A Study of Financial Crises Similarities in a time-scale domain via Earth Mover’s Distance
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Recently, there has been growing interest in the application of frequential and time-scale analysis to financial time series. These techniques are mainly oriented to different fields such as volatility analysis, forecasting, detection of cycles, co-movements and so on. One of the most powerful tools in this sense is the wavelet transform because of its ability in analyzing dynamics that change over time. Several approaches have been then proposed for forecasting, denoising, and identifying correlations and seasonal cycles. They estimate classical statistical quantities over empirically selected sets of scales. However, they usually work exploring the same sets of scales while a comparison of different events like financial crises at different sets of scales has not yet been thoroughly explored. One may wonder, for example, whether a weekly trend in one crisis could be similar to a daily trend in another. This study proposes a wavelet-based analysis using scalogram inspection with Generalized Heisenberg Boxes (GHB) and the Earth Mover’s Distance (EMD), which allows comparison between similar structures even if they differ in size. Only local maxima and their energy are considered to reduce computational effort.The proposed method has been tested on the S&P500 index, revealing interesting similarities between different crises. Compared to previous approaches, the use of EMD provides greater robustness and generalization, paving the way for new analyses of financial time series.
