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...

Estimation of the memory parameter (d) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.

This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and...

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.

Estimation of the memory parameter in time series with long range dependence is considered. A pooled log periodogram regression estimator is proposed that utilizes a set of mL periodogram ordinates with L approaching infinity rather than m ordinates used in the conventional log periodogram...

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 provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can...

We develop stochastic expansions with remainder oP(n-2 mu), where 0 mu 1/2, for a standardised semiparametric GLS estimator, a standard error, and a studentized statistic, in the linear regression model with heteroskedasticity of unknown form. We calculate the second moments of the truncated...

This paper discusses some uses econometrics of functional limit theory for dependent random variables. Attention is focused on empirical process-type results rather than partial sum results that are prevalent in unit root econometrics. Examples considered include nonstandard parametric...