Identification of Nonlinear Time Series: First Order Characterization and Order Determination
研究了利用条件均值和条件方差的非参数估计来识别非线性时间序列，并提出了确定非线性模型阶数的准则，通过模拟实验验证了方法的有效性。
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.