Financial nonlinear and financial time series

The theme of the project: Analysis the volatility process of the time series of stock indexes and detect chaotic type of patterns around the financial crises and bubbles in order to do some prediction.

Volatility models of the financial time series:

We are going to apply the multi-fractals and power laws to give the description of the volatility of the stock indexes. Hurst exponent of the time series would be calculated in order to capture the persistence of the volatility of the time series. And standard programs will be used to identify the existences of the power laws in the indexes of stock market, especially the US stock market.

Patterns, phase states, chaos and embedding dimensions:

This part is the more exciting section of the project, in it, we are going to do some prediction of the crises and bubbles by using the technical tools of embedding dimensions and the phase states and chaotic approach. Embedding dimension can used to unfold the phase states, and the later can be applied to detect chaotic behavior in the time series.