Beautiful Fractals as a Crystal Ball for Financial Markets? - Investment Decision Support System Based on Image Recognition Using Artificial Intelligence

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The work by Mandelbrot develops a basic understanding of fractals and the artwork of Jackson Pollok to reveal the beauty fractal geometry. The pattern of recurring structures is also reflected in share prices. Mandelbrot himself speaks of the fractal heart of the financial markets. Previous research has shown the potential of image recognition. This paper presents the possibility of using the structure recognition capability of modern machine learning methods to make forecasts based on fractal course information. We generate training data from real and simulated data. These data are represented in images to train a special artificial neural network. Subsequently, real data are presented to the network for use in predicting. The results show that the forecast of time series based on stock price illustration, compared to a benchmark, delivers promising results. This paper makes two essential contributions to research. From a theoretical point of view, fractal geometry shows that it can serve as a means of legitimation for technical analysis. From a practical point of view, highly developed methods from the field of machine learning are able to recognize patterns in data through appropriate data transformation, and that models such as random walk have an informational content that can be used to train machine learning models.

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L. A. Abad and K. Khalifa (2015). What are stylized facts? Journal of Economic Methodology 22

S. M. W. Alizadeh Brandt, and F. X. Diebold (2002). Range-based estimation of stochastic volatility models. The Journal of Finance 57

G. S. Atsalakis, E. M. Dimitrakakis, and C. D. Zopounidis (2011). Elliott wave theory and neuro-fuzzy systems, in stock market prediction: The wasp system. Expert Systems with Applications 38

E. Baitinger (2014). Neue Ansätze für das quantitative Asset Management (Portfoliomanagement). Bad Soden/Ts.: Uhlenbruch Verlag.

J. Y. Campbell and S. B. Thompson (2008). Predicting excess stock returns out of sample: Can anything beat the historical average? The Review of Financial Studies 21(4), 1509– 1531.

H. Chen, R. H. L. Chiang and V. C. Storey (2012). Business intelligence and analytics: From big data to big impact. MIS Quarterly 36

T. E. Clark and M. W. McCracken (2010). Improving forecast accuracy by combining recursive and rolling forecasts. International Economic Review 50

R. Cont (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance 1

D. Delen, H. Zaim, C. Kuzey, and S. Zaim (2013). A comparative analysis of machine learning systems for measuring the impact of knowledge management practices. Decision Support Systems 54

G. Dewandaru, R. Masih, O. I. Bacha, and A. M. M. Masih (2015). Developing trading strategies based on fractal finance: An application of mf-dfa in the context of islamic equities. Physica A 438.

V. Dhar, T. Geva, G. Oestreicher-Singer and A. Sundararajan (2014). Prediction in economic networks. Information Systems Research 25

S. Essendorfer, I. Diaz-Rainey and M. Falta (2015). Creative destruction in wall street’s technological arms race: Evidence from patent data. Technological Forecasting and Social Change 99.

A. Esteva, B. Kuprel, R. A. Novoa, J. Ko, S. M. Swetter, H. M. Blau, and S. Thrun (2017). Dermatologist-level classification of skin cancer with deep neural networks. Nature 542

E. F. Fama (1965). The behavior of stock-market prices. The Journal of Business 38

E. F. Fama (1970). Efficient capital markets - a review of theoriy and empirical work. Journal of Finance 25

E. F. Fama (1991). Efficient capital markets ii. The Journal of Finance 46

J.-P. Fouque, G. Papanicolaou, R. Sircar, and K. Solna (2003). Short time-scale in s&p500 volatility. Journal of Computational Finance 6

S. J. Grossmann and J. E. Stiglitz (1980). On the impossibility of informationally efficient markets. The American Economic Review 70

M. I. Jordan and T. M. Mitchell (2015). Machine learning - trends, perspectives, and prospects. Science 349

M. A. Kashefia (2016). Effect of salvage market on strategic technology choice and capacity investment decision of firm under demand uncertainty. Journal of Business Economics and Management 17

H. Kim and S. T. Han (2016). The enhanced classification for the stock index prediction. Procedia Computer Science 91

S. Lahmiri (2016). Intraday stock price forecasting based on variational mode decomposition. Journal of Computational Science 12

S-J. Lee, T. Chen, L. Yu, and C.-H. Lai (2018). Image classification based on the boost convolutional neural network. IEEE Access 6

A. W. Lo, A. W. (2008). Efficient markets hypothesis. In S. N. Durlauf and L. E. Blume (Eds.), The new Palgrave Dictionary of Economics, Band 2, Basingstoke, pp 782–794. Palgrave Macmillan.

B. G. Malkiel (2003). The efficient markt hypothesis and its critics. The Journal of Economic Perspectives 17(1

B. Mandelbrot (1963). The variation of certain speculative prices. The Journal of Business 36

B. Mandelbrot, W. Freeman, and Company (1983). The Fractal Geometry of Nature. Einaudi paperbacks. Macmillan.

B. Mandelbrot (2004). Behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Great Britain: Profile Books.

E. Mjolsness and D. DeCoste (2001). Machine learning for science: State of the art and future prospects. Science 293(5537), 2051–2055.

K. Muhammad, J. Ahmad, I. Mehmood, S. Rho, and S. W. Baik (2018). Convolutional neural networks based fire detection in surveillance videos. IEEE Access 6

R. T. F. Nazárioa, J. L. e Silvab, V. A. Sobreiroa, and H. Kimura (2017). A literature review of technical analysis on stock markets. The Quarterly Review of Economics and Finance 66

C. J. Neely, P. A. Weller, and J. M. Ulrich (2009). The adaptive markets hypothesis: Evidence from the foreign exchance market. Journal of Finance and Quantitative Analysis 44

A. Oztekin, R. Kizilaslanb, S. Freundc, and A. Iserid (2016). A data analytic approach to forecasting daily stock returns in an emerging market. European Journal of Operational Research 253(3), 697–710.

C. Park and S. H. Irwin (2007). What do we know about the profitability of technical analysis. Journal of Economic Survey 9

M. H. Pesaran and A. Timmermann (1995). Predictability of stock returns: Robustness and economic significance. The Journal of Finance 50

T. Poddig, A. Varmaz, and C. Fieberg (2015). Computational Finance. Bad Soden: Uhlenbruch.

F. Rosenblatt (1958). The perceptron. a probabilistic model for information storage and organization in the brain. Psychological Reviews 65

A. E. Tsekrekosa and A. N. Yannacopoulos (2016). Optimal switching decisions under stochastic volatility with fast mean reversion. European Journal of Operational Research 251

L.-Y. Wei, L.-Y. Chen, and T.-H. Ho (2011). A hybrid model based on adaptive-networkbased fuzzy inference system to forecast taiwan stock market. Expert Systems with Applications 38

I. Welch and A. Goyal (2008). A comprehensive look at the empirical performance of equity premium prediction. Review of Financial Studies 21

A. K. White and S. K. Safi (2016). The efficiency of artificial neural networks for forecasting in the presence of autocorrelated disturbances. International Journal of Statistics and Probability 5

R. Yamamoto (2012). Intraday technical analysis of individual stocks on the tokyo stock exchange. Journal of Banking & Finance 36

L. B. Yann Yoshua, and H. Geoffrey (2015, 05). Deep learning. Nature 521