arXiv subjects

Buddha Nath Sharma

Publications and source records attributed to Buddha Nath Sharma.

7 recordsLinked to original sources

arXiv2026

Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile

We develop a framework for detecting regime transitions in dynamical systems using the Mixup Euler Characteristic Profile (Mixup ECP) -- the Euler characteristic of the geometric intersection of ball unions around adjacent delay-embedded trajectory segments, viewed as a function of filtration scale. The Mixup ECP provides a detection statistic with a built-in null and guaranteed stability. We formalize regime detection as a low-side-permutation test, establish its validity and consistency, and introduce a multi-delay extension that automatically selects the most informative dynamical timescale. Complementing the topological signal with Complexity Variance, Higuchi fractal dimension, and a rolling mean baseline, the four-signal combined method achieves $9.50$ days MAE on Indian monsoon onset (Nepal target) -- a $32\%$ improvement over the rolling mean baseline and $9\%$ over CUSUM. Validated on the Lorenz system, logistic map, and three monsoon systems spanning both hemispheres (Indian/Nepal, Indian/Kerala, Western North Pacific), plus ENSO and a synthetic EEG dataset, the framework adds value precisely when the transition is gradual or obscured by noise.

math.DS↗

arXiv2026

Interpretable Classification of Time Series Using Euler Characteristic Surfaces

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic ($χ$) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On $\textit{ECG5000}$, our single-feature ECS classifier achieves $98\%$ accuracy with $O(n+R\cdot T)$ complexity, compared to $62\%$ reported by a recent PH-based method. An AdaBoost extension raises accuracy to $98.6\%$, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on $\textit{TwoLeadECG}$ ($94.1\%$) and $\textit{Epilepsy2}$ ($92.6\%$).

cs.LG↗

arXiv2026

Regime Discovery and Intra-Regime Return Dynamics in Global Equity Markets

Financial markets alternate between tranquil periods and episodes of stress, and return dynamics can change substantially across these regimes. We study regime-dependent dynamics in developed and developing equity indices using a data-driven Hilbert--Huang-based regime identification and profiling pipeline, followed by variable-length Markov modeling of categorized returns. Market regimes are identified using an Empirical Mode Decomposition-based Hilbert--Huang Transform, where instantaneous energy from the Hilbert spectrum separates Normal, High, and Extreme regimes. We then profile each regime using Holo--Hilbert Spectral Analysis, which jointly resolves carrier frequencies, amplitude-modulation frequencies, and amplitude-modulation energy (AME). AME, interpreted as volatility intensity, declines monotonically from Extreme to High to Normal regimes. This decline is markedly sharper in developed markets, while developing markets retain higher baseline volatility intensity even in Normal regimes. Building on these regime-specific volatility signatures, we discretize daily returns into five quintile states $\mathtt{R}_1$ to $\mathtt{R}_5$ and estimate Variable-Length Markov Chains via context trees within each regime. Unconditional state probabilities show tail states dominate in Extreme regimes and recede as regimes stabilize, alongside persistent downside asymmetry. Entropy peaks in High regimes, indicating maximum unpredictability during moderate-volatility periods. Conditional transition dynamics, evaluated over contexts of length up to three days from the context-tree estimates, indicate that developed markets normalize more effectively as stress subsides, whereas developing markets retain residual tail dependence and downside persistence even in Normal regimes, consistent with a coexistence of continuation and burst-like shifts.

q-fin.ST↗

arXiv2026

Intraday Limit Order Price Change Transition Dynamics Across Market Capitalizations Through Markov Analysis

Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency NASDAQ100 tick data. Employing a discrete-time Markov chain framework, we categorize consecutive price changes into nine states and estimate transition probability matrices (TPMs) for six intraday intervals across High ($\mathtt{HMC}$), Medium ($\mathtt{MMC}$), and Low ($\mathtt{LMC}$) market cap stocks. Element-wise TPM comparison reveals systematic patterns: price inertia peaks during opening and closing hours, stabilizing midday. A capitalization gradient is observed: $\mathtt{HMC}$ stocks exhibit the strongest inertia, while $\mathtt{LMC}$ stocks show lower stability and wider spreads. Markov metrics, including spectral gap, entropy rate, and mean recurrence times, quantify these dynamics. Clustering analysis identifies three distinct temporal phases on the bid side -- Opening, Midday, and Closing, and four phases on the ask side by distinguishing Opening, Midday, Pre-Close, and Close. This indicates that sellers initiate end-of-day positioning earlier than buyers. Stationary distributions show limit order dynamics are dominated by neutral and mild price changes. Jensen-Shannon divergence confirms the closing hour as the most distinct phase, with capitalization modulating temporal contrasts and bid-ask asymmetry. These findings support capitalization-aware and time-adaptive execution algorithms.

