Recurrence and transience for autoregressive nonlinear time series
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Date
1995
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Abstract
It is a known fact that drift criteria can be used to study autoregressive nonlinear time series. In fact, they have been applied to some special cases and satisfactory results are obtained. We extend the results to general AR(1) nonlinear processes [ ] where [alpha] is a nonlinear locally bounded function from [ ] is a sequence of i.i.d. random variables with density function f positive on [ ] and [ ] if I is a compact interval. [ ] We refine the results for the special case when [ ] is of one sign for large x [ ] We pay special attention to the case [ ] and obtain conditions for erogodicity and null recurrence. We also illustrate our results by examples.
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