Estimating Correlation Dimension on Japanese Candlestick, Application to FOREX Time Series

Authors: S. Mahmoodzadeh, J. Shahrabi, M. A. Torkamani, J. Sabaghzadeh Ghomi

Abstract:

Recognizing behavioral patterns of financial markets is essential for traders. Japanese candlestick chart is a common tool to visualize and analyze such patterns in an economic time series. Since the world was introduced to Japanese candlestick charting, traders saw how combining this tool with intelligent technical approaches creates a powerful formula for the savvy investors. This paper propose a generalization to box counting method of Grassberger-Procaccia, which is based on computing the correlation dimension of Japanese candlesticks instead commonly used 'close' points. The results of this method applied on several foreign exchange rates vs. IRR (Iranian Rial). Satisfactorily show lower chaotic dimension of Japanese candlesticks series than regular Grassberger-Procaccia method applied merely on close points of these same candles. This means there is some valuable information inside candlesticks.

Keywords: Chaos, Japanese candlestick, generalized box counting, strange attractor.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070591

References:

[1] Gary S. Wagner, Bradley L. Matheny A," Trading Applications of Japanese Candlestick Charting ", John Wiley and Sons Press, Oct 28, 1993, ISBN 0471587281.
[2] Grassberger, P. and I. Procaccia, 1983," Measuring the Strangeness of Strange Attractors", Physica 9D, 189-208.
[3] J. Banks, D. Valentina, J.Arthur; "Chaos: A Mathematical Introduction", Cambridge University Press, 2003.
[4] Granger, C. W. J. and Terasvirta, T. (1993), Modeling Nonlinear Economic Relationships, Oxford University Press.
[5] Shintani, Mototsugu, Oliver Linton. 2001. Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors. Vanderbilt University Department of Economics Working Paper.
[6] S. Boccaletti, C. Grebogi, C. Lai, H. Mancini, D. Maza, "The control of chaos: theory and applications", Physics Reports 329, 103-197, 2000.
[7] A M. Ataei, B. Lohmann, A. Khaki-Sedigh, C. Lucas, "Determining minimum embedding dimension from chaotic time series", Nonlinear Phenomena in Complex Systems, 6:4, pp. 842 - 851, 2003.
[8] H. Dewachter, M. Lyrio "The cost of technical trading rules in the Forex market: A utility-based evaluation" International Money and Finance, Vol.25, pp1072-1089, 2006.
[9] B. Davies; "Exploring Chaos: Theory And Experiment (Studies in Nonlinearity S.)",Westview Press, 2005.
[10] W. Barnett, A. Serletis; "Martingales, nonlinearity, and chaos", Journal of Economic Dynamics & Control 703-724, 2000.