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Iterations Of Dependent Random Maps And Exogeneity In Nonlinear Dynamics

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  • Debaly, Zinsou Max
  • Truquet, Lionel

Abstract

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

Suggested Citation

  • Debaly, Zinsou Max & Truquet, Lionel, 2021. "Iterations Of Dependent Random Maps And Exogeneity In Nonlinear Dynamics," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1135-1172, December.
    • Handle: RePEc:cup:etheor:v:37:y:2021:i:6:p:1135-1172_3
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    Cited by:

    1. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    2. Debaly, Zinsou Max & Marchand, Philippe & Girona, Miguel Montoro, 2022. "Autoregressive models for time series of random sums of positive variables: Application to tree growth as a function of climate and insect outbreak," Ecological Modelling, Elsevier, vol. 471(C).
    3. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.

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