The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be innacurate when there are covariates that could have a large influence on the dependence structure of the data. To account for this, a Bayesian framework for the estimation of conditional copulas is proposed. In this framework the parameters of a copula are non-linearly related to some arbitrary conditioning variables.

Directional forecasting in financial markets requires both accuracy and interpretability. Before the advent of deep learning, interpretable approaches based on human-defined patterns were prevalent, but their structural vagueness and scale ambiguity hindered generalization. In contrast, deep learning models can effectively capture complex dynamics, yet often offer limited transparency. To bridge this gap, we propose a two-stage framework that integrates unsupervised pattern extracion with interpretable forecasting. (i) SIMPC segments and clusters multivariate time series, extracting recurrent patterns that are invariant to amplitude scaling and temporal distortion, even under varying window sizes. (ii) JISC-Net is a shapelet-based classifier that uses the initial part of extracted patterns as input and forecasts subsequent partial sequences for short-term directional movement. Experiments on Bitcoin and three S&P 500 equities demonstrate that our method ranks first or second in 11 out of 12 metric--dataset combinations, consistently outperforming baselines. Unlike conventional deep learning models that output buy-or-sell signals without interpretable justification, our approach enables transparent decision-making by revealing the underlying pattern structures that drive predictive outcomes.

Financial markets are complex, non-stationary systems where the underlying data distributions can shift over time, a phenomenon known as regime changes, as well as concept drift in the machine learning literature. These shifts, often triggered by major economic events, pose a significant challenge for traditional statistical and machine learning models. A fundamental problem in developing and validating adaptive algorithms is the lack of a ground truth in real-world financial data, making it difficult to evaluate a model's ability to detect and recover from these drifts. This paper addresses this challenge by introducing a novel framework, named ProteuS, for generating semi-synthetic financial time series with pre-defined structural breaks. Our methodology involves fitting ARMA-GARCH models to real-world ETF data to capture distinct market regimes, and then simulating realistic, gradual, and abrupt transitions between them. The resulting datasets, which include a comprehensive set of technical indicators, provide a controlled environment with a known ground truth of regime changes. An analysis of the generated data confirms the complexity of the task, revealing significant overlap between the different market states. We aim to provide the research community with a tool for the rigorous evaluation of concept drift detection and adaptation mechanisms, paving the way for more robust financial forecasting models.

Predicting cryptocurrency returns is notoriously difficult: price movements are driven by a fast-shifting blend of on-chain activity, news flow, and social sentiment, while labeled training data are scarce and expensive. In this paper, we present Meta-RL-Crypto, a unified transformer-based architecture that unifies meta-learning and reinforcement learning (RL) to create a fully self-improving trading agent. Starting from a vanilla instruction-tuned LLM, the agent iteratively alternates between three roles-actor, judge, and meta-judge-in a closed-loop architecture. This learning process requires no additional human supervision. It can leverage multimodal market inputs and internal preference feedback. The agent in the system continuously refines both the trading policy and evaluation criteria. Experiments across diverse market regimes demonstrate that Meta-RL-Crypto shows good performance on the technical indicators of the real market and outperforming other LLM-based baselines.

Simulating realistic financial time series is essential for stress testing, scenario generation, and decision-making under uncertainty. Despite advances in deep generative models, there is no consensus metric for their evaluation. We focus on generative AI for financial time series in decision-making applications and employ the nested optimal transport distance, a time-causal variant of optimal transport distance, which is robust to tasks such as hedging, optimal stopping, and reinforcement learning. Moreover, we propose a statistically consistent, naturally parallelizable algorithm for its computation, achieving substantial speedups over existing approaches.

