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Nonlinear nonnegative AR(1) processes. (English) Zbl 0696.62347

Summary: Let \(\{e_ t\}\) be a nonnegative strict white noise and \(X_ 1\) an independent nonnegative random variable. For \(t\geq 2\) define \(X_ t=b g(X_{t-1})+e_ t\) where g is a nonnegative function and \(b\geq 0\). Then \(b^*_ n= \min \{X_ 2/g(X_ 1),...,X_ n/g(X_{n-1})\}\) is an estimator for b. Under some general conditions, which do not include stationarity, it is proved that \(b^*_ n\) is strongly consistent.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
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[1] DOI: 10.1080/03610928808829693 · Zbl 0639.62082 · doi:10.1080/03610928808829693
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[5] DOI: 10.1080/03610928608829248 · Zbl 0604.62087 · doi:10.1080/03610928608829248
[6] DOI: 10.1080/02331888708802055 · Zbl 0636.62087 · doi:10.1080/02331888708802055
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