This article is concerned by testing the nullity of coefficients in GARCH models. The problem is nonstandard because the quasi-maximum likelihood estimator is subject to positivity constraints. The paperestablishes the asymptotic null and local alternative distributions of Wald, score, and...

Jensen and Rahbek (2004a) claim that consistency and asymptotic normality hold for the quasi-maximumlikelihood estimator (QMLE) of (!0, 0) in nonstationary ARCH(1) models. In fact their result onlyconcerns a constrained QMLE, in which the intercept is fixed, and under a reinforced...

The main estimation methods of the univariate GARCH models are reviewed. A special attention is givento the asymptotic results and the quasi-maximum likelihood method.Keywords : Asymptotic properties of estimators, Efficient estimation, GARCH model, Quasi MaximumLikelihood Estimation, Weighted...

In order to be consistent with volatility processes, the autoregressiveconditional heteroskedastic (ARCH) models are constrained to havenon-negative coefficients. The estimators incorporating these constraints possessnon standard asymptotic distributions when the true parameter has...

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