# zbMATH — the first resource for mathematics

Stationary distribution of some nonlinear AR(1) processes. (English) Zbl 0701.60029
Summary: Let $$e_ t$$ be a sequence of independent, identically distributed random variables such that $$P(e_ t=0)=p$$, $$P(e_ t=c)=1-p$$, where $$c>0$$ and $$p\in (0,1)$$ are given numbers. Let F be a stationary distribution function of the nonlinear AR(1) process $$X_ t=aX^{1/h}_{t-1}+e_ t$$, where $$a>0$$, $$h>1$$. A method for calculating F and its moments is introduced. The results are demonstrated on some numerical examples.

##### MSC:
 60G10 Stationary stochastic processes 62M20 Inference from stochastic processes and prediction
##### Keywords:
stationary distribution function; numerical examples
Full Text:
##### References:
 [1] J. Anděl: On nonlinear models for time series. Statistics [2] D. A. Jones: Stationarity of Non-linear Autoregressive Processes. Technical Report, Institute of Hydrology, Wallingford, Oxon, U. K. 1977. [3] D. A. Jones: The Statistical Treatment of Non-linear Autoregressive Processes. Technical Report, Institute of Hydrology, Wallingford, Oxon, U. K. 1977. [4] D. A. Jones: Nonlinear autoregressive processes. Proc. Roy. Soc. London Ser. A 360 (1978), 71-95. · Zbl 0378.62076 · doi:10.1098/rspa.1978.0058 [5] W. Loges: Note on parameter estimation for general non-linear time series models. Statistics 18 (1987), 587-590. · Zbl 0636.62087 · doi:10.1080/02331888708802055
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.