Synthetic Time Series Generation via Complex Networks

TL;DR

This paper introduces a Quantile Graph (QG)–based framework for synthetic time series generation by transforming time series into graphs via quantile transitions and reconstructing new series from the resulting Markov matrix (InvQG). The method is interpretable and parameter-efficient, requiring only the quantile count $\mathcal{Q}$, and it enables multiple realizations that preserve key statistical and short-term dynamical properties. Across 11 artificial models and real smart-meter data, InvQG achieves fidelity comparable to or better than GAN-based baselines TimeGAN and DoppelGANger, with additional gains in diversity and interpretability. Topological analysis using NetF shows synthetic networks largely retain important structural features, though long-range dependencies and some clustering metrics may diverge for certain models, highlighting areas for future improvement and broader applicability for data augmentation and privacy-preserving synthesis.

Abstract

Time series data are essential for a wide range of applications, particularly in developing robust machine learning models. However, access to high-quality datasets is often limited due to privacy concerns, acquisition costs, and labeling challenges. Synthetic time series generation has emerged as a promising solution to address these constraints. In this work, we present a framework for generating synthetic time series by leveraging complex networks mappings. Specifically, we investigate whether time series transformed into Quantile Graphs (QG) -- and then reconstructed via inverse mapping -- can produce synthetic data that preserve the statistical and structural properties of the original. We evaluate the fidelity and utility of the generated data using both simulated and real-world datasets, and compare our approach against state-of-the-art Generative Adversarial Network (GAN) methods. Results indicate that our quantile graph-based methodology offers a competitive and interpretable alternative for synthetic time series generation.

Figures (25)

• Figure 1: Illustration of Quantile Graph mapping method with a toy time series. Source: Adapted from Campanharo2011silva2021time.
• Figure 2: Illustration of the Inverse Quantile Graph (InvQG) mapping method, including the quantile graph derived from the synthetic time series. Source: Adapted from Campanharo2011.
• Figure 3: Diagram of the methodology implemented in this work.
• Figure 4: Boxplots of the paired samples statistical features: trend, linearity, curvature and entropy (synthetic - original).
• Figure 5: Boxplots of the paired samples statistical features: e_acf1, e_acf10, x_acf1 and x_acf10 (synthetic - original).