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....

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...

An asymptotic theory is given for autoregressive time series with a root of the form rho_{n} = 1+c/n^{alpha}, which represents moderate deviations from unity when alpha in (0,1). The limit theory is obtained using a combination of a functional law to a diffusion on D[0,infinity) and a central...

Nielsen (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 co-explosive system extension and an illustrative example that helps to explain the finding, gives a...

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...

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 I(1) processes. We show that this kind of nonlinearity in the regression function can...

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...

An error is corrected in Yu and Phillips (2001) (Econometrics Journal, 4, 210-224) where a time transformation was used to induce Gaussian disturbances in the discrete time equivalent model. It is shown that the error process in this model is not a martingale and the Dambis, Dubins-Schwarz (DDS)...

Turbulence in the world of banking and finance over the last two years has riveted media attention on the financial industry, exposing practices, products and risks in the industry to widespread public scrutiny. Questions continue to be asked about the management and regulation of an industry...

Eric Ghysels is the Bernstein Distinguished Professor of Economics and Professor of Finance at University of North Carolina at Chapel Hill. In 2008, Eric Ghysels and Robert Engle (2003 Nobel co-Laureate in Economic Science with Clive Granger) founded the Society for Financial Econometrics...