Early Warning Signals of Financial Crises Using Persistent Homology and Critical Slowing Down: Evidence From Different Correlation Tests - Ismail, Mohd Sabri; Md Noorani, Mohd Salmi; Ismail, Munira; Abdul Razak, Fatimah (Frontiers in Applied Mathematics and Statistics, 2022)
In this study, a new market representation from persistence homology is known as the L^1-norm time series is used and applied independently with three critical slowing down indicators (autocorrelation function at lag 1, variance, and mean for power spectrum) to examine two historical financial crises (Dotcom crash and Lehman Brothers bankruptcy) in US market. The captured signal is the rising trend in the indicator time series, which can be determined by the Kendall tau correlation test. Furthermore, we also examine Pearson and Spearman rho correlation tests as potential substitutes for the Kendall tau. After that, we determine a correlation threshold and predict the whole available date. The point of comparison between these correlation tests is to determine which test is significant and consistent in classifying the rising trend. The results of such a comparison will suggest the best test that can classify the observed rising trend and detect early warning signals of impending financial crises. Our outcome shows that the L^1-norm time series is more likely to increase before the two financial crises. Kendall tau, Pearson, and Spearman rho correlation tests consistently indicate a significant rising trend in the mean for power spectrum time series before the two financial crises. Based on the two evaluation scores (the probability of successful anticipation and probability of erroneous anticipation), by using the L^1-norm time series with mean for power spectrum, our result in the whole prediction demonstrated that Spearman rho correlation (46.15% and 53.85%) obtains the best score as compared to Kendall tau (42.31% and 57.69%) and Pearson (40% and 60%). Therefore, by using the Spearman rho correlation test, L^1-norm time series with mean for power spectrum is shown as a better way to detect early warning signals of US financial crises.