Characterizing Colored Noise Time Series Patterns with Deep Learning Models

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 1∕fβ noise time series. The predictive characterization of different noise patterns is determined by the respective spectral index β, which works as a regression-based training attribute. The study is based on synthetic canonical colored noises (white: β=0, pink: β=1, red: β=2) and also turbulent-like pattern with β=5∕3. 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.