Abstract
By introducing a random interference into the typical of nonlinear time series model, this paper establishes a RENLAR model: \(X_{n+1}=T(X_n)+ e_{n+1}(Z_{n+1})\). The author introduces the definition of adjoint non-recurrence, and utilizing general state space Markov chain theorem, we obtain some criteria for non-recurrence and adjoint non-recurrence of nonlinear time series models in random environment domain and analyze adjoint non-recurrence of some models by using these criteria.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
An HZ, Chen M (1998) Nonlinear time series analysis. Shang Hai Science Press, Shang Hai
Hou ZT, Yu Z, Shi P (2005) Study on a class of nonlinear time series models and ergodicitiy in random environment domain. Math Meth Oper Res 61:299–310
Meyn SP, Tweedie RL (1993) Markov chain and stochastic stability. Springer, Berlin Heidelberg New York
Bhattacharya R, Lee C (1995) On geometric ergodicity of nonlinear autoregressive models. Statist Probab Lett 22:311–315
Sheng ZH, Wang T, Liu DL (1993) On the stability properties Of nonlinear time series models—theorem of ergocity and its application. Science Press, Bei Jing
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported Science Foundation of China (10171009).
Rights and permissions
About this article
Cite this article
Zhu, E., Zou, J. & Hou, Z. Analysis on adjoint non-recurrent property of nonlinear time series in random environment domain. Math Meth Oper Res 65, 353–360 (2007). https://doi.org/10.1007/s00186-006-0128-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00186-006-0128-7