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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.06.024 Byline: Willa W. Chen (a), Rohit S. Deo (b) Abstract: We study the asymptotic behaviour of frequency domain maximum likelihood estimators of mis-specified models of long memory Gaussian series. We show that even if the long memory structure of the time series is correctly specified, mis-specification of the short memory dynamics may result in estimators of both long- and short-memory parameters that are slower than n consistent for the pseudo-true parameter values, which in general differ from the true values. The conditions under which this happens are provided and the asymptotic distribution of the estimators is shown to be non-Gaussian. Conditions under which estimators of the parameters of the mis-specified model have the standard n consistency for the pseudo-true values and are asymptotically normal are also provided. Author Affiliation: (a) Department of Statistics, Texas A&M University, College Station, Texas 77843, USA (b) New York University, 44 W. 4'th Street, New York NY 10012, USA

We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator (NBLSE) of the cointegration parameter [beta] in the framework of fractional cointegration. This tapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrary linear time trends that often occur in practice. Our simulations show that, in the case of no deterministic trends, the estimator is superior to ordinary least squares (OLS) and the nontapered NBLSE proposed by P.M. Robinson when the levels have a unit root and the cointegrating relationship between the series is weak. In terms of rate of convergence, our estimator converges faster under certain circumstances, and never slower, than either OLS or the nontapered NBLSE. In a data analysis of interest rates, we find stronger evidence of cointegration if the tapered NBLSE is used for the cointegration parameter than if OLS is used. JEL classification: C13; C14; C32 Keywords: Fractional cointegration; Long memory; Tapering; Periodogram

The restricted likelihood is known to produce estimates with significantly less bias in AR( p) models with intercept and/or trend. In AR(1) models, the corresponding restricted likelihood ratio test (RLRT), unlike the t-statistic or the usual LRT, has been recently shown to be well approximated by the chi-square distribution even close to the unit root, thus yielding confidence intervals with good coverage properties. In this article, we extend this result to AR( p) processes of arbitrary order p by obtaining the expansion of the RLRT distribution around that of the limiting chi-squared and showing that the error is bounded even as the unit root is approached. Next, we investigate the correspondence between the AR coefficients and the partial autocorrelations, which is well known in the stationary region, and extend to the more general situation of potentially multiple unit roots. In the case of one positive unit root, which is of most practical interest, the resulting parameter space is shown to be the bounded p-dimensional hypercube (−1, 1] × (−1, 1) p−1. This simple parameter space, in addition with a stable algorithm that we provide for computing the restricted likelihood, allows its easy computation and optimization as well as construction of confidence intervals for the sum of the AR coefficients. In simulations, the RLRT intervals are shown to have not only near exact coverage in keeping with our theoretical results, but also shorter lengths and significantly higher power against stationary alternatives than other competing interval procedures. An application to the well-known Nelson-Plosser data yields RLRT based intervals that can be markedly different from those in the literature. [ABSTRACT FROM AUTHOR]