Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale...

Nonlinearities in the drift and diffusion coefficients influence temporal dependence in diffusion models. We study this link using three measures of temporal dependence: rho-mixing, beta-mixing and alpha-mixing. Stationary diffusions that are rho-mixing have mixing coefficients that decay...

An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have...

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...

In this paper, we prove the validity of an Edgeworth expansion to the distribution of the Whittle maximum likelihood estimator for stationary long-memory Gaussian models with unknown parameter theta in Theta subset R^{d_{theta}} . The error of the (s-2)-order expansion is shown to be...

May 2008 A commonly used defining property of long memory time series is the power law decay of the autocovariance function. Some alternative methods of deriving this property are considered working from the alternate definition in terms of a fractional pole in the spectrum at the origin. The...

An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d in (-1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,q) model. The leading...

It has been know since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such...

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 < d < 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory.