State Space Filtering, Sensor Fusion, and Algorithmic Trading: An Integrated Statistical and Machine Learning Framework for Financial Time Series Forecasting

Abstract

Financial markets are inherently dynamic, noisy, and driven by latent processes that evolve over time under uncertainty. Accurate forecasting, risk management, and trading strategy design therefore require methodologies capable of extracting hidden states from imperfect observations while adapting to structural changes in the data-generating process. This research develops a comprehensive and theoretically grounded framework that integrates state space modeling, Kalman filter-based sensor fusion, constrained and estimating-function-based regression, and modern machine learning approaches within the context of algorithmic trading and financial time series forecasting. Drawing strictly on the provided literature, the study synthesizes insights from classical state space theory, nonnormal and generalized filtering, and contemporary algorithmic and high-frequency trading research to demonstrate how filtering methodologies form a unifying backbone for statistical and machine learning models in finance. Particular attention is given to equivalences between Kalman filtering and constrained regression, the role of estimating functions in relaxing distributional assumptions, and the practical relevance of these methods in pairs trading, volatility forecasting, Value at Risk prediction, foreign exchange markets, and crypto-native hedging strategies. The results are presented through an extensive descriptive analysis of methodological outcomes rather than numerical experiments, emphasizing interpretability, robustness, and economic intuition. The discussion critically evaluates limitations related to model assumptions, nonstationarity, and computational complexity, while outlining future research directions that bridge statistical filtering with hybrid neural and evolutionary learning systems. The article contributes a unified conceptual narrative that positions state space filtering as a central paradigm for modern quantitative finance, capable of coherently integrating classical econometrics, machine learning, and algorithmic trading practice.