Gaussian Processes

Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data ArXiv ID: 2506.17244 “View on arXiv” Authors: Arif Pathan Abstract Short-term sentiment forecasting in financial markets (e.g., stocks, indices) is challenging due to volatility, non-linearity, and noise in OHLC (Open, High, Low, Close) data. This paper introduces a novel CMG (Chaos-Markov-Gaussian) framework that integrates chaos theory, Markov property, and Gaussian processes to improve prediction accuracy. Chaos theory captures nonlinear dynamics; the Markov chain models regime shifts; Gaussian processes add probabilistic reasoning. We enhance the framework with transformer-based deep learning models to capture temporal patterns efficiently. The CMG Framework is designed for fast, resource-efficient, and accurate forecasting of any financial instrument’s OHLC time series. Unlike traditional models that require heavy infrastructure and instrument-specific tuning, CMG reduces overhead and generalizes well. We evaluate the framework on market indices, forecasting sentiment for the next trading day’s first quarter. A comparative study against statistical, ML, and DL baselines trained on the same dataset with no feature engineering shows CMG consistently outperforms in accuracy and efficiency, making it valuable for analysts and financial institutions. ...

Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs) ArXiv ID: 2311.10935 “View on arXiv” Authors: Unknown Abstract The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [“1”]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data. ...

Tasks Makyth Models: Machine Learning Assisted Surrogates for Tipping Points ArXiv ID: 2309.14334 “View on arXiv” Authors: Unknown Abstract We present a machine learning (ML)-assisted framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them. Our illustrative example is an event-driven, stochastic agent-based model (ABM) describing the mimetic behavior of traders in a simple financial market. Given high-dimensional spatiotemporal data – generated by the stochastic ABM – we construct reduced-order models for the emergent dynamics at different scales: (a) mesoscopic Integro-Partial Differential Equations (IPDEs); and (b) mean-field-type Stochastic Differential Equations (SDEs) embedded in a low-dimensional latent space, targeted to the neighborhood of the tipping point. We contrast the uses of the different models and the effort involved in learning them. ...