Deterministic chaos and forecasting in Amazon?s share prices

• Authors: Michael Hanias , Stefanos Tsakonas , Lykourgos Magafas , Eleftherios I. Thalassinos , Loukas Zachilas

Abstracts

EN

Research background: The application of non-linear analysis and chaos theory modelling on financial time series in the discipline of Econophysics. Purpose of the article: The main aim of the article is to identify the deterministic chaotic behavior of stock prices with reference to Amazon using daily data from Nasdaq-100. Methods: The paper uses nonlinear methods, in particular chaos theory modelling, in a case study exploring and forecasting the daily Amazon stock price. Findings & Value added: The results suggest that the Amazon stock price time series is a deterministic chaotic series with a lot of noise. We calculated the invariant parameters such as the maxi-mum Lyapunov exponent as well as the correlation dimension, managed a two-days-ahead forecast through phase space reconstruction and a grouped data handling method.

Keywords

EN

time series; chaos theory; econophysics; forecasting

• Publisher: Instytut Badań Gospodarczych
• Journal: Equilibrium. Quarterly Journal of Economics and Economic Policy
• Year: 2020
• Volume: 15
• Issue: 2
• Pages: 253-273

Dates

published

2020

Contributors

author

Michael Hanias

• International Hellenic University in Thessaloniki

• https://orcid.org/0000000209189343

author

Stefanos Tsakonas

• University of Thessaly in Volos

• https://orcid.org/0000000328787741

author

Lykourgos Magafas

• International Hellenic University in Thessaloniki

• https://orcid.org/0000000282539653

author

Eleftherios I. Thalassinos

• University of Piraeus, University of Malta

• https://orcid.org/0000000335264930

author

Loukas Zachilas

• University of Thessaly in Volos

• https://orcid.org/0000000170212955

References

• Abarbanel, H. D. I. (1996). Analysis of observed chaotic data. Springer, New York.
• Balakin, A. S, Matamoros, O. M., Ernesto-Galves, M., & Alfonso-Perez, A. (2004). Crossover from anti-persistent to persistent behavior in time series possessing the generalized dynamic scaling law. Physics Review, E69, 03612. doi: 10.1103/PhysRevE.69.036121.
• Bildirici, M., Sonüstün, B., & Gökmenoğlu, S. M. (2019). Chaotic structure of CDS. In AIP conference proceedings (Vol. 2178, No. 1). AIP Publishing LLC. doi: 10.1063/1.5020458.
• Diaz, J. F. (2013). Evidence of noisy chaotic dynamics in the returns of four Dow Jones Stock indices. Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, 4.
• Faggini, M. (2014). Chaotic time series analysis in economics: balance and perspectives. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24, 042101-1-10. doi: doi.org/10.1063/1.4903797.
• Fallahi, S., Saverdi, M., & Bashiri, V. (2001). Applying GMDH- type neural network and genetic algorithm for stock price prediction of Iranian cement sector. Applications and Applied Mathematics: An International Journal, 6(12).
• Fan, X. H., Xu, H. H., Yin, J. L., & Ning, C. (2017). Chaotic behavior in a resource-economy-pollution dynamic system. Journal of Multidisciplinary Engineering Science and Technology, 4(1).
• Fraser, A. M., & Swinney, H. L. (1986). Independent coordinates for strange attractors for mutual information. Physics Review, A33. doi: 10.1103/PhysRevA. 33.1134.
• Garas, A., & Argyrakis, P. (2007). Correlation study of the Athens Stock Exchange. Physica A: Statistical Mechanics and its Applications, 380. doi: 10.1016/j.physa.2007.02.097.
• Hanias, M., Curtis, P., & Ozun, A. (2008). Chaos theory in predicting the Istanbul Stock Exchange Index. Empirical Economics Letters, 7(4).
• Hanias, M. P., Avgerinos, Z., & Tombras, G. S. (2009). Period doubling, Feingenbaum constant and time series prediction in an experimental chaotic RLD circuit. Chaos Solitons & Fractals, 40(3). doi: 10.1016/j.chaos.2007.08.061.
• Hanias, M., Magafas, L., & Konstantaki, P. (2013). Non linear analysis of S&P index. Equilibrium. Quarterly Journal of Economics and Economic Policy, 8(4). doi: 10.12775/EQUIL.2013.030.
• Ivakhenko, A. G. (1968). The group method of data handling: a rival of the method of stochastic approximation. Soviet Automatic Control, 13(3).
• Ivakhenko, A. G., & Ivakhenko, G. A. (1995). The review of problems solvable by algorithms of the group method of data handling (GMDH). Pattern Recognition and Image Analysis, 5(4).
