A simple specification test based on fully modified residuals and the cumulative sum (CUSUM) test for cointegration of Xiao and Phillips (2002, <italic>Journal of Econometrics</italic>, 108, 43–61) are considered as means of testing for functional form in long-run cointegrating relations. It is shown that both...

We examine the limit properties of the nonlinear least squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips (2001, <italic>Econometrica</italic> 69, 117–161). We show that the limit behavior of...

A limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the...

Nielsen (Working paper, University of Oxford, 2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a coexplosive system extension and an illustrative example that...

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form <italic>ρ</italic> = 1 + <italic>c</italic>/<italic>n</italic>, involving moderate deviations from unity when <italic>α</italic> null (0, 1) and <italic>c</italic>...

It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory, producing a faster rate of convergence, a limiting Cauchy...

This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated processes of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to...