Many economic models imply that ratios, simple differences, or “spreads” of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's, and —1's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of...

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit...

A method is presented for computing maximum likelihood, or Gaussian, estimators of the structural parameters in a continuous time system of higherorder stochastic differential equations. It is argued that it is computationally efficient in the standard case of exact observations made at equally...

This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that consistently classify x as I(1) or I(0), exhibit large size distortions when regressors...