Signal analysis of global financial crises using Fourier series

Abstract

In this paper, we analyze the annual signals generated by the US stock market, using the returns of US monthly stock-indices. To this end, we transform the signals into a Fourier series and deduce financial information from the amplitude and phase of each component of the Fourier series. We show that, as global financial crises approach, low frequency components increase more sharply than high frequency components. We also show that they react selectively to specific financial crises, under four major modes, and generate sharp peaks, showing their own characteristics of monthly propagation. By comparing these results with the same type of analyses for the UK and German stock markets, we demonstrate that this method works well for detecting global financial crises. Further, we apply this method to recent US stock-indices, and find that remarkable signals are being generated, suggesting that the current status is unstable. In other words, a financial crisis may be approaching. (C) 2019 Elsevier B.V. All rights reserved.