On consistent nonparametric order determination and chaos

Cheng, B. and Tong, Howell (1992) On consistent nonparametric order determination and chaos. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 54 (2). pp. 427-449. ISSN 1369-7412. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.2307/2346136

Abstract

We give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models. We argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos. Setting the stochastic models within the framework of non-linear autoregression, we introduce the notion of a generalized partial autocorrelation and an order. We approach the estimation of the embedding dimension via order determination of an unknown non-linear autoregression by cross-validation, and give justification by proving its consistency under global boundedness. As a by-product, we provide a theoretical justification of the final prediction error approach of Auestad and Tjostheim. Some illustrations based on the Henon map and several real data sets are given. The bias of the residual sum of squares as essentially a noise variance estimator is quantified.

Item Type: Article
Additional information: MEETING OF THE ROYAL STATISTICAL SOC ON CHAOS LONDON, ENGLAND, OCT 16, 1991 ROYAL STAT SOC, RES SECT
Uncontrolled keywords: ATTRACTORS; BANDWIDTH; BIAS CORRECTION; BINARY SHIFT MAP; CANADIAN LYNX; CHAOS; CONSISTENCY; CROSS-VALIDATION; DIMENSION; DOUBLE WINDOWS; EMBEDDING DIMENSION; EPIDEMICS; EXPERIMENTAL DATA; FINAL PREDICTION ERROR; FRACTALS; GENERALIZED PARTIAL AUTOCORRELATION FUNCTION; GLOBAL BOUNDEDNESS; HENON MAP; KERNEL ESTIMATION; LIMIT CYCLES; LIMIT POINTS; LOCAL INSTABILITY; LYAPUNOV EXPONENT; MAP RECONSTRUCTION; MEASLES; NONLINEAR AUTOREGRESSION; ORDER DETERMINATION; ORDER OF NONLINEAR AUTOREGRESSION; PREDICTIVE RESIDUALS; RESIDUAL SUM OF SQUARES; SKELETON; U-STATISTICS; WOLF SUNSPOT NUMBERS
Subjects: H Social Sciences > HA Statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: A. Xie
Date Deposited: 01 Nov 2009 14:56
Last Modified: 25 Jun 2014 09:37
Resource URI: http://kar.kent.ac.uk/id/eprint/23257 (The current URI for this page, for reference purposes)
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