Yao, Q.W and Tong, H.W (1994) Quantifying the Influence of Initial Values on Nonlinear Prediction. Journal of the Royal Statistical Society Series B-Methodological, 56 (4). pp. 701-725. ISSN 0035-9246.
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Motivated by the m-step-ahead prediction problem in non-linear time series, a brief sketch of stochastic chaotic systems is provided. The accuracy of the prediction depends on the initial value, which is a typical feature of non-linear but not necessarily chaotic models. However, if the model is chaotic, small noise can be amplified very quickly through time evolution at some initial values, thereby decreasing dramatically the reliability of the prediction. Further, if the model is chaotic, small shifts in some initial values can lead to considerable errors in prediction, which can be monitored by the newly defined Lyapunov-like indices. For the nonparametric predictor constructed by the locally linear regression method, the mean-squared error may be decomposed into two parts: the conditional variance and the divergence resulting from a small shift in initial values. The decomposition also holds for more general predictors. A consistent estimator of the Lyapunov-like index is also constructed by the locally linear regression method. Both simulated and real data are used as illustrations.
|Uncontrolled keywords:||ABSOLUTELY REGULAR; CHAOS; LOCALLY LINEAR REGRESSION; LYAPUNOV EXPONENT; LYAPUNOV-LIKE INDEX; NOISE AMPLIFICATION; NONLINEAR PREDICTION; NONLINEAR TIME SERIES; NONPARAMETRIC REGRESSION; STOCHASTIC DYNAMICAL SYSTEM|
|Subjects:||H Social Sciences > HA Statistics|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics|
|Depositing User:||P. Ogbuji|
|Date Deposited:||09 Jun 2009 11:16|
|Last Modified:||09 Jun 2009 11:16|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/20121 (The current URI for this page, for reference purposes)|
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