This paper derives second-order expansions for the distributions of the Whittle and profile plug-in maximum likelihood estimators of the fractional difference parameter in the ARFIMA(0,d,0) with unknown mean and variance. Both estimators are shown to be second-order pivotal. This extends earlier...

This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector autoregressive process. As a multivariate generalization of the Tsay (1987, <italic>Journal of the American Statistical Association</italic> 82, 590–604)...

A typical statistic encountered can be characterized as a ratio of polynomials of arbitrary degree in a random vector. This vector may possess any admissible cumulant structure. We provide in this paper general formulae for the effect of nonnormality on the density and distribution functions of...

We establish the validity of an Edgeworth expansion to the distribution of the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The result covers ARFIMA type models, including fractional Gaussian noise. The method of proof consists of three...

We provide in this paper asymptotic theory for the multivariate GARCH (p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau [19] in conjunction with a result given by Boussama [9] concerning the existence of...

We apply and extend Firth's (1993) modified score estimator to deal with a class of stationary Gaussian long-memory processes. Our estimator removes the first order bias of the maximum likelihood estimator. A small simulation study reveals the reduction in the bias is considerable, while it does...

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et al. (2004)). The present paper provides some analytical explanations for this evidence and shows...

This paper establishes error orders for integral limit approximations to traces of powers to the pth order) of products of Toeplitz matrices. Such products arise frequently in the analysis of stationary time series and in the development of asymptotic expansions. The elements of the matrices are...