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Non Linear ARX-Models : Probabilistic Properties and Consistent Recursive Estimation

Author

Listed:
  • DOUKHAN, P.

    (U.R.A., Université Paris-Sud, France)

  • TSYBAKOV, A.

    (Institute for Problems of Information Transmission Academy of Sciences, Moscow and CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve Belgium)

Abstract

Consider the general ARX(k, q) nonlinear process defined by the recurrence relation Yn = f(Y_(n-1),... y_(n-k), x_n,..., x_(n-q+1)) +([ xi ]_n) where { x_n},{ [xi]_n} are independent i.i.d. sequences. We study some probabilistic properties of this process in the ergodic situation and propose a recursive estimator of the stochastic gradient kind of the function f which is strongly consistent.

Suggested Citation

  • Doukhan, P. & Tsybakov, A., 1992. "Non Linear ARX-Models : Probabilistic Properties and Consistent Recursive Estimation," LIDAM Discussion Papers CORE 1992056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1992056
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp1992.html
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