q-fin.ST↗

arXiv2025

Early-Warning Signals of Political Risk in Stablecoin Markets: Human and Algorithmic Behavior Around the 2024 U.S. Election

We study how the 2024 U.S. presidential election, viewed as a major political risk event, affected cryptocurrency markets by distinguishing human-driven peer-to-peer stablecoin transactions from automated algorithmic activity. Using structural break analysis, we find that human-driven Ethereum Request for Comment 20 (ERC-20) transactions shifted on November 3, two days before the election, while exchange trading volumes reacted only on Election Day. Automated smart-contract activity adjusted much later, with structural breaks appearing in January 2025. We validate these shifts using surrogate-based robustness tests. Complementary energy-spectrum analysis of Bitcoin and Ethereum identifies pronounced post-election turbulence, and a structural vector autoregression confirms a regime shift in stablecoin dynamics. Overall, human-driven stablecoin flows act as early-warning indicators of political stress, preceding both exchange behavior and algorithmic responses.

q-fin.ST↗

arXiv2025

Causality Analysis of COVID-19 Induced Crashes in Stock and Commodity Markets: A Topological Perspective

The paper presents a comprehensive causality analysis of the US stock and commodity markets during the COVID-19 crash. The dynamics of different sectors are also compared. We use Topological Data Analysis (TDA) on multidimensional time-series to identify crashes in stock and commodity markets. The Wasserstein Distance WD shows distinct spikes signaling the crash for both stock and commodity markets. We then compare the persistence diagrams of stock and commodity markets using the WD metric. A significant spike in the $WD$ between stock and commodity markets is observed during the crisis, suggesting significant topological differences between the markets. Similar spikes are observed between the sectors of the US market as well. Spikes obtained may be due to either a difference in the magnitude of crashes in the two markets (or sectors), or from the temporal lag between the two markets suggesting information flow. We study the Granger-causality between stock and commodity markets and also between different sectors. The results show a bidirectional Granger-causality between commodity and stock during the crash period, demonstrating the greater interdependence of financial markets during the crash. However, the overall analysis shows that the causal direction is from stock to commodity. A pairwise Granger-causal analysis between US sectors is also conducted. There is a significant increase in the interdependence between the sectors during the crash period. TDA combined with Granger-causality effectively analyzes the interdependence and sensitivity of different markets and sectors.

q-fin.ST↗

arXiv2024

Identifying Extreme Events in the Stock Market: A Topological Data Analysis

This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices separately, could not detect EEs for multiple time series in one go. TDA provides a robust framework for such analysis and identifies the EEs during the crashes for different indices. The TDA analysis shows that $L^1$, $L^2$ norms and Wasserstein distance ($W_D$) of the world leading indices rise abruptly during the crashes, surpassing a threshold of $μ+4*σ$ where $μ$ and $σ$ are the mean and the standard deviation of norm or $W_D$, respectively. Our study identified the stock index crashes of the 2008 financial crisis and the COVID-19 pandemic across continents as EEs. Given that different sectors in an index behave differently, a sector-wise analysis was conducted during the COVID-19 pandemic for the Indian stock market. The sector-wise results show that after the occurrence of EE, we have observed strong crashes surpassing $μ+2*σ$ for an extended period for the banking sector. While for the pharmaceutical sector, no significant spikes were noted. Hence, TDA also proves successful in identifying the duration of shocks after the occurrence of EEs. This also indicates that the Banking sector continued to face stress and remained volatile even after the crash. This study gives us the applicability of TDA as a powerful analytical tool to study EEs in various fields.

q-fin.ST↗