Volatility Clustering

Visibility-Graph Asymmetry as a Structural Indicator of Volatility Clustering ArXiv ID: 2512.02352 “View on arXiv” Authors: Michał Sikorski Abstract Volatility clustering is one of the most robust stylized facts of financial markets, yet it is typically detected using moment-based diagnostics or parametric models such as GARCH. This paper shows that clustered volatility also leaves a clear imprint on the time-reversal symmetry of horizontal visibility graphs (HVGs) constructed on absolute returns in physical time. For each time point, we compute the maximal forward and backward visibility distances, $L^{"+"}(t)$ and $L^{"-"}(t)$, and use their empirical distributions to build a visibility-asymmetry fingerprint comprising the Kolmogorov–Smirnov distance, variance difference, entropy difference, and a ratio of extreme visibility spans. In a Monte Carlo study, these HVG asymmetry features sharply separate volatility-clustered GARCH(1,1) dynamics from i.i.d.\ Gaussian noise and from randomly shuffled GARCH series that preserve the marginal distribution but destroy temporal dependence; a simple linear classifier based on the fingerprint achieves about 90% in-sample accuracy. Applying the method to daily S&P500 data reveals a pronounced forward–backward imbalance, including a variance difference $Δ\mathrm{“Var”}$ that exceeds the simulated GARCH values by two orders of magnitude and vanishes after shuffling. Overall, the visibility-graph asymmetry fingerprint emerges as a simple, model-free, and geometrically interpretable indicator of volatility clustering and time irreversibility in financial time series. ...

Long-Range Dependence in Financial Markets: Empirical Evidence and Generative Modeling Challenges ArXiv ID: 2509.19663 “View on arXiv” Authors: Yifan He, Svetlozar Rachev Abstract This study presents a comprehensive empirical investigation of the presence of long-range dependence (LRD) in the dynamics of major U.S. stock market indexes–S&P 500, Dow Jones, and Nasdaq–at daily, weekly, and monthly frequencies. We employ three distinct methods: the classical rescaled range (R/S) analysis, the more robust detrended fluctuation analysis (DFA), and a sophisticated ARFIMA–FIGARCH model with Student’s $t$-distributed innovations. Our results confirm the presence of LRD, primarily driven by long memory in volatility rather than in the mean returns. Building on these findings, we explore the capability of a modern deep learning approach, Quant generative adversarial networks (GANs), to learn and replicate the LRD observed in the empirical data. While Quant GANs effectively capture heavy-tailed distributions and some aspects of volatility clustering, they suffer from significant limitations in reproducing the LRD, particularly at higher frequencies. This work highlights the challenges and opportunities in using data-driven models for generating realistic financial time series that preserve complex temporal dependencies. ...

Chaotic Bayesian Inference: Strange Attractors as Risk Models for Black Swan Events ArXiv ID: 2509.08183 “View on arXiv” Authors: Crystal Rust Abstract We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches: Model A, which emphasizes geometric stability, and Model B, which highlights rare bursts using Fibonacci diagnostics. Together, they provide a dual perspective for systemic risk analysis, linking Black Swan theory to practical tools for stress testing and volatility monitoring. ...

A Framework for Predictive Directional Trading Based on Volatility and Causal Inference ArXiv ID: 2507.09347 “View on arXiv” Authors: Ivan Letteri Abstract Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning models to enhance the identification and exploitation of predictive relationships between equities. Methods: We employed a Gaussian Mixture Model (GMM) to cluster nine prominent stocks based on their mid-range historical volatility profiles over a three-year period. From the resulting clusters, we constructed a multi-stage causal inference pipeline, incorporating the Granger Causality Test (GCT), a customised Peter-Clark Momentary Conditional Independence (PCMCI) test, and Effective Transfer Entropy (ETE) to identify robust, predictive linkages. Subsequently, Dynamic Time Warping (DTW) and a K-Nearest Neighbours (KNN) classifier were utilised to determine the optimal time lag for trade execution. The resulting strategy was rigorously backtested. Results: The proposed volatility-based trading strategy, tested from 8 June 2023 to 12 August 2023, demonstrated substantial efficacy. The portfolio yielded a total return of 15.38%, significantly outperforming the 10.39% return of a comparative Buy-and-Hold strategy. Key performance metrics, including a Sharpe Ratio up to 2.17 and a win rate up to 100% for certain pairs, confirmed the strategy’s viability. Conclusion: This research contributes a systematic and robust methodology for identifying profitable trading opportunities derived from volatility-based causal relationships. The findings have significant implications for both academic research in financial modelling and the practical application of algorithmic trading, offering a structured approach to developing resilient, data-driven strategies. ...

