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Biometrika 1990 77(4):669-687; doi:10.1093/biomet/77.4.669
© 1990 by Biometrika Trust
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Identification of nonlinear time series: First order characterization and order determination

BJØRN AUESTAD and DAG TJØSTHEIM

Department of Mathematics, University of Bergen 5007 Bergen, Norway

We study the possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance. It is shown that most nonlinear models satisfy the assumptions needed to apply nonparametric asymptotic theory. Sampling variations of the conditional quantities are studied by simulation and explained by asymptotic arguments for a number of first-order nonlinear autoregressive processes. The conditional mean and variance can be used for identification purposes, but one must be aware of bias and misspecification effects. We also propose a criterion for determining the order of a general nonlinear model. The criterion is justified in parts by heuristics, but encouraging results are obtained from a limited set of simulation experiments. Several open problems are identified and stated.

Key Words: Conditional mean and variance • FPE criterion • Nonlinear order determination • Nonlinear time series • Nonparametric estimation


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