ITERATIONS OF DEPENDENT RANDOM MAPS AND EXOGENEITY IN NONLINEAR DYNAMICS

We discuss the existence and uniqueness of stationary ergodic nonlinear autoregressive processes when exogenous regressors are incorporated into dynamic. To this end, we consider convergence backward iterations dependent random maps. In particular, give a new result classical condition contraction on average is replaced with in conditional expectation. Under some conditions, also dependence properties these using functional measure Wu (2005, Proceedings National Academy Sciences 102, 14150–14154) that delivers central limit theorem giving wide range applications. Our results illustrated heteroscedastic models, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) processes, count time series, binary choice categorical series for which provide many extensions existing results.