Time-resolved topological data analysis of market instabilities

Katz, Yuri A.; Biem, Alain

doi:10.1016/j.physa.2021.125816

Cited by 11 publications

(2 citation statements)

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“…Furthermore, the daily sliding window of length 50 approach was applied to segment the X to obtain PCDs. For financial data analysis, it had been demonstrated that a length of 50 was enough to extract topological information through PH as reported in the previous literature reviews [3,25,26,35]. Consequently, each respective PCD from X at the date t also can be illustrated in matrix form as follows:…”

Section: Persistent Homologymentioning

confidence: 99%

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

Ismail

Noorani²,

Ismail³

et al. 2022

Front. Appl. Math. Stat.

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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.

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Section: Persistent Homologymentioning

confidence: 99%

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

Ismail

Noorani²,

Ismail³

et al. 2022

Front. Appl. Math. Stat.

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“…Initial potential for financial market dynamics of the type described by Hsieh (1991) comes from the applications in the detection of phase transitions and system instability (Stolz et al, 2017;Smith et al, 2021). Promising advancements on correlation and volatility show how each alter the topology of the time series, but that neither correlation or volatility alone can explain persistence norms (Aromi et al, 2021;Leaverton et al, 2020;Katz and Biem, 2021). Focus in this literature has been on the strength of the volatility-norm relationship.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty, volatility and the persistence norms of financial time series

Rudkin¹,

Qiu²,

Dłotko³

2021

Preprint

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Norms of Persistent Homology introduced in topological data analysis are seen as indicators of system instability, analogous to the changing predictability that is captured in financial market uncertainty indexes. This paper demonstrates norms from the financial markets are significant in explaining financial uncertainty, whilst macroeconomic uncertainty is only explainable by market volatility. Meanwhile, volatility is insignificant in the determination of norms when uncertainty enters the regression. Persistence norms therefore have potential as a further tool in asset pricing, and also as a means of capturing signals from financial time series beyond volatility.

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