In this paper, we consider a gaussian autoregressive model of order p , which may be nonstationary and includes a drift term (where p ≥ 1). Exact inference methods are developed for the autoregressive coefficients. We consider first the problem of testing any hypothesis that fixes the vector of the autoregressive coefficients. This is done by first transforming the observations in a way that eliminates serial dependence under the null hypothesis, and then testing whether autocorrelation remains present in the transformed data. The latter task is accomplished by combining several independence tests against serial correlation at lags 1, 2, ..., p . A valid confidence region for the autoregressive coefficients may then be obtained by inverting the latter tests. We show that this confidence region can be built numerically on solving 2 p polynomials of order 2, where in each case p – 1 autoregressive coefficients are fixed, and then using a grid search over the latter p – 1 coefficients. For inference on individual coefficients or more general transformations of the autoregressive coefficients, we propose the use of a projection approach. The proposed method is applied to a time series model of real G.D.P. in Tunisia.