Time Series Modeling

Investigating Conditional Restricted Boltzmann Machines in Regime Detection ArXiv ID: 2512.21823 “View on arXiv” Authors: Siddhartha Srinivas Rentala Abstract This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted Boltzmann Machines (RBMs) by incorporating autoregressive conditioning and utilizing Persistent Contrastive Divergence (PCD) to incorporate complex temporal dependency structures. Comparing a discrete Bernoulli-Bernoulli architecture against a continuous Gaussian-Bernoulli variant across a multi-asset dataset spanning 2013-2025, we observe a dichotomy between generative fidelity and regime detection. While the Gaussian CRBM successfully preserves static asset correlations, it exhibits limitations in generating long-range volatility clustering. Thus, we analyze the free energy as a relative negative log-likelihood (surprisal) under a fixed, trained model. We demonstrate that the model’s free energy serves as a robust, regime stability metric. By decomposing the free energy into quadratic (magnitude) and structural (correlation) components, we show that the model can distinguish between pure magnitude shocks and market regimes. Our findings suggest that the CRBM offers a valuable, interpretable diagnostic tool for monitoring systemic risk, providing a supplemental metric to implied volatility metrics like the VIX. ...

On Bitcoin Price Prediction ArXiv ID: 2504.18982 “View on arXiv” Authors: Grégory Bournassenko Abstract In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability of Bitcoin’s price movements, drawing a parallel with traditional financial markets. We examine whether the cryptocurrency market operates under the efficient market hypothesis (EMH) or if inefficiencies still allow opportunities for arbitrage. Our methodology combines theoretical reviews, empirical analyses, machine learning approaches, and time series modeling to assess the extent to which Bitcoin’s price can be predicted. We find that while, in general, the Bitcoin market tends toward efficiency, specific conditions, including information asymmetries and behavioral anomalies, occasionally create exploitable inefficiencies. However, these opportunities remain difficult to systematically identify and leverage. Our findings have implications for both investors and policymakers, particularly regarding the regulation of cryptocurrency brokers and derivatives markets. ...

Mean-Field Microcanonical Gradient Descent ArXiv ID: 2403.08362 “View on arXiv” Authors: Unknown Abstract Microcanonical gradient descent is a sampling procedure for energy-based models allowing for efficient sampling of distributions in high dimension. It works by transporting samples from a high-entropy distribution, such as Gaussian white noise, to a low-energy region using gradient descent. We put this model in the framework of normalizing flows, showing how it can often overfit by losing an unnecessary amount of entropy in the descent. As a remedy, we propose a mean-field microcanonical gradient descent that samples several weakly coupled data points simultaneously, allowing for better control of the entropy loss while paying little in terms of likelihood fit. We study these models in the context of financial time series, illustrating the improvements on both synthetic and real data. ...