Dimension estimation with the BDS-G statistic

References

• Albano , AM , Muench , J , Schwartz , C , Mees , AI and Rapp , PE . 1988 . Singular-value decomposition and the Grassberger-Procaccia Algorithm . Physical Review A , 38 : 3017 – 27 .
   Web of Science ®Google Scholar
• Aparicio , MT , Pozo , E and Saura , D . 1999 . Investigating the chaotic behavior in economic series: the delay-time in the Grassberger-Procaccia Algorithm . International Journal of Theoretical and Applied Finance , 2 : 357 – 80 .
   Google Scholar
• Bajo-Rubio , O , Fernández-Rodríguez , F and Sosvilla-Rivero , S . 1992 . Chaotic behavior in exchange-rate series: first results for the peseta-US dollar case . Economic Letters , 39 : 207 – 11 .
   Web of Science ®Google Scholar
• Barnett WA Chen P 1988 The aggregation-theoretic monetary aggregates are chaotic and have strange attractor: an econometric application of mathematical chaos Dynamic Econometric Modelling (Eds) W. Barnett, E. Bernt and H. White Cambridge University Press Cambridge
   Google Scholar
• Brock , W . 1986 . Distinguishing random and deterministic systems: abridged version . Journal of Economic Theory , 4 : 168 – 95 .
   Google Scholar
• Brock , W and Sayers , CL . 1988 . Is the business cycle charactericed by deterministic chaos? . Journal of Monetary Economics , 22 : 71 – 90 .
   Web of Science ®Google Scholar
• Brock W Dechert D 1989 Statistical inference theory for measures of complexity in Chaos theory and nonlinear science Measures of Complexity and Chaos (Eds) N. B. Abraham, A. M. Albano, A. Passamante and P. E. Rapp Plenum Press New York
   Google Scholar
• Brock , WA , Dechert , WD , Scheinkman , JA and LeBaron , B . 1996 . A test for independence based on the Correlation Dimension . Econometric Reviews , 15 : 197 – 235 .
   Google Scholar
• Buzug , Th. , Reimeres , T and Pfister , G . 1990 . Optimal reconstruction of strange attractors from purely geometrical arguments . Europhysics Letters , 13 : 605 – 10 .
   Google Scholar
• Cecen , A and Erkal , C . 1996 . Distinguishing between stochastic and deterministic behavior in high frequency foreign exchange rate returns: can non-linear dynamics help forecasting? . International Journal of Forecasting , 12 : 465 – 73 .
   Web of Science ®Google Scholar
• De Grauwe P Dewacher H Embrechts M 1993 Exchange Rate Theory, Blackwell Publishers Cambridge
   Google Scholar
• Frank , M and Stengos , T . 1989 . Measuring the strangeness of gold and silver rates of returns . Review of Economic Studies , 56 : 553 – 67 .
   Web of Science ®Google Scholar
• Fraser , AM and Swinney , HL . 1986 . Independent coordinates for strange attractors from mutual information . Physical Review Letters , 33 : 1134 – 40 .
   Google Scholar
• Grassberger , P and Procaccia , I . 1983 . Measuring the strangeness of strange attractors . Physica D , 9 : 189 – 208 .
   Web of Science ®Google Scholar
• Matilla M 2002 Algunas aportaciones de la teoría del caos al análisis empírico de series temporales Ph.D. thesis Universidad Autónoma de Madrid
   Google Scholar
• Matilla M Queralt R Sanz P Vázquez FJ 2004 The BDS test and delay time: a generalized statistic of the BDS forthcoming
   Google Scholar
• Mayfield , E and Mizrach , B . 1992 . On determining the dimension of real time stock-price data . Journal of Business and economic Statistics , 10 : 367 – 74 .
   Web of Science ®Google Scholar
• Panas , E and Ninni , V . 2000 . Are oil markets chaotic ?  A non-linear dynamic analysis . Energy Economics , 22 : 548 – 68 .
   Google Scholar
• Ramsey , JB , Sayers , CL and Rothman , P . 1990 . The statistical properties of dimension calculations using small data sets: some economic applications . International Economic Review , 31 : 991 – 1020 .
   Web of Science ®Google Scholar
• Renyi A 1970 Probability Theory, North-Holland Amsterdam
   Google Scholar
• Scheinkman , JA and LeBaron , B . 1989 . Nonlinear dynamics and stock returns . Journal of Business , 63 : 311 – 37 .
   Google Scholar
• Takens F 1981 Detecting strange attractors in turbulence Dynamical Systems and Turbulence (Eds) D. Rand and L. Young Springer-Verlag Berlin
   Google Scholar