Complex Systems Methods to describe Financial Time Series

Financial markets are a perfect example of a complex system due to the behaviour of millions of investors who try to gain money each second, evolving as a chaotic environment very difficult to predict. In the last 20 years physicists and economists have tried to explain the price dynamics using tools from Statistical Mechanics, Theory of Turbulence and even Quantum Mechanics, combining concepts from financial world and theoretical physics. In the first part of the thesis we will expound these models both in a mathematical and in a historical point of view, retracing the development of Econophysics. In the second part of thesis we will compare these mathematical models with the aim of describing real historical data very different from each other; from financial indices to single stocks, from commodities to cryptovalues like Bitcoin, also analyzing the trend of Forex. We will also employ ideas from natural selection with Genetic Algorithms to evolve sets of parameters in order to better describe the real world data, solving optimization problems writing code on Python. For each time series we will also discuss the results in order to comprehend the accuracy of the algorithm, matching their outcomes.