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Estimating an autoregressive function and its derivatives is important to analyze chaotic time series, especially to estimate the Lyapunov exponent. In this article, we propose an adaptive variable se...lection method to estimate a nonlinear autoregressive function and its derivatives. Our method has a number of advantages. Since an attractor of chaotic time series is bounded, most kernel-based local mean nonparametric methods have the bias near the boundary of the attractor. In contrast, the order of the bias of our method is higher than that of most existing methods. To estimate derivatives of nonlinear function, we approximate it locally using a linear function. Since correlation dimension of the attractor is not integer, local linear regression has multicollinearity at many points and makes the variance of the estimator of the nonlinear function large. Our method reduces this problem by adaptive variable selection in local linear regression problem.続きを見る
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