FractalTS: Time Series Dataset for Controlled Scaling Dynamics and Multifractal Processes

A major challenge in time-series machine learning (ML) is separating genuine learning of temporal structure from successful matching of low-order statistics. This problem is particularly important for fractional, fractal, and multifractal (MF) processes, whose defining properties are expressed across multiple scales. Two sequences may exhibit similar marginal distributions and short-range correlations while following different scaling laws. Existing datasets are predominantly collected from natural or engineered systems, where the generating mechanism and its scaling parameters are only partially known. Thus, model failures cannot be simply separated from uncertainty in the target properties. We introduce FractalTS, a theory-grounded benchmark dataset for controlled time-series research in which process families, scaling regimes, and stochastic parameters are explicitly specified at generation time. The core dataset contains independent realizations of monofractal fractional Brownian motion and six multifractal constructions spanning anti-correlated, uncorrelated, correlated, $1/f$, $1/f^2$, and non-stationary regimes. The generator exposes interpretable controls, including the Hurst exponent ($H$), multifractal intermittency, cascade parameter, spectral slope, envelope, and drift, and supports arbitrary numbers of independently seeded realizations. Rather than evaluating a particular downstream model, this paper establishes the dataset as a reproducible scientific testbed. A reproducible manifest and train/calibration/validation/test protocol is provided. Validation covers covariance, spectral scaling, Hurst behaviour, generalized scaling functions $h(q)$, multifractal spectra, and stationarity. The dataset is primarily designed for controlled evaluation of time-series generative models (GANs, VAEs, normalizing flows, and diffusion models), which are rarely tested on whether they preserve multiscale structure. It also supports representation learning, forecasting, anomaly detection, and estimator benchmarking under known multiscale dynamics.