underlying process. We propose using an estimator obtained by maximization of the "quasi-marginal" likelihood, which is a likelihood written as...

This paper introduces the concept of risk parameter in conditional volatility models of the form ϵt=σt(θ0)ηt 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 coefficients θ0 and the...

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are...

This paper considers a class of finite-order autoregressive linear ARCH models. The model captures the leverage effect, allows the volatility to be arbitrarily close to zero and to reach its minimum for non-zero innovations, and is appropriate for long-memory modeling when infinite orders are...

This paper provides a probabilistic and statistical comparison of the log-GARCH and EGARCH models, which both rely on multiplicative volatility dynamics without positivity constraints. We compare the main probabilistic properties (strict stationarity, existence of moments, tails) of the EGARCH...

We establish the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameters of a class of multivariate asymmetric generalized autoregressive conditionally heteroskedastic processes, allowing for cross leverage effects. The conditions required...