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An alternative to the BDS test: integration across the correlation integral. (English) Zbl 1047.62038
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)
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References:
[1] Anderson P. W., Santa Fe Institute Studies in the Sciences of Complexity 5 (1988)
[2] Brock W., Journal of Economic Theory 40 pp 168– (1986) · Zbl 0616.62125 · doi:10.1016/0022-0531(86)90014-1
[3] Brock W., The Economy as an Evolving Complex System 5 (1988)
[4] Brock W., Econometric Reviews 15 pp 197– (1996) · Zbl 0893.62034 · doi:10.1080/07474939608800353
[5] Brock W. A., Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence (1991)
[6] Cecen A. A., Economics Letter 51 (3) pp 323– (1996) · Zbl 06278690 · doi:10.1016/0165-1765(96)00819-1
[7] Chwee V., Energy Journal 19 (2) pp 149– (1998) · doi:10.5547/ISSN0195-6574-EJ-Vol19-No2-10
[8] Collings B. J., Journal of the American Statistical Association, Theory and Methods 82 pp 525– (1987) · doi:10.1080/01621459.1987.10478457
[9] de Lima P., Journal of Business and Economic Statistics 16 (2) pp 227– (1998)
[10] Engle R. F., Econometrica 50 pp 987– (1982) · Zbl 0491.62099 · doi:10.2307/1912773
[11] Fishman G. S., Journal of the American Statistical Association, Theory and Methods 77 pp 129– (1982)
[12] Grassberger P., Physica D 9 pp 189– (1983) · Zbl 0593.58024 · doi:10.1016/0167-2789(83)90298-1
[13] Hsieh D. A., Journal of Finance 46 pp 1839– (1991) · doi:10.1111/j.1540-6261.1991.tb04646.x
[14] Hsieh D. A., Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence (1998)
[15] Hsieh D. A., Journal of Financial and Quantitative Analysis 28 (1) pp 41– (1993) · doi:10.2307/2331150
[16] Kočenda E., Eastern European Economics 34 (6) pp 37– (1996) · doi:10.1080/00128775.1996.11648603
[17] Kugler P., Schweizerische Zeitschrift für Volkswirtschaft und Statistik 126 (2) pp 113– (1990)
[18] Kugler P., Rivista Internazionale di Scienze Economiche e Commerciali 40 (2) pp 127– (1993)
[19] Olmeda I., Investigaciones Economicas 19 (2) pp 217– (1995)
[20] Serletis A., Research in Economics 51 (4) pp 359– (1997) · Zbl 0914.90055 · doi:10.1006/reec.1997.0050
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