Deniz Kenan Kılıç, M.Sc.
Department of Financial Mathematics
June 2015
Supervisor: Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)
Abstract
Time series analysis is an essential research area for almost all people who are dealing with scientific and engineering problems. Main aim is to understand the underlying characteristics of the time series by using time as well as frequency domain analyses. Then one can make a prediction for the desired system to forecast observations ahead. Time series modeling, frequency domain analysis and some descriptive statistical analysis are main subjects of this thesis. Choosing an appropriate model is the main focus of all analysis in order to make a good prediction. In this thesis financial time series are focused, particularly S&P500 daily closing prices and it's return values are handled. Fourier transform and wavelet transform are creatively at the center of the frequency domain analysis. Knowing the fact that financial time series are complex data sets to sufficiently predict the future, multiresolution analysis is handled in this thesis using the wavelet transforms to figure out specialties of S&P500 data. Also, apparently, models that are appropriate for the financial time series are discussed in the application part.
Keywords: Time Series Analysis, Wavelets, Multiresolution Analysis, Statistical Analysis