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Functional-coefficient autoregressive models. (English) Zbl 0776.62066
A process \(x_ t\) follows a functional coefficient autoregressive (FAR) model if \[ x_ t=f_ 1(X^*_{t-1}) x_{t-1}+\cdots+ f_ p(X^*_{t-1}) x_{i-p}+\varepsilon_ t, \] where \(\varepsilon_ t\) is a strict white noise with vanishing mean and finite variance and \(X^*_{t-1}=(x_{t-i_ 1}\), \(\dots,x_{t-i_ k})'\) is a threshold vector. The authors give two sufficient stationarity conditions for FAR models. They propose a method based on arranged local regression for building FAR models and introduce a consistency result to support the procedure. A simulated example of a threshold AR(2) model shows how the method works. Two sets of real data (chickenpox in New York City 1949- 1972 and sunspot numbers) are analyzed. It is shown that the proposed model improves multi-step ahead forecasts over other methods.
Reviewer: J.Anděl (Praha)

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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