The adaptive Fourier decomposition for financial time series

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.

Automated summary

This paper explores the application of adaptive Fourier decomposition (AFD) in deconstructing financial time series. After decomposing the series into mono-components using AFD, we reconstruct them to obtain the trend and detailed components. Compared to the Empirical Mode Decomposition (EMD) and Fourier decomposition method (FDM), AFD's extracted trends are more sensitive to peaks and can better track the tendencies of financial time series with fewer energy differences. Additionally, AFD's detailed components better reflect structural breaks in the original time series.