Wavelet Theory and Its Applications in Economics and Finance

Wavelets orthogonally decompose data into different frequency components, and the temporal and frequency information of the data could be studied simultaneously. This analysis belongs within local nature analysis. Wavelets are therefore useful for managing time-varying characteristics found in most real-world time series and are an ideal tool for studying non-stationary or transient time series while avoiding the assumption of stationarity. Given the promising properties of wavelets, this thesis thoroughly discusses wavelet theory and adds three new applications of wavelets in economic and financial fields, providing new insights into three interesting phenom-ena. The second chapter introduces wavelet theory in detail and presents a thorough survey of the economic and financial applications of wavelets. In the third chapter, wavelets are applied in time series to extract business cycles or trend. They are use-ful for capturing the changing volatility of business cycles. The extracted business cycles and trend are linearly independent. We provide detailed comparisons with four alternative filters, including two of each detrending filters and bandpass filters