Characterizing Colored Noise Time Series Patterns with Deep Learning Models
Luan Orion de Oliveira Baraúna Ferreira, Reinaldo Roberto Rosa, Carlos Alexandre Wuensche, Rubens Andreas Sautter, Valdivino Alexandre de Santiago Júnior, Elcio Hideiti Shiguemori, Marcelo B. Pádua · Fluctuation and Noise Letters · 2024
Motivated by the unpredictability of stochastic time series, this paper presents an alternative deep learning approach to characterize long-term stochastic fluctuation patterns. The proposed approach considers different deep neural networks (DNNs) carefully applied to [Formula: see text] noise time series. The predictive characterization of different noise patterns is determined by the respective spectral index [Formula: see text], which works as a regression-based training attribute. The study is based on synthetic canonical colored noises (white: [Formula: see text], pink: [Formula: see text], red: [Formula: see text]) and also turbulent-like pattern with [Formula: see text]. Five DNNs are used for training based on the spectral patterns of each noise class. A new Fast Fourier Transform centric loss function for training different DNNs models drives hyperparameter exploration for each model using the optuna python package, resulting in 2560 well-established unique Deep Learning Models (DLMs) for the presented methodology. The results show that a predictive characterization of the fluctuation pattern of a stochastic time series is feasible when stochastic fluctuation is the main pattern to be addressed. Considering future applications in radio astronomy, method performance and results are interpreted and discussed in a data science context.