Parameter inference for a nearly nonstationary first-order autoregressive model

The finite sample behaviour of the score function in a first-order autoregression is investigated. An object is to interpret the transition of the distribution of the score when the model approaches a nonstationary situation with a unit root. A framework is presented wherein the nonnormality of the score is clearly seen. Also, a simple interpretation for the behaviour of the distribution in terms of two chi-squared variables is given. Approximate finite sample distributions for practical use are also proposed.