## Estimating Lyapunov Exponents In Chaotic Time Series With Locally Weighted Regression (1994)

Citations: | 4 - 1 self |

### BibTeX

@MISC{Lu94estimatinglyapunov,

author = {Zhan-qian Lu},

title = {Estimating Lyapunov Exponents In Chaotic Time Series With Locally Weighted Regression},

year = {1994}

}

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### Abstract

Nonlinear dynamical systems often exhibit chaos, which is characterized by sensitive dependence on initial values or more precisely by a positive Lyapunov exponent. Recognizing and quantifying chaos in time series represents an important step toward understanding the nature of random behavior and revealing the extent to which short-term forecasts may be improved. We will focus on the statistical problem of quantifying chaos and nonlinearity via Lyapunov exponents. Predicting the future or determining Lyapunov exponents requires estimation of an autoregressive function or its partial derivatives from time series. The multivariate locally weighted polynomial fit is studied for this purpose. In the nonparametric regression context, explicit asymptotic expansions for the conditional bias and conditional covariance matrix of the regression and partial derivative estimators are derived for both the local linear fit and the local quadratic fit. These results are then generalized to the time s...