Multi-Scaling Analysis of the S&P500 under Different Regimes in Wavelet Domain

Abstract

In this article, the authors investigate the multi-scale structure of the S&P500 minute-by-minute time series. The authors attempt to find the answer to the following question: Are upward and downward regimes in the S&P500 time series exhibit different long-range power-law correlations? To answer this question, the authors apply the discrete wavelet transform (DWT) to the original time series for de-noising purpose. Then, the authors apply the generalized Hurst exponent (GHE) to the de-noised data to characterize the multi-scaling complexity of the signal (time series) under each regime and using different q-order moments. The authors found that S&P500 intra-day time series show long-range power-law correlations. In addition, this behavior varies depending on the stock market regime. This finding should be taken into account in active investment management.