Deviation inequalities and Cramér-type moderate deviations for the explosive autoregressive process
Hui Jiang, Yilong Wan, Guangyu Yang
Abstract
This paper concerns the asymptotic properties of the quadratic functionals and associated ordinary least squares estimator in the explosive first-order Gaussian autoregressive process. By the deviation inequalities for multiple Wiener-Itô integrals and asymptotic analysis techniques, Cramér-type moderate deviations are achieved under the explosive and mildly explosive frameworks. As applications, the global and local powers for the unit root test are shown to approach one at exponential rates. Simulation experiments are conducted to confirm the theoretical results.
Topics & Concepts
MathematicsAutoregressive modelExplosive materialEstimatorApplied mathematicsUnit rootType (biology)Wiener processLarge deviations theoryUnit root testGaussianQuadratic equationStatisticsCointegrationQuantum mechanicsBiologyOrganic chemistryEcologyPhysicsGeometryChemistryStatistical Methods and InferenceFinancial Risk and Volatility ModelingAdvanced Statistical Methods and Models