The Characteristic Function from a Family of Truncated Normal Distributions -- Solution proposed by Karim Abadir and Tassos Magdalinos. The posers of the problem have raised an important question. We can offer a solution to a more general problem, which covers characteristic functions of...

The unrestricted estimator of the information matrix is shown to be inconsistent for an autoregressive process with a root lying in a neighbourhood of unity with radial length proportional or smaller than 1/n, i.e. a root that takes the form rho=1+c/n^alpha, alpha=1. In this case the information...

A limit theory is developed for mildly explosive autoregression under both weakly and strongly dependent innovation errors. We find that the asymptotic behaviour of the sample moments is affected by the memory of the innovation process both in the in the form of the limiting distribution and, in...

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...

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>...

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...

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...

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...