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...

A general Markov-Switching autoregressive conditional mean model, valued in the set of nonnegative numbers, is considered. The conditional distribution of this model is a finite mixture of nonnegative distributions whose conditional mean follows a GARCH-like dynamics with parameters depending on...

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range...

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...

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

Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also...

We consider linearity testing in a general class of nonlinear time series model of order 1, involving a nonnegative nuisance parameter which (i) is not identified under the null hypothesis and (ii) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the...

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

We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as...