• Kantz, H., & Schreiber, T. (1997). Nonlinear time series analysis. Cambridge University Press.
• Kenett, D. Y., Shapira, Y., Madi, A., Zabary, S. B., Gershgoren, G. G, & Jacob, E. B. (2010). Dynamics of stock market correlations. AUCO Czech Economic Review, 4.
• Kodba, S., Perc, M., & Marhl, M. (2005). Detecting chaos from a time series. European Journal of Physics, 26. doi: 10.1088/0143-0807/26/1/021.
• Lahmiri, S. (2017). On fractality and chaos in Moroccan family business stock returns and volatility. Physica A: Statistical Mechanics and its Applications, 473(C). doi: 10.1016/j.physa.2017.01.033.
• Magafas, L. (2013). Has the Greek financial problem triggered the debt problem for the whole Eurozone? An analysis based on EconoPhysics. China-USA Business Review, 12(7).
• Magafas, L., Hanias, M., Tavlatou, A., & Kostantaki, P. (2017). Non–linear properties of VIX Index. International Journal of Productivity Management and Assessment Technologies, 5(2). doi: 10.4018/IJPMAT.2017070102.
• Mantegna, R. N., & Stanley, H. E. (1995). Scaling behavior in the dynamics of an economic index. Nature, 376. doi: 10.1038/376046a0.
• Ott, E., Sauer, T., & Yorke, J. A. (1994). Coping with chaos. New York: Wiley Interscience Publication.
• Ozun, A., Hanias, M. P., & Curtis, P. G. (2010). A chaos analysis for Greek and Turkish equity markets. EuroMed Journal of Business, 5(1). doi: 10.1108/ 14502191011043189.
• Ozun, A., Contoyiannis, Y. F., Diakonos, F. K., Hanias, M., & Magafas, L. (2014). Intermittency in stock market dynamics. Journal of Trading, 9(3). doi: 10.3905/ jot.2014.9.3.034.
• Peng, C. K., Havlin, S., & Goldberger, A. L (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos, 5(1). doi: 10.1063/1.166141.
• Peters, E. E. (1991). Chaos and order in the capital markets. New York: Wiley Finance Editions.
• Peters, E. E. (1994). Fractal market analysis. New York: Wiley.
• Provenzale, A., Smith, L. A., Vio, R., & Murante, G. (1992). Distinguishing between low dimensional dynamics and randomness in measures time series. Physica D, 58.
• Sahni, R. (2018). Analysis of stock market behavior by applying chaos theory. In 2018 9th international conference on computing, communication and networking technologies (ICCCNT). IEEE.
• Schouten, J. C., Takens, F., & Bleek, C. M. (1994). Estimation of the dimension of a noisy attractor. Physics Review E, 50(3). doi; 10.1103/physreve.50.1851.
• Schwartz, B., & Yousefi, S. (2013). On complex behavior and exchange rate dynamics. Chaos, Solitons and Fractals, 18(3).
• Sprott, J. C. (2003). Chaos and time series analysis. Oxford University Press.
• Stavrinides, S. G., Hanias, M. P., Magafas, L., & Banerjee, S. (2015). Control of economic situations by utilizing an electronic circuit. International Journal of Productivity Management and Assessment Technologies, 3(2). doi: 10.4018/ IJPMAT.2015070101.
• Su, X., Wang, Y., Duan, S., & Ma, J. (2014). Detecting chaos from agricultural product price time series. Entropy, 16(12). doi: 10.3390/e16126415.
• Sugihara, G., & May, R. M.(1990). Nonlinear forecasting as a way of distinguishing chaos from measurement time error in time series. Nature, 344. doi: 10.339 0/e16126415
• Takens, F. (1981). Dynamical systems and turbulence. Lecture Notes in Mathematics, 898.
• Tassis, D. H., Stavridides, S., Hanias, M. P., Theodorou, C., Ghibaudo, G., & Dimitriadis, C. (2017). Chaotic behavior of random telegraph noise in nanoscale UTBB FD SOI MOSFETs. IEEE Electron Devices Letters, 38(4).
• Thalassinos, I. E., Hanias, M. P., Curtis, P. G, Thalassinos, E. Y. (2009). Chaos theory: forecasting the freight rate of an oil tanker. International Journal of Computational Economics and Econometrics, 1(1). doi: 10.1504/IJCEE. 2009.029154.
• Weron, R. (2002). Estimating long - range dependence: finite sample properties and confidence intervals. Physica A, 312. doi: 10.1016/S0378-4371(02)00961-5.
• Xu, Y., Ke, Z., Xie, C., & Zhou, W. (2018). Dynamic evolution analysis of stock price fluctuation and its control. Complexity, 2018. doi: 10.1155/2018/5728090.
• Zaychenko, Y. (2008). The investigations of fuzzy group method of data handling with fuzzy inputs in the problem of forecasting in financial sphere. In Proceedings of the II international conference on inductive modeling. ICIM-2008. Kyiv: IRTC ITS NASU.

Identifiers

DOI

10.24136/eq.2020.012

Biblioteka Nauki

22444422