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Functional identification in nonlinear time series. (English) Zbl 0727.62082

Nonparametric functional estimation and related topics, NATO ASI Ser., Ser. C 335, 493-507 (1991).
Summary: [For the entire collection see Zbl 0722.00032.]
We study functional identification of nonlinear time series models of the type \(X_ t=g(X_{t-1},...,X_{t-p})+e_ t\). Nonparametric estimation is used to estimate the function g and to single out the most significant lags in a stepwise analysis. We also define projections at a fixed lag of the model and show how this concept can be used to identify the model among familiar nonlinear time series classes. The case of additive models is given special emphasis. The results are illustrated by simulations and by a real data example. Some asymptotics are derived, partly by heuristic means, and the bootstrap is introduced in one of the examples. We indicate the possibility of using this approach as a first step in a general empirical modelling of time series.

MSC:

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

Citations:

Zbl 0722.00032