Estimation and Inference in Autoregressive Models with Trending Innovation Variance

This paper develops the asymptotic theory for stable autoregressive models in which the noise variance grows in a polynomial-like fashion. It is shown that the asymptotic distribution of the OLS estimator of the coefficient vector is multivariate normal with a covariance matrix that depends on the order, k, of the variance growth. A consistent estimator of k is proposed, which delivers heteroscedasticity-robust test statistics. The opposite case of quot;variance declinequot; is studied as well. It is demonstrated that by means of a simple data transformation producing the time reversed image of the original series, the problem of quot;variance decreasequot; can be reformulated in terms of that of polynomial-like variance growth. Simulation evidence suggests that the new procedures work quite well in small samples