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Fractal and Wavelet Market Analysis in Pattern Recognition
Abstract
Fractal geometry can be seen as a universal language by which nature can be explained or at least described and quantified. Financial markets are one of them. Therefore, in this chapter, I set my focus on complex dynamics, an area that was around for about one hundred year ago and continues to inspire much ongoing research. I show that wavelet-based modelling underlies the process that generates financial market data. It is a method that decomposes a time series into several layers of time series, making it possible to analyze how the local variance, or wavelet power, changes both in the frequency and time domain. Then I calculate the local Holder exponent which is applied to estimate stable and unstable fixed point, or regularity and singularity and based on them, one can adapt its buy-sell strategy timely. The model successfully detects the hoarding effect, noise traders, and the pattern of the short-run price fluctuation. An algorithmic construction of the model is developed in Wolfram Mathematica 9 and MatLab R2016b.
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