Master's Thesis Defense

Statistical self-similarity in time series from financial data
& chaotic dynamical systems

Panpan Zhang

May 1, 2012, at 3:30pm, 125 Manchester Hall

In this paper, I am going to introduce statistical self-similarity for discrete time series. My thesis is divided into three parts: In the first part, I will give a mathematical definition of self-similarity and detect the main properties of self-similar processes. At the end of this part, fractional Brownian motion(fBm) will be used as an example to check these properties.

In the second part, Discrete Wavelet Transform(DWT) and wavelet coefficients will be introduced. The way to construct wavelet coefficients and their natural properties which are especially related to self-similarity will also be presented. Daubechies wavelet family will be proposed as an example, and Haar wavelet from Daubechies family is used for further study.

Finally, I will use wavelet transform methods to determine if certain time series from financial data and chaotic dynamical systems are self-similar processes with stationary increments. The whole process of check will be run in MATLAB.

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