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Nonlinear AR modeling. (English) Zbl 0834.62079

Summary: A major reason for the success of linear autoregressive (AR) modeling is that A. N. Kolmogorov [Bull. Acad. Sci. USSR, Ser. Math. 5, 3-14 (1941; Zbl 0024.15901)] proved that every linear system could be represented by a linear AR model of infinite order. The computation of a finite order AR approximation is, of course, the practical goal. We prove that every nonlinear system with a Volterra series expansion can be represented as a nonlinear AR model of infinite order. Our method shows how an approximation to any desired order and degree can be achieved.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
41A99 Approximations and expansions

Citations:

Zbl 0024.15901
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References:

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