Early Warning Signals of Financial Crises Using Persistent Homology and Critical Slowing Down: Evidence From Different Correlation Tests

Abstract

In this study, a new market representation from persistence homology, known as the L1-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 (MPS)] to examine two historical financial crises (Dotcom crash and Lehman Brothers bankruptcy) in the US market. The captured signal is the rising trend in the indicator time series, which can be determined by Kendall's tau correlation test. Furthermore, we examined Pearson's and Spearman's rho correlation tests as potential substitutes for Kendall's tau correlation. After that, we determined a correlation threshold and predicted 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 (EWSs) of impending financial crises. Our outcome shows that the L1-norm time series is more likely to increase before the two financial crises. Kendall's tau, Pearson's, and Spearman's rho correlation tests consistently indicate a significant rising trend in the MPS 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 L1-norm time series with MPS, our result in the whole prediction demonstrated that Spearman's rho correlation (46.15 and 53.85%) obtains the best score as compared to Kendall's tau (42.31 and 57.69%) and Pearson's (40 and 60%) correlations. Therefore, by using Spearman's rho correlation test, L1-norm time series with MPS is shown to be a better way to detect EWSs of US financial crises.

Multifractal Early Warning Signals about Sudden Changes in the Stock Exchange States

“…e log-cumulant c 3 , which characterizes the asymmetry of the spectrum, decreases not only in the vicinity of the time of the critical transition, but also in some noncritical time interval (see Figure 3). In our opinion, such behavior of parameter c 3 contradicts the existence of one of the precursors of the critical transition, known as the critical slowing down (e.g., see papers [19,21,24,48]). Perhaps the incorrect estimation of the asymmetry parameter is one of the drawbacks of the expansion (8) or, moreover, a drawback of the WL method.…”

“…ere are many studies that substantiate the concept of the similarity of the mechanisms of behavior of economic systems, stock markets, and financial time series with the behavior of the model variables (e.g., see papers [11][12][13][14][15][16][17]), as well as studies on the search for early warning signals (EWS) for critical transitions in financial and stock markets (e.g., see papers [18][19][20][21][22][23][24]). e determination of the time interval preceding the occurrence of a critical transition in the system not only has important theoretical value, but also has important applied value.…”

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

“…The most notable features of the critical slowing down are a slower rate of recovery from perturbations ( Wissel, 1984 ), as well as a persistent increase in variance, autocorrelation (AC), and cross-correlation among different elements of the system (also called spatial correlation in ecology; Scheffer et al, 2009 ). Early warning signals (EWSs) have been developed to capture these dynamic changes, usually reflecting B-tipping scenarios indicating bifurcation of the system ( Ashwin, 1999 ; Ashwin et al, 2012 ; Perryman and Wieczorek, 2014 ), and have been widely used to study critical transitions in diverse systems, including ecosystems ( Wouters et al, 2015 ; Pedersen et al, 2017 ; Xu et al, 2023 ), financial markets ( Diks et al, 2019 ; Tu et al, 2020 ; Ismail et al, 2022 ), and climate systems ( Dakos et al, 2008 ; Dylewsky et al, 2023 ). Application to clinical contexts is also gaining a growing interest, with applications in tumor detection ( Xu et al, 2022 ; Zhong et al, 2022 ; Huang et al, 2023 ), detection of emerging infectious diseases ( Chen P. et al, 2019 ; Brett et al, 2020 ; Li et al, 2022 ; Proverbio et al, 2022 ), mental disorders ( van de Leemput et al, 2014 ; Bayani et al, 2017 ; Bos et al, 2022 ), sepsis ( Tambuyzer et al, 2014 ; Almeida and Nabney, 2016 ; Ghalati et al, 2019 ), environmental health ( Wang et al, 2018 ), alcohol use disorders ( Foo et al, 2017 ), epileptic seizures ( Maturana et al, 2020 ; Karasmanoglou et al, 2023 ), intestinal health ( Lahti et al, 2014 ), and chronic diseases ( Venegas et al, 2005 ; Li et al, 2014 ; Liu et al, 2021 ; Cohen et al, 2022 ).…”