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Nonparametric recursive estimation in nonlinear ARX-models. (English. Russian original) Zbl 0804.62041

Probl. Inf. Transm. 29, No. 4, 318-327 (1993); translation from Probl. Pereda. Inf. 29, No. 4, 24-34 (1993).
Summary: Consider the general \(\text{ARX} (k,q)\) nonlinear process defined by the recurrence relation \[ y_ n= f(y_{n-1}, \dots, y_{n-k}, x_ n,\dots, x_{n-q+1})+ \xi_ n, \] where \(\{x_ n\}\), \(\{\xi_ n\}\) are sequences of independent, identically distributed random variables. We propose a recursive nonparametric estimator of the function \(f\) and we prove its strong consistency under general assumptions on the model. We study the model properties guaranteeing that these assumptions are satisfied.

MSC:

62G07 Density estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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