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The stationarity and invertibility of a class of nonlinear ARMA models

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Abstract

We investigate some probabilistic properties of a new class of nonlinear time series models. A suffcient condition for the existence of a unique causal, strictly and weakly stationary solution is derived. To understand the proposed models better, we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants, which can also be used for identification purpose. A suffcient condition for invertibility is also provided.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Fujian University of Technology, Fuzhou, 350108, China

    DanQing Chen

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    DanQing Chen & HaiBin Wang

Authors
  1. DanQing Chen
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  2. HaiBin Wang
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Correspondence to HaiBin Wang.

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Chen, D., Wang, H. The stationarity and invertibility of a class of nonlinear ARMA models. Sci. China Math. 54, 469–478 (2011). https://doi.org/10.1007/s11425-010-4160-y

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  • DOI: https://doi.org/10.1007/s11425-010-4160-y

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