# Fractal Market Analysis: Applying Chaos Theory to Investment and Economics

For the interpretation of the powers, the hotter the color the higher the power variance for the particular scale and time. For all the analyzed indices, we observe at least two common features.

## Fractal Market Analysis - Applying Chaos Theory to Investment and Economics

Firstly, most of the time, there is no scale-characteristic power which can be distinguished from a pure noise so that no investment horizon dominates. This is true mainly for the period between and the first half of Note that this period is connected to a very stable growth after the long-lasting decline following the DotCom bubble. The period is thus connected to a uniformly distributed activity at separate investment horizons or at least, there is no dominating horizon , which is well in hand with FMH. The whole period between and is characterized by low total variance at all frequencies and the colors of the power spectra remain cold.

Secondly, the turning point between the post-DotCom decreases and the upcoming upward trends is connected with an increased power at high frequencies. This is true for the European and the US indices, the Asian indices do not experience such behavior. Note that for all the indices, the frequent dips in the market are connected with a short-term increased power at the highest frequencies, which shows that these short-lived corrections of the markets are mainly dominated by the short-term investors.

Turning now to the current Global Financial Crisis, recall that the biggest movements occurred after the bankruptcy of Lehman Brothers on In Figs. Even though the variance increases at more scales, the dominance of the very low scales is apparent very hot colors even bordering with black for October and November and is again in hand with the predictions of FMH — the turbulent times are connected with the dominance of specific investment horizons so that the efficient market clearing is not possible.

The situation calmed around May where the total variance decreased markedly. Apart from the most severe periods of the GFC, we also observe a changing structure of the active participants at the European stock markets during the second half of Note that during this period, the Eurozone and the EU in general underwent probably the most severe financial and economic turmoil of its existence.

## What is fractal market hypothesis (FMH)? definition and meaning - apromsili.tk

The situation is known by various names as the symptoms were many — the EU debt crisis, the PIIGS for Portugal, Ireland, Italy, Greece and Spain as the most troublesome countries in that times crisis, the Greek crisis and several more. Again the dominance of the shortest investment horizons is evident.

In summary, we have analyzed whether the prediction of the fractal markets hypothesis about the dominance of specific investment horizons during the turbulent times holds. To do so, we have utilized the continuous wavelet transform analysis and the wavelet power spectra which give crucial information about the variance distribution across scales and its evolution in time. We have showed that the most turbulent times of the current Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is well in hand with the fractal markets hypothesis.

Misbalance between short and long investment horizons thus created a tension between supply and demand, leading to decreased liquidity which has been repeatedly shown to lead to occurrence of extreme events 18 , 19 , 20 , Fractal markets hypothesis is thus able to describe events of the Global Financial Crisis in a more satisfying way than the mainstream efficient markets hypothesis.

Any time series can be reconstructed back from its wavelet transform if the admissibility condition. Wavelet has a zero mean so that and is usually normalized so that. Importantly, the continuous wavelet transform decomposes the series into frequencies and can then reconstruct the original series so that there is no information loss, and energy of the examined series is maintained as well, i. There is a large number of specific wavelets 26 out of which we choose the Morlet wavelet standardly used in the economic and financial applications 14 , 27 , 28 , National Center for Biotechnology Information , U.

Sci Rep. Published online Oct 4. Ladislav Kristoufek a, 1, 2. Author information Article notes Copyright and License information Disclaimer. Received Aug 5; Accepted Sep All rights reserved. This article has been cited by other articles in PMC.

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Abstract We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. Results To show whether the predictions of the fractal markets hypothesis hold, we analyze six developed liquid world indices. Open in a separate window. Figure 1. Figure 2.

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Wavelet power spectrum for FTSE. Figure 3. Wavelet power spectrum for CAC. Figure 4. Wavelet power spectrum for DAX. Figure 5. Wavelet power spectrum for HSI. Figure 6. Discussion In summary, we have analyzed whether the prediction of the fractal markets hypothesis about the dominance of specific investment horizons during the turbulent times holds.

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