A new approach to robust testing in cointegrated systems is proposed using nonparametric HAC estimators without truncation. While such HAC estimates are inconsistent, they still produce asymptotically pivotal tests and, as in conventional regression settings, can improve testing and inference....

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.

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...

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an...

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...

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...

This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR's) and Johansen-type error correction models (ECM's) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate...