Stability and asymptotics for autoregressive processes

The paper studies infinite order autoregressive models for both temporal and spatial processes. We present sufficient conditions for the existence of stationary distributions. To understand the underlying dynamics and to capture the dependence structure, we introduce functional dependence measures and relate them with Lipschitz coefficients of the data-generating mechanisms. Our stability result allows both short-and long-range dependence. With functional dependence measures, we can establish an asymptotic theory for the underlying processes.