This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data...

This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with...

This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons...

We study large-sample properties of likelihood ratio tests of the unit root hypothesis in an autoregressive model of arbitrary, finite order. Earlier research on this testing problem has developed likelihood ratio tests in the autoregressive model of order one, but resorted to a plug-in approach...