Dynamic Linear Coregionalization for Realistic Synthetic Multivariate Time Series

Annita Vapsi; Penghang Liu; Saheed Obitayo; Aakriti; Manoj Cherukumalli; Prathamesh Patil; Amit Varshney; Nicolas Marchesotti

cs.LGApr 6, 2026

Dynamic Linear Coregionalization for Realistic Synthetic Multivariate Time Series

Authors: Annita Vapsi, Penghang Liu, Saheed Obitayo, Aakriti, Manoj Cherukumalli, Prathamesh Patil, Amit Varshney, Nicolas Marchesotti, +3 more

Organizations: JPMorganChase

Abstract

Synthetic data is essential for training foundation models for time series (FMTS), but most generators assume static correlations, and are typically missing realistic inter-channel dependencies. We introduce DynLMC, a Dynamic Linear Model of Coregionalization, that incorporates time-varying, regime-switching correlations and cross-channel lag structures. Our approach produces synthetic multivariate time series with correlation dynamics that closely resemble real data. Fine-tuning three foundational models on DynLMC-generated data yields consistent zero-shot forecasting improvements across nine benchmarks. Our results demonstrate that modeling dynamic inter-channel correlations enhances FMTS transferability, highlighting the importance of data-centric pretraining.

Figures & tables

Panel of Figure 1 — Figure 1: Left: Correlation drift comparison across real and synthetic datasets. Right: Argmax-lag distribution comparison across real-world and synthetic datasets.

Model	ECL	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Solar	Traffic	Weather	Wins
TimePFN Backbone
Baseline pretrained on KS + LMC	0.369	0.440	0.369	0.483	0.298	0.226	1.063	0.596	0.297	–
Fine-tuned (KS + LMC + DynLMC - Drift)	0.371	0.436	0.374	0.496	0.299	0.225	1.077	0.596	0.297	2
Fine-tuned (KS + LMC + DynLMC - Lag)	0.456	0.459	0.382	0.529	0.321	0.229	0.967	0.666	0.300	1
Fine-tuned (KS + LMC + DynLMC - Regime Shift)	0.360	0.438	0.369	0.492	0.301	0.229	1.009	0.593	0.301	4
Fine-tuned (KS + LMC + DynLMC - Combined)	0.356	0.437	0.367	0.476	0.297	0.228	1.021	0.596	0.294	7

Table 1: Mean Absolute Error (MAE) performance and number of wins over pretrained baseline, across benchmarks (averaged over 5 seeds). KS = KernelSynth, LMC = static LMCSynth generator, and DynLMC = our dynamic extension with time-varying correlations and lag-structures. The best result is highlighted in bold and the second-best is underlined.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2: An illustration of DynLMC with evolving inter-channel structures (drift).

\phi^{(k)}\leftarrow\text{Train}(f_{\phi},(X^{(k)},Y^{(k)}),\phi_{0})

Appendix

Algorithm 2 Bayesian Optimization for Time Series Dataset Mixing

Model	ECL	ETTh1	ETTh2	ETTm1	ETTm2	Exchange	Solar	Traffic	Weather	Wins
TimePFN Backbone
Fine-tuned (KernelSynth + LMCSynth + DynLMC - Combined)	0.356	0.437	0.367	0.476	0.297	0.228	1.021	0.596	0.294	-
Fine-tuned (KernelSynth + LMCSynth + DynLMC - Combined BO)	0.378	0.440	0.363	0.502	0.294	0.226	0.882	0.592	0.270	6

Appendix

Table 2: Mean Absolute Error (MAE) performance across datasets combining drift, lag and regime shift characteristics, naively and using a Bayesian mixing method. Results averaged over 5 seeds. The best result is highlighted in bold.

x\leftarrow\text{concat}(x_{1},x_{2},x_{3}),\quad y\leftarrow\text{concat}(y_{1},y_{2},y_{3})

Appendix

Algorithm 3 Progressive Interleaved Mixing of Three Datasets

Explore similar work

RMISC: A Large-scale Real-world Multivariate Corpus for Time Series Foundation Models
Jul 7, 2026Qian Sun, Yong-Ming Tian, Jia-Wei Huang +2Synthetic Data Pretraining Multivariate Time Series