Time-Series Clustering

Kullback-Leibler cluster entropy to quantify volatility correlation and risk diversity ArXiv ID: 2409.10543 “View on arXiv” Authors: Unknown Abstract The Kullback-Leibler cluster entropy $\mathcal{“D_{C”}}[“P | Q”] $ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (SP&500, NASDAQ, DJIA, DAX, FTSEMIB). The Kullback-Leibler functional $\mathcal{“D_{C”}}[“P | Q”] $ provides complementary perspectives about the stochastic volatility process compared to the Shannon functional $\mathcal{“S_{C”}}[“P”]$. While $\mathcal{“D_{C”}}[“P | Q”] $ is maximum at the short time scales, $\mathcal{“S_{C”}}[“P”]$ is maximum at the large time scales leading to complementary optimization criteria tracing back respectively to the maximum and minimum relative entropy evolution principles. The realized volatility is modelled as a time-dependent fractional stochastic process characterized by power-law decaying distributions with positive correlation ($H>1/2$). As a case study, a multiperiod portfolio built on diversity indexes derived from the Kullback-Leibler entropy measure of the realized volatility. The portfolio is robust and exhibits better performances over the horizon periods. A comparison with the portfolio built either according to the uniform distribution or in the framework of the Markowitz theory is also reported. ...

Towards Financially Inclusive Credit Products Through Financial Time Series Clustering ArXiv ID: 2402.11066 “View on arXiv” Authors: Unknown Abstract Financial inclusion ensures that individuals have access to financial products and services that meet their needs. As a key contributing factor to economic growth and investment opportunity, financial inclusion increases consumer spending and consequently business development. It has been shown that institutions are more profitable when they provide marginalised social groups access to financial services. Customer segmentation based on consumer transaction data is a well-known strategy used to promote financial inclusion. While the required data is available to modern institutions, the challenge remains that segment annotations are usually difficult and/or expensive to obtain. This prevents the usage of time series classification models for customer segmentation based on domain expert knowledge. As a result, clustering is an attractive alternative to partition customers into homogeneous groups based on the spending behaviour encoded within their transaction data. In this paper, we present a solution to one of the key challenges preventing modern financial institutions from providing financially inclusive credit, savings and insurance products: the inability to understand consumer financial behaviour, and hence risk, without the introduction of restrictive conventional credit scoring techniques. We present a novel time series clustering algorithm that allows institutions to understand the financial behaviour of their customers. This enables unique product offerings to be provided based on the needs of the customer, without reliance on restrictive credit practices. ...

Automated regime detection in multidimensional time series data using sliced Wasserstein k-means clustering ArXiv ID: 2310.01285 “View on arXiv” Authors: Unknown Abstract Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to identify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of the Wasserstein k-means clustering algorithm applied to synthetic one-dimensional time series data. We study the dynamics of the algorithm and investigate how varying different hyperparameters impacts the performance of the clustering algorithm for different random initialisations. We compute simple metrics that we find are useful in identifying high-quality clusterings. Then, we extend the technique of Wasserstein k-means clustering to multidimensional time series data by approximating the multidimensional Wasserstein distance as a sliced Wasserstein distance, resulting in a method we call `sliced Wasserstein k-means (sWk-means) clustering’. We apply the sWk-means clustering method to the problem of automated regime detection in multidimensional time series data, using synthetic data to demonstrate the validity of the approach. Finally, we show that the sWk-means method is effective in identifying distinct market regimes in real multidimensional financial time series, using publicly available foreign exchange spot rate data as a case study. We conclude with remarks about some limitations of our approach and potential complementary or alternative approaches. ...

Dynamic Time Warping for Lead-Lag Relationships in Lagged Multi-Factor Models ArXiv ID: 2309.08800 “View on arXiv” Authors: Unknown Abstract In multivariate time series systems, lead-lag relationships reveal dependencies between time series when they are shifted in time relative to each other. Uncovering such relationships is valuable in downstream tasks, such as control, forecasting, and clustering. By understanding the temporal dependencies between different time series, one can better comprehend the complex interactions and patterns within the system. We develop a cluster-driven methodology based on dynamic time warping for robust detection of lead-lag relationships in lagged multi-factor models. We establish connections to the multireference alignment problem for both the homogeneous and heterogeneous settings. Since multivariate time series are ubiquitous in a wide range of domains, we demonstrate that our algorithm is able to robustly detect lead-lag relationships in financial markets, which can be subsequently leveraged in trading strategies with significant economic benefits. ...

Portfolio Selection via Topological Data Analysis ArXiv ID: 2308.07944 “View on arXiv” Authors: Unknown Abstract Portfolio management is an essential part of investment decision-making. However, traditional methods often fail to deliver reasonable performance. This problem stems from the inability of these methods to account for the unique characteristics of multivariate time series data from stock markets. We present a two-stage method for constructing an investment portfolio of common stocks. The method involves the generation of time series representations followed by their subsequent clustering. Our approach utilizes features based on Topological Data Analysis (TDA) for the generation of representations, allowing us to elucidate the topological structure within the data. Experimental results show that our proposed system outperforms other methods. This superior performance is consistent over different time frames, suggesting the viability of TDA as a powerful tool for portfolio selection. ...