Evaluating Sequence Assembly Strategies for Differentially Private Synthetic Time-Series Forecasting

Guoxiong Long; Huizhen Huang; Qikun Cai; Tao Huang; Chen Hou

cs.LGOct 7, 2026

Evaluating Sequence Assembly Strategies for Differentially Private Synthetic Time-Series Forecasting

Authors: Guoxiong Long, Huizhen Huang, Qikun Cai, Tao Huang, Chen Hou

Organizations: School of Computer and Big Data, Minjiang University, No. 200 Xiyuangong Road, Fuzhou, 350108, Fujian, China

Abstract

Differentially private time-series generators commonly produce fixed-length synthetic windows, whereas downstream forecasting models often require long continuous training sequences. How these windows are assembled after generation can therefore alter the effective synthetic data presented to a forecaster, even when the trained generator remains unchanged. We study this post-generation sequence assembly process by systematically varying overlap rates and window-weighting schemes and evaluating the resulting sequences in terms of boundary continuity, statistical and temporal fidelity, and Train-on-Synthetic-Test-on-Real (TSTR) forecasting utility. Across four types of public datasets (ETTh1, ETTm1, Weather, and Appliances) and five forecasting models, the results reveal a clear forecaster-dependent assembly principle: downstream TSTR utility is jointly shaped by the forecaster, overlap rate, and window-weighting scheme, leading to distinct assembly preferences across forecasting models. Increased overlap generally improves boundary continuity, but improvements in continuity or individual fidelity diagnostics do not consistently reduce forecasting error, indicating that these diagnostics alone are insufficient for selecting assembly configurations. Complete five-forecaster assembly grids, together with matched Train-on-Real-Test-on-Real (TRTR) references, further characterize these regularities and quantify assembly-dependent utility relative to real-data training. We then validate the identified principles through additional analyses of robustness and generator variability.

Figures & tables

Figure 1: Illustration of post-generation sequence assembly on ETTh1. Left: direct concatenation of independently generated windows creates a visible boundary discontinuity. Right: forecasting performance of the real-data training reference (blue) under Train-on-Real-Test-on-Real (TRTR) evaluation and the naive-concatenation synthetic-data baseline (red) under Train-on-Synthetic-Test-on-Real (TSTR) evaluation.

Dataset	Naive $J_{\mathrm{jump}}$	Evaluated assembly $J_{\mathrm{jump}}$	Reduction
ETTh1	4.7745	0.3964	91.7%
ETTm1	4.1697	0.1412	96.6%
Weather	47.711	29.853	37.4%
Appliances	216.001	94.367	56.3%

Table 2: Boundary discontinuity reduction across datasets. Values are seed-averaged means; the assembly column reports the lowest

J_{\mathrm{jump}}

among the evaluated high-overlap settings.

Figure 2: ETTh1 assembly path under triangular weighting. Boundary discontinuity decreases while the physical 24-hour autocorrelation deviation changes; LSTM and ARIMA TSTR MAE show different downstream responses. The corresponding endpoint comparisons across the four public evaluation datasets are reported in Table 3 .

Figure 3: Minimum-MAE assembly configurations identified from the seed-averaged grids for the four public evaluation datasets. Each cell represents one dataset–forecaster pair. Color intensity represents overlap rate $\rho$ ; text labels denote Tri (Triangular weighting), Hann (Hann weighting), and None (no explicit windowing).

Forecaster	TRTR MAE	Naive TSTR MAE	TSTR range
LSTM	0.955	1.685	1.147–1.724
RNN	1.306	1.961	1.640–2.645
LightGBM	0.882	0.900	0.900–1.435
ARIMA	1.542	2.667	2.599–3.092
Prophet	1.399	2.220	2.220–3.148

Table 5: Operational electricity-load forecasting results. All entries are MAE; the TSTR range spans the evaluated assembly settings.

Dataset	$J_{\mathrm{jump}}$	LSTM MAE	ARIMA MAE
ETTh1	0.6892 $\rightarrow$ 0.1233 $\rightarrow$ 0.0549	3.080 $\rightarrow$ 2.947 $\rightarrow$ 2.814	2.952 $\rightarrow$ 3.215 $\rightarrow$ 4.154
ETTm1	0.4812 $\rightarrow$ 0.2125 $\rightarrow$ 0.1770	2.848 $\rightarrow$ 2.822 $\rightarrow$ 2.776	4.020 $\rightarrow$ 4.225 $\rightarrow$ 4.319

Table 6: DP-ConvVAE results across three assembly settings. Values are means; entries are ordered C0

\rightarrow

\rightarrow

C2.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
Backbone	Conditional 1D U-Net
Input channels	1
Output channels	1
Base model channels	144
Channel multipliers	$1,2,3,4$
Number of residual blocks	2

Appendix

Table A.3: Diffusion architecture and DP-SGD training hyperparameters.

Dataset	Noise multiplier $\sigma$
ETTh1	2.019
ETTm1	2.078
Weather	2.024
Appliances	2.024
Operational load	2.041

Appendix

Table B.1: Dataset-specific DP-SGD noise multipliers used for generator training. The values are calibrated using Opacus to satisfy the target

(\epsilon_{\mathrm{train}},\delta_{\mathrm{train}})

guarantee under the corresponding training schedule.

Figure C.1: Additional diagnostic relationship analysis. Left: relationship between boundary discontinuity ( $J_{\mathrm{jump}}$ ) and TSTR MAE for LSTM. Right: relationship between 24-hour autocorrelation deviation ( $\Delta\mathrm{ACF}_{24h}$ ) and TSTR MAE for ARIMA. Each point corresponds to one overlap configuration in the evaluated assembly path.

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Synthetic Data Generation Time Series Forecasting Time Series Generation Forecasting Benchmarks Privacy-Preserving ML Synthetic Data Evaluation

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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.

Abstract

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