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...

In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in 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...

Present econometric methodology of inference in cointegrating regression is extended to mildly integrated time series of the type introduced by Magdalinos and Phillips (2007, 2009). It is well known that conventional approaches to estimating cointegrat- ing regressions fail to produce even...

A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given....