| Nonlinear time series analysis is a more common and more extensive using prospect than the linear one. At present, it has become an important research direction in the time series analysis theory. One of the important methods of researching nonlinear time series is models' analysis. Recently, many nonlinear time series models have been proposed and obtained widely used as well. But nowadays in the widely studied models, the disturbance is a single white noise. This kind of models has obvious limit, that is the models don't consider disturbance caused by environments. In the actual situation, the disturbance to the system varies with the different environments. On the other hand,so far,the study on non-line time series is on the length of delay is a constant. However ,in fact,it is not true sometimes. The time series models studied by this master' thesis under random environment and random delay simulate the phenomenon that dynamic system is interfered by random environment much better than previous ones. At this respect, Hou Zhenting et al, professors of Institute of Probability & Statistics of Central South University have carried correlative studies and analysis. The author adopts their ideas, and by applying the ergodicity theory of Markov chains on general state space, discussed two kinds of the Random Coefficient Functional Autoregressive, and obtained sufficient conditions for their convergence under some conditions.This thesis consists of four chapters: Chapter 1 briefly introduces the situations of time series analysis. Chapter 2, as basic knowledge, presents some ergodicity theory of Markov chains on general state space so we can use later. Chapter 3, the author proposes a kind of Random Coefficient Functional Autoregressive model under random environment and it's geometric ergodicity is discussed.. Chapter 4, a kind of Random Coefficient Functional Autoregressive model with random delay is proposed and it's geometric ergodicity is discussed. |
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