Time series analysis is an essential research area for those who are dealing with scientific and engineering problems. The main objective, in general, is to understand the underlying characteristics of selected time series by using the time as well as the frequency domain analysis. Then one can make a prediction for desired system to forecast ahead from the past observations. Time series modeling, frequency domain and some other descriptive statistical data analyses are the primary subjects of this study: indeed, choosing an appropriate model is at the core of any analysis to make a satisfactory prediction. In this study Fourier and wavelet transform methods are used to analyze the complex structure of a financial time series, particularly, S&P500 daily closing prices and return values. Multiresolution analysis is naturally handled by the help of wavelet transforms in order to pinpoint special characteristics of S&P500 data, like periodicity as well as seasonality. Besides, further case study discussions include the modeling of S&P500 process by invoking linear and nonlinear methods with wavelets to address how multiresolution approach improves fitting and forecasting results.
Keywords: Time series analysis, Frequency domain analysis, Wavelets, Multiresolution analysis, Statistical analysis