Clustering and classification of time series using topological data analysis with applications to finance

Majumdar, Sourav; Laha, Arnab Kumar

doi:10.1016/j.eswa.2020.113868

Cited by 55 publications

(11 citation statements)

References 24 publications

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“…Baitinger and Flegel [38] also demonstrated that investment strategies relying on a PH-based turbulence detection outperform investment strategies based on other popular turbulence indices. In clustering and classification of financial time series, Majumdar and Laha [39] showed that PH outperforms other methods in this task.…”

Section: Literature Reviewmentioning

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: Literature Reviewmentioning

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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“…WDTW (Weighted Dynamic Time Warping) is a weighted version of DTW [21,22]. There are many researches which used DTW as the distance measurement [23][24][25]. In HRP that we used, the distance measurement based the correlation coefficient is used.…”

Section: Related Workmentioning

confidence: 99%

Time-series Clustering of Global Automakers Stock Prices

Shirota

Murakami

2021

Information Engineering Express

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In the paper, we describe the stock price data analysis using the hierarchical clustering method named Hierarchical Risk Parity. In the financial engineering, clustering is important for the portfolio development. The data we used are the top 100 global industries' stock prices from 2018 to 2019. The industry field is automobile manufacturing. The countries of the industries are Japan, US and Germany. We analyzed sequentially a bi-month data for the two years. Then we found that when the stock price drastically decreased, there could clearly appear country-based clusters.In the global turmoil period by the US-China trade friction in 2018, we could identify that the Japan cluster and the US cluster appeared with clear boundaries. To verify the hypothesis, we traced the time series changes of the clusters through the two years. As a result, we proved the hypothesis was correct, as far as the period was what we used. In addition, we visualized the resultant country-based clusters of the largest damage period, as a stock price fluctuation plot and the Markowitz's risk-return plot, to see the difference of the three countries' trend.

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“…Examples of these hybrid TDA+ML methods are: TDA+SVM for image classification [5], and TDA+k-NN, TDA+CNN and TDA+SVM for time series classification [6,7,8]. Self-Organized Maps were combined with PH tools to cluster and classify time series in the financial domain [9].…”

Section: Related Workmentioning

confidence: 99%

A Topological Data Analysis Based Classifier

Kindelan¹,

Frías²,

Cerda³

et al. 2021

Preprint

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Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes an algorithm that applies TDA directly to multi-class classification problems, without any further ML stage, showing advantages for imbalanced datasets. The proposed algorithm builds a filtered simplicial complex on the dataset. Persistent Homology (PH) is applied to guide the selection of a sub-complex where unlabeled points obtain the label with the majority of votes from labeled neighboring points. We select 8 datasets with different dimensions, degrees of class overlap and imbalanced samples per class. On average, the proposed TDABC method was better than KNN and weighted-KNN. It behaves competitively with Local SVM and Random Forest baseline classifiers in balanced datasets, and it outperforms all baseline methods classifying entangled and minority classes. IntroductionClassification is a Machine Learning (ML) task that employs known data labels to label data with an unknown category. Classification faces challenges such as high dimensionality, noise, and imbalanced data distributions. TDA has been 1 This paper is under consideration at Pattern Recognition Letters Journal.

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Clustering and classification of time series using topological data analysis with applications to finance

Cited by 55 publications

References 24 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

Time-series Clustering of Global Automakers Stock Prices

A Topological Data Analysis Based Classifier

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