Time series data are essential for a wide range of applications, yet access to high-quality datasets is often constrained by privacy concerns, acquisition costs, and labelling challenges. Synthetic time series generation has emerged as a promising approach to address these limitations. In this work, we investigate the use of complex network mappings for synthetic time series generation, focusing on the Quantile Graph (QG) representation and its inverse. While the inverse QG mapping has been previously proposed, its potential as a general-purpose data generator has not been systematically evaluated. We address this gap through a comprehensive empirical study assessing both the fidelity and utility of synthetic time series generated by the Inverse Quantile Graph (InvQG) framework. The evaluation combines statistical feature analysis, network-based topological characteristics, and performance in downstream clustering and classification tasks, using simulated and real-world datasets. The results show that InvQG effectively preserves marginal distributions and short-term temporal dependencies across a wide range of models, while exhibiting predictable limitations in capturing long-range or higher-order dynamics.
Time-series data augmentation plays a crucial role in regression-oriented forecasting tasks, where limited data restricts the performance of deep learning models. While Generative Adversarial Networks (GANs) have shown promise in synthetic time-series generation, existing approaches primarily focus on matching marginal data distributions and often overlook the temporal dynamics that naturally exist in the original multivariate time series. When generating multivariate time series, this mismatch leads to distribution shift and temporal drift, thereby degrading the fidelity of the synthetic sequences. In this work, we propose a model-agnostic Markov Chain Monte Carlo (MCMC)-based framework to mitigate distribution shift and preserve temporal dynamics in synthetic time series. We provide a theoretical analysis of how conditional generative models accumulate deviations under sequential generation and demonstrate that the MCMC algorithm can correct these discrepancies by enforcing consistency with empirical transition statistics between neighboring time points. Extensive experiments on the Lorenz, Licor, ETTh, and ILI datasets using RCGAN, GCWGAN, TimeGAN, SigCWGAN, and AECGAN demonstrate that the proposed MCMC framework consistently improves autocorrelation alignment, skewness error, kurtosis error, R2, discriminative score, and predictive score. These results suggest that synthetic time series consistent with the original data require explicit preservation of transition laws rather than solely relying on adversarial distribution matching, thereby offering a principled direction for improving generative modeling of time-series data.
Time series forecasting in privacy-sensitive domains often requires training models on released data rather than original observations. Synthetic time series generation has been developed primarily for data augmentation, where generated series supplement the original training set. How well these methods perform when fully replacing the original data - and how much privacy risk the released series carry - remains underexplored. We address this gap through a benchmark evaluating synthetic generation methods and noise-based anonymization baselines under a Train on Synthetic, Test on Real (TSTR) protocol. We jointly assess forecasting performance and distance-based empirical privacy risk across seven datasets, characterizing the trade-off between these objectives. We also introduce Grasynda-P, a privacy-motivated extension of the graph-based generator Grasynda, incorporating matrix ensembling and kernel density estimation. Our results show that: (1) no generation method fully substitutes for original training data; (2) noise-based anonymization yields the strongest privacy but the worst forecasting performance; (3) simple transformation-based generators outperform deep generative models for forecasting in this setting; and (4) Grasynda-P lies on the Pareto frontier, achieving competitive forecasting with stronger privacy separation than other generators. This benchmark establishes a reference point for evaluating and developing new privacy-aware synthetic time series generation methods.
Synthetic data has transformed language model training, yet its role in time series forecasting remains poorly understood. We present a large-scale empirical study: nine experiment groups, 4,218 runs systematically evaluating synthetic time series augmentation across five architectures, four synthetic signals and seven datasets. The effect is sharply architecture-conditional: channel-mixing models (TimesNet, iTransformer) benefit in the majority of trials, while channel-independent models (DLinear, PatchTST) are consistently degraded. In selected low-resource settings the gains are striking: TimesNet trained on only 10% of Weather data with synthetic augmentation surpasses the full-data baseline (4 of 16 sparsity-dataset combinations). Averaged across all architectures, augmentation hurts in 67% of trials. We further find that only the Seasonal-Trend generator reliably helps across the tested benchmarks, and that hard curriculum switching is actively harmful (+24% MSE degradation). These results provide concrete, actionable guidelines on how to use synthetic data: use synthetic augmentation with channel-mixing architectures, use gradual annealing schedules, and treat low-resource augmentation as architecture- and dataset-dependent. Code is available at \href{https://github.com/hugoiscracked/synthetic-ts/tree/main}
Hugo Cazaux, Eyjólfur Ingi Ásgeirsson, Hlynur Stefánsson