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 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...

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

A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The method leads to substantial simplifications in the asymptotics and offers a unified approach to strong laws and central limit theory for linear processes....

An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form rho_{n} = 1+c/n^{alpha}, involving moderate deviations from unity when alpha in (0,1) and c in R are constant parameters. The limit theory combines a functional law to a...