An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form … limit theory combines a functional law to a diffusion on D[0,infinity) and a central limit theorem. For c > 0, the limit … theory of the first-order serial correlation coefficient is Cauchy and is invariant to both the distribution and 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 …