The aim of this work is to investigate the asymptotic properties of weighted least squares (WLS) estimation for causal and invertible periodic autoregressive moving average (PARMA) models with uncorrelated but dependent errors. Under mild assumptions, it is shown that the WLS estimators of PARMA...

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...

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...

We consider joint estimation of conditional Value-at-Risk (VaR) at several levels, in the framework of general GARCH-type models. The conditional VaR at level $\alpha$ is expressed as the product of the volatility and the opposite of the $\alpha$-quantile of the innovation. A standard method is...

We study the estimation risk induced by univariate and multivariate methods for evaluating the conditional Value-at-Risk (VaR) of a portfolio of assets. The composition of the portfolio can be time-varying and the individual returns are assumed to follow a general multivariate dynamic model....

The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. In FDA, densely observed data are transformed into curves and then each (random) curve is...

We investigate the problem of testing finiteness of moments for a class of semi-parametric augmented GARCH models encompassing most commonly used specifications. The existence of positive-power moments of the strictly stationary solution is characterized through the Moment Generating Function...

We investigate the problem of testing the finiteness of moments for a class of semi-parametric time series encompassing many commonly used specifications. The existence of positive-power moments of the strictly stationary solution is characterized by the Moment Determining Function (MDF) of the...

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations of nonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as the sum of two terms. The first term corresponds to the standard Bartlett's formula for linear...

Variance targeting estimation is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood (QML) estimation of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining...