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...

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/pi2). This paper develops a second order asymptotic expansion to the distribution of this statistic. The correction term for the density is...

This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d_0 are included. The results establish that the bootstrap...

This paper extends recent findings of Lieberman and Phillips (2014) on stochastic unit root (SUR) models to a multivariate case including a comprehensive asymptotic theory for estimation of the model's parameters. The extensions are useful because they lead to a generalization of the...

A time-varying autoregression is considered with a similarity-based coefficient and possible drift. It is shown that the random walk model has a natural interpretation as the leading term in a small-sigma expansion of a similarity model with an exponential similarity function as its...

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...

An agent is asked to assess a real-valued variable Y_{p} based on certain characteristics X_{p} = (X_{p}^{1},...,X_{p}^{m}), and on a database consisting (X_{i}^{1},...,X_{i}^{m},Y_{i}) for i = 1,...,n. A possible approach to combine past observations of X and Y with the current values of X to...

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...