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Wavelet theory and its applications in economics and finance

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posted on 29.05.2015, 08:47 by Wenlong Lai
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 phenomena. 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 useful 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. The result shows that wavelets are a good alternative filter for extracting business cycles or trend based on multiresolution wavelet analysis. The fourth chapter distinguishes contagion and interdependence. To achieve this purpose, we define contagion as a significant increase in short-run market commovement after a shock to one market. Following the application of wavelets to 27 global representative markets’ daily stock-return data series from 1996.1 to 1997.12, a multivariate GARCH model and a Granger-causality methodology are used on the results of wavelets to generate short-run pair-wise contemporaneous correlations and lead-lag relationships, respectively, both of which are involved in short-run relationships. The empirical evidence reveals no significant increase in interdependence during the financial crisis; contagion is just an illusion of interdependence. In addition, the evidence explains the phenomenon in which major negative events in global markets began to occur one month after the outbreak of the crisis. The view that contagion is regional is not supported. The fifth chapter studies how macroeconomic news announcements affect the U.S. stock market and how market participants’ responses to announcements vary over the business cycle. The arrival of scheduled macroeconomic announcements in the U.S. stock market leads to a two-stage adjustment process for prices and trading transactions. In a short first stage, the release of a news announcement induces a sharp and nearly instantaneous price change along with a rise in trading transactions. In a prolonged second stage, it causes significant and persistent increases in price volatility and trading transactions within about an hour. After allowing for different stages of the business cycle, we demonstrate that the release of a news announcement induces larger immediate price changes per interval in the expansion period, but more immediate price changes per interval in the contraction period, from the old equilibrium to the approximate new equilibrium. It costs smaller subsequent adjustments of stock prices along with a lower number of trading transactions across a shorter time in the contraction period, when the information contained in the news announcement is incorporated fully in stock prices. We use a static analysis to investigate the immediate effects of news announcements, as measured by the surprise in the news, on prices, and adopt a wavelet analysis to examine their eventual effects on prices. The evidence shows that only 6 out of 17 announcements have a significant immediate impact, but all announcements have an eventual impact over different time periods. The combination of the results of both analyses gives us the time-profile of each news announcement’s impact on stock prices, and shows that the impact is significant within about an hour, but is exhausted after a day.



Hall, Stephen; Mise, Emi

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Department of Economics

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University of Leicester

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