Dynamic allocation: extremes, tail dependence, and regime Shifts ArXiv ID: 2506.12587 “View on arXiv” Authors: Yin Luo, Sheng Wang, Javed Jussa Abstract By capturing outliers, volatility clustering, and tail dependence in the asset return distribution, we build a sophisticated model to predict the downside risk of the global financial market. We further develop a dynamic regime switching model that can forecast real-time risk regime of the market. Our GARCH-DCC-Copula risk model can significantly improve both risk- and alpha-based global tactical asset allocation strategies. Our risk regime has strong predictive power of quantitative equity factor performance, which can help equity investors to build better factor models and asset allocation managers to construct more efficient risk premia portfolios. ...

Scaling and shape of financial returns distributions modeled as conditionally independent random variables ArXiv ID: 2504.20488 “View on arXiv” Authors: Hernán Larralde, Roberto Mota Navarro Abstract We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S&P 500 index, Apple and Paramount stocks; and Bitcoin. ...

Phase Transitions in Financial Markets Using the Ising Model: A Statistical Mechanics Perspective ArXiv ID: 2504.19050 “View on arXiv” Authors: Bruno Giorgio Abstract This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the absence of autocorrelation in returns, and the presence of autocorrelation in absolute returns. A significant portion of the dissertation is dedicated to Ising model-based simulations. Due to the lack of an analytical or deterministic solution, the Monte Carlo method was employed to explore the model’s statistical properties. The results demonstrate that the Ising model is capable of replicating the majority of the statistical features analyzed. ...

Stylized facts in Web3 ArXiv ID: 2408.07653 “View on arXiv” Authors: Unknown Abstract This paper presents a comprehensive statistical analysis of the Web3 ecosystem, comparing various Web3 tokens with traditional financial assets across multiple time scales. We examine probability distributions, tail behaviors, and other key stylized facts of the returns for a diverse range of tokens, including decentralized exchanges, liquidity pools, and centralized exchanges. Despite functional differences, most tokens exhibit well-established empirical facts, including unconditional probability density of returns with heavy tails gradually becoming Gaussian and volatility clustering. Furthermore, we compare assets traded on centralized (CEX) and decentralized (DEX) exchanges, finding that DEXs exhibit similar stylized facts despite different trading mechanisms and often divergent long-term performance. We propose that this similarity is attributable to arbitrageurs striving to maintain similar centralized and decentralized prices. Our study contributes to a better understanding of the dynamics of Web3 tokens and the relationship between CEX and DEX markets, with important implications for risk management, pricing models, and portfolio construction in the rapidly evolving DeFi landscape. These results add to the growing body of literature on cryptocurrency markets and provide insights that can guide the development of more accurate models for DeFi markets. ...

Quantifying neural network uncertainty under volatility clustering ArXiv ID: 2402.14476 “View on arXiv” Authors: Unknown Abstract Time-series with volatility clustering pose a unique challenge to uncertainty quantification (UQ) for returns forecasts. Methods for UQ such as Deep Evidential regression offer a simple way of quantifying return forecast uncertainty without the costs of a full Bayesian treatment. However, the Normal-Inverse-Gamma (NIG) prior adopted by Deep Evidential regression is prone to miscalibration as the NIG prior is assigned to latent mean and variance parameters in a hierarchical structure. Moreover, it also overparameterizes the marginal data distribution. These limitations may affect the accurate delineation of epistemic (model) and aleatoric (data) uncertainties. We propose a Scale Mixture Distribution as a simpler alternative which can provide favorable complexity-accuracy trade-off and assign separate subnetworks to each model parameter. To illustrate the performance of our proposed method, we apply it to two sets of financial time-series exhibiting volatility clustering: cryptocurrencies and U.S. equities and test the performance in some ablation studies. ...

What is mature and what is still emerging in the cryptocurrency market? ArXiv ID: 2305.05751 “View on arXiv” Authors: Unknown Abstract In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to the present time. Several main characteristics commonly recognized as financial stylized facts of mature markets were quantitatively studied here. In particular, it is shown that the return distributions, volatility clustering effects, and even temporal multifractal correlations for a few highest-capitalization cryptocurrencies largely follow those of the well-established financial markets. The smaller cryptocurrencies are somewhat deficient in this regard, however. They are also not as highly cross-correlated among themselves and with other financial markets as the large cryptocurrencies. Quite generally, the volume V impact on price changes R appears to be much stronger on the cryptocurrency market than in the mature stock markets, and scales as $R(V) \sim V^α$ with $α\gtrsim 1$. ...