Pentti Saikkonen: Subgeometrically ergodic autoregressions (with Mika Meitz)

In this paper, we consider subgeometric ergodicity in the context of univariate nonlinear autoregressions. The notion of subgeometric ergodicity was introduced in the Markov chain literature in 1980s and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric. This convergence rate is also closely related to the convergence rate of β-mixing coefficients. One feature of subgeometrically ergodic autoregressions is that they can behave similarly to a unit root process for large values of the observed series but their behavior is almost unrestricted for moderate values of the observed series. The earlier papers discussing subgeometrically ergodic autoregressions (or related β-mixing coefficients) we have found have mainly appeared in the probability literature and focused only on first order autoregressions with a nonparametric regression function. In a recent paper (Meitz and Saikkonen, Econometric Theory, in press), we extend these earlier first-order results to a higher-order case providing also parametric examples with simulated illustrations and results on the convergence rate of β-mixing coefficients. So far, our results assume a homoskedastic error term, but obtaining extensions with heteroskedastic ARCH-type errors as well as empirical examples is under way.