Finite-sample inference methods for autoregressive\ processes: an approach based on truncated pivotal autoregression

In this paper, we develop exact inference procedures (tests and confidence region)\ for autoregressive models [AR($p$), $p\geq 1$]. Proposed approaches test hypotheses, which fix the complete vector of autoregressive coefficients with Fisher-type statistics. Distribution of each statistic is independent of nuisance parameters, and is relatively easy to simulate. To test the multiple unit root hypothesis with order $d$ (possibly $d\geq 2)$, we generalize parameterization of \QCITE{cite}{}{Dickey(1976)}, \QCITE{cite}{}{Fuller(1976)}, \QCITE{cite}{}{Hasza-Fuller(1979)}, \QCITE{cite}{}{Beveridge-Nelson(1981)} and \QCITE{cite}{}{Diebold-Nerlove(1990)}. This reformulation for the AR$(p)$ model has the advantage to express directly the multiple unit root hypothesis. Statistical properties (power and size control) of proposed tests and asymptotic tests are compared by Monte Carlo experience. Robustness (towards normality) for proposed tests are also studied. Poposed approaches are applied to the U.S. velocity model