Buchmann, BorisChan, Ngai Hang2015-12-100304-4149http://hdl.handle.net/1885/69747A unified asymptotic theory for nearly unstable higher order autoregressive processes and their least squares estimates is established. A novel version of Jordan's canonical decomposition with perturbations together with a suitable plug-in principle is proposed to develop the underlying theories. Assumptions are stated in terms of the domain of attraction of partial Fourier transforms. The machinery is applied to recapture some of the classical results with the driving noise being martingale differences. Further, we show how to extend the results to higher order fractional ARIMA models in nearly unstable settings, thereby offering a comprehensive theory to analyse nearly unstable time series.Keywords: Auto regressive models; Fractional brownian motion; Jordan canonical form; Least Square; Unit root; Fourier transforms; Machinery; Asymptotic analysis Fractional Brownian motion; Jordan canonical form; Lévy area; Least squares; Nearly unstable autoregressive model; Unit root test201310.1016/j.spa.2012.09.0142016-02-24