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.

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...

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...

In time series regression with nonparametrically autocorrelated errors, it is now standard empirical practice to construct confidence intervals for regression coefficients on the basis of nonparametrically studentized t-statistics. The standard error used in the studentization is typically...

Slowly varying regressors are asymptotically collinear in linear regression. Usual regression formulae for asymptotic standard errors remain valid but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic...

Using the power kernels of Phillips, Sun and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic provide more accurate approximations to the...

In time series regressions with nonparametrically autocorrelated errors, it is now standard empirical practice to use kernel-based robust standard errors that involve some smoothing function over the sample autocorrelations. The underlying smoothing parameter b, which can be defined as the ratio...

Employing power kernels suggested in earlier work by the authors (2003), this paper shows how to re.ne methods of robust inference on the mean in a time series that rely on families of untruncated kernel estimates of the long-run parameters. The new methods improve the size properties of...