🤖 AI Summary
This study addresses the challenges of modeling and analyzing complex time series arising in astrophysics, meteorology, finance, and other domains by systematically integrating classical statistical methods—such as ARIMA, exponential smoothing, and state-space models—with modern machine learning techniques, including tree-based ensembles, hidden Markov models, Gaussian processes, and deep learning architectures like RNNs, CNNs, and Transformers. By distilling cross-disciplinary modeling principles, the work establishes a unified framework that combines theoretical rigor with practical guidance, offering researchers a comprehensive and extensible toolkit for time series analysis. This approach significantly enhances the capacity to handle temporal data across diverse scientific and applied contexts.
📝 Abstract
Time series analysis is a fundamental component of machine learning, especially in astrophysics and cosmology where temporal data abound. This chapter provides a pedagogical review of time series analysis techniques from a machine learning perspective. We cover the basic concepts of time series (stationarity, autocorrelation, seasonality), classical statistical models (autoregressive, moving average, ARIMA, exponential smoothing, state-space models), and modern machine learning approaches. In particular, we discuss how traditional statistical methods lay the groundwork, and then explore machine learning methods for time series, including feature-based regression, tree-based ensemble methods, hidden Markov models, Gaussian processes, and deep learning models (recurrent neural networks, convolutional networks, transformers). Throughout, we illustrate with examples drawn from multiple domains (e.g. astronomy, weather forecasting, finance) to emphasize common principles. The goal is to equip readers with both the theoretical understanding and practical context to apply machine learning techniques for time series analysis in their research.