Early warning signals of financial crises using persistent homology

Ismail, Mohd Sabri; Noorani, Mohd Salmi Md; Ismail, Munira; Razak, Fatimah Abdul; Alias, Mohd Almie

doi:10.1016/j.physa.2021.126459

Cited by 18 publications

(10 citation statements)

References 34 publications

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Section: Literature Reviewmentioning

confidence: 99%

“…After that, Ismail et al [26] expanded the study of Gidea and Katz [25] by using PH and CSD indicators to examine financial crises in the US, Singapore, and Malaysia markets. Aspects of the method's robustness and prediction performance have been rigorously evaluated in Ismail et al [26]. Meanwhile, Aromi et al [27] substantiated that PH reflects changes in the underlying multivariate distribution and strong covariance could nullify the persistence of homologies.…”

Section: Literature Reviewmentioning

confidence: 99%

“…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%

“…Consequently, the L 1 -normtime series Y= λ 1,t |t = 50, • • • , 1000 was segmented by using the daily sliding window of the length 500 to obtain sequences of 500 L 1 -norm values. The length 500 was selected based on the literature mentioned in Guttal et al [21], Diks et al [23], and Ismail et al [ 26], which uses half of the length of the pre-crisis dataset. Each sequence of 500 L 1 -norm values at the date t can be denoted as below:…”

Section: Critical Slowing Down Indicatorsmentioning

confidence: 99%

“…In addition, the length of 250 was chosen as half data of the previous sliding window with length of 500. This length was considered sufficient to capture rising trend in the indicators as shown in Guttal et al [21] and Ismail et al [26]. Therefore, three tests based on Kendall's tau, Pearson's, and Spearman's rho correlations from each sequence containing 250 indicator values were computed.…”

Section: Correlation Testsmentioning

confidence: 99%

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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: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Persistent Homologymentioning

confidence: 99%

Section: Critical Slowing Down Indicatorsmentioning

confidence: 99%

Section: Correlation Testsmentioning

confidence: 99%

See 3 more Smart Citations

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.

Self Cite

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Topological Data Analysis to Characterize Fluctuations in the Latin American Integrated Market

Domínguez Monterroza,

Mateos Caballero,

Jiménez-Martín

2023

Communications in Computer and Information Science

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Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs

Chaplin,

Harrington,

Tillmann

2024

Found Comput Math

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Weighted digraphs are used to model a variety of natural systems and can exhibit interesting structure across a range of scales. In order to understand and compare these systems, we require stable, interpretable, multiscale descriptors. To this end, we propose grounded persistent path homology (GrPPH)—a new, functorial, topological descriptor that describes the structure of an edge-weighted digraph via a persistence barcode. We show there is a choice of circuit basis for the graph which yields geometrically interpretable representatives for the features in the barcode. Moreover, we show the barcode is stable, in bottleneck distance, to both numerical and structural perturbations.

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Early warning signals of financial crises using persistent homology

Cited by 18 publications

References 34 publications

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

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

Topological Data Analysis to Characterize Fluctuations in the Latin American Integrated Market

Grounded Persistent Path Homology: A Stable, Topological Descriptor for Weighted Digraphs

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