The theory of Fourier transforms of generalized functions is used to extract general formulas for the tail behavior of a probability distribution from the behavior of its characteristic function in the locality of the origin. The theory is applied to develop asymptotic formula for the tails of...

Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia)...

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions. The framework of study is based on earlier work by Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). In particular, the results in these papers are...

This paper studies the sampling distribution of the conventional t-ratio when the sample comprises independent draws from a standard Cauchy (0,1) population. It is shown that this distribution displays a striking bimodality for all sample sizes and that the bimodality persists asymptotically. An...

This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is...

Results published recently by Hendry (1979) for the limiting distribution of inconsistent instrumental variable estimators in misspecified dynamic systems are incorrect. In particular, Hendry's derivations involve the use of an appropriate control variate and lead to an expression for the...

Discrete Fourier transforms (dft's) of fractional processes are studied and an exact representation of the dft is given in terms of the component data. The new representation gives the frequency domain form of the model for a fractional process, and is particularly useful in analyzing the...

Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the...

Conditional independence almost everywhere in the space of the conditioning variates does not imply unconditional independence, although it may well imply unconditional independence of certain functions of the variables. An example that is important in linear regression theory is discussed in...

This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These...