The adaptive Fourier decomposition for financial time series

Abstract

This paper explores the application of the adaptive Fourier decomposition (AFD) to a deconstruction of financial time series. After the decomposition of the time series into mono-components through AFD, we reconstruct the mono-components to obtain the series’ trend and the detailed components. AFD is compared with the Empirical Mode Decomposition (EMD) and Fourier decomposition method (FDM), which could decompose time series into trends and detailed components as well. The results based on the data from stock, commodity, exchange rate, and carbon markets show that, compared to EMD and FDM, the trends extracted by AFD are more sensitive to the peaks so that they can generally track the tendencies of the financial time series better with fewer energy differences. Besides, the detailed components of AFD better reflect the structural breaks of the original time series.