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Stability results for nonlinear vector autoregressions with an application to a nonlinear error correction model

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  • Saikkonen, Pentti

Abstract

This paper improves previous sufficient conditions for stationarity obtained in the context of a general nonlinear vector autoregressive model with nonlinear autoregressive conditional heteroskedasticity. The results are proved by using the stability theory developed for Markov chains. Stationarity, existence of second moments of the stationary distribution, and useful mixing results are obtained by establishing appropriate versions of geometric ergodicity. The results are applied to a nonlinear error correction model to obtain an analog of Granger's representation theorem.

Suggested Citation

  • Saikkonen, Pentti, 2001. "Stability results for nonlinear vector autoregressions with an application to a nonlinear error correction model," SFB 373 Discussion Papers 2001,93, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200193
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    Cited by:

    1. Chengchun Shi & Sheng Zhang & Wenbin Lu & Rui Song, 2022. "Statistical inference of the value function for reinforcement learning in infinite‐horizon settings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 765-793, July.
    2. De Gooijer, Jan G. & Vidiella-i-Anguera, Antoni, 2004. "Forecasting threshold cointegrated systems," International Journal of Forecasting, Elsevier, vol. 20(2), pages 237-253.
    3. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(1), pages 37-70, February.
    4. Shi, Chengchun & Zhang, Shengxing & Lu, Wenbin & Song, Rui, 2022. "Statistical inference of the value function for reinforcement learning in infinite-horizon settings," LSE Research Online Documents on Economics 110882, London School of Economics and Political Science, LSE Library.

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