An alternative to the BDS test: integration across the correlation integral. (English) Zbl 1047.62038

Kočenda, Evžen

Econ. Rev. 20, No. 3, 337-351 (2001).

This paper extends and generalizes the BDS test presented by W. A. Brock, W. D. Dechert, J. A. Scheinkman and B. Le Baron [ibid. 15, 197–235 (1996; Zbl 0893.62034)]. In doing so it aims to remove the limitation of having to arbitrarily select a proximity parameter by integrating across the correlation integral. Monte Carlo simulation is used to tabulate critical values of the alternative statistic. Previously published empirical studies are replicated as well as power tests executed in order to evaluate the relative performance of the suggested alternative to the BDS test. The results are favorable for the suggested alternative.

MSC:

62G10	Nonparametric hypothesis testing
65C05	Monte Carlo methods
37N40	Dynamical systems in optimization and economics
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B28	Finance etc. (MSC2000)

Keywords:

chaos; nonlinear dynamics; correlation integral; Monte Carlo; exchange rates

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