Time series forecasting plays a critical role in decision-making processes across diverse fields including meteorology, traffic, electricity, economics, finance, and so on. Especially, predicting returns on financial instruments is a challenging problem. Some researchers have proposed time series foundation models applicable to various forecasting tasks. Simultaneously, based on the recognition that real-world time series exhibit chaotic properties, methods have been developed to artificially generate synthetic chaotic time series, construct diverse datasets and train models. In this study, we propose a methodology for modeling financial time series by generating artificial chaotic time series and applying resampling techniques to simulate financial time series data, which we then use as training samples. Increasing the resampling interval to extend predictive horizons, we conducted large-scale pre-training using 10 billion training samples for each case. We subsequently created test datasets for multiple timeframes using actual Bitcoin trade data and performed zero-shot prediction without re-training the pre-trained model. The results of evaluating the profitability of a simple trading strategy based on these predictions demonstrated significant performance improvements over autocorrelation models. During the large-scale pre-training process, we observed a scaling law-like phenomenon that we can achieve predictive performance at a certain level with extended predictive horizons for chaotic time series by increasing the number of training samples exponentially. If this scaling law proves robust and holds true across various chaotic models, it suggests the potential to predict near-future events by investing substantial computational resources. Future research should focus on further large-scale training and verifying the applicability of this scaling law to diverse chaotic models.

Financial time series forecasting relies on historical data and time series modeling to predict key financial indicators, such as stock prices, indexes, returns, and volatility. Accurate forecasting helps identify market trends and volatility, supports national financial regulation, and assists institutional investors in making informed investment decisions. Traditional econometric models include ARCH (Autoregressive Conditional Heteroske-dasticity Model) and GARCH (Generalized-ARCH), which describe volatility clustering and leptokurtosis in financial time series [1][2]. In the 21st century, deep learning has become prominent. Neural network models such as convolutional neural networks (CNN), deep belief networks (DBN), and autoencoders (AE) have been widely applied to sequence prediction. Among these, recurrent neural networks (RNNs) and particularly long short-term memory (LSTM) networks [3], introduced by Hochreiter and Schmidhuber in 1997 [4], address vanishing gradient problems and are suitable for capturing long-term dependencies.

Applications range from technical analysis of a company's fundamental value, wider market sentiment, factor analysis and most tasks involving some form of natural language processing (NLP) [1, 2]. The implications to trading systems will likely be a dramatic increase in the rate and volume of market insights that can be generated to inform decisions. The overall capabilities of LLMs have dramatically increased over the last five years [3]. This has led to an increase in the number of LLMs available, both as proprietary models from frontier labs or as smaller models with open-weights which can be run locally. Given this, the influence of LLMs on trading decisions is expected to be varied and highly model specific. Early work is starting to compare and benchmark these models in tasks specific to financial applications, such as trading decisions, portfolio optimisation, and market analysis [4-10]. As the number of models increases, and their underlying strengths and weaknesses become more apparent, it is expected that different classes of pre-trained models will be more regularly deployed to achieve certain objectives [11, 12]. While these objectives are likely to be significantly linked to NLP-based tasks, such as text summarisation, analysis, and generation, recent LLM architectures give early evidence that more complex tasks can also be automated. These LLMs, such as the'o' series from OpenAI or'R1' from DeepSeek, generate'reasoning' tokens which result in the model performing more in-context analysis of the generated output and has lead to improved performance over a number of key evaluation measures [13, 14].

For financial time series, the shortage of samples makes it statistically hard for empirical processes to achieve an acceptable confidence level in describing the underlying market distribution. In practice, it is widely recognized among financial engineers that back-testing exclusively on empirical market data results in significant over-fitting, which leads to unpredictably high risks in decision making based on these tests [Bai+16]. Synthetic data are therefore generated to augment scarce market data, and used to improve backtesting, stress-testing, exploring new scenarios, and in deep learning processes in financial applications; see the overview given in [Ass+20a]. For those purposes, the generated data should look like plausible samples from the underlying market distribution, for example reproducing stylized facts observed in the market. In particular, we want the distribution of the generated data to be close to the underlying market distribution in their performance on decision making problems, such as pricing and hedging, as well as optimal stopping and utility maximization. Notably, these problems are not continuous with respect to widely used distances, such as the Maximum Mean Discrepancy (MMD) and the Wasserstein distances (W-distances). On the other hand, these problems are Lipschitz-continuous with respect to stronger metrics, called adapted Wasserstein distances (AW-distances) [Bac+20; PP14].

Summary This paper describes an approach to learning the dynamics of financial time series. The authors describe a parametric quantile function with four parameters (modelling location, scale, and the shapes of the left and right hand tails of the conditional distribution of returns). The time dynamics of these parameters are learned using LSTM neural network. The performance of the algorithm is compared to various GARCH-type specifications and a TQR model (which combines "traditional" quantile regression with a LTSM neural network). Strengths I enjoyed reading the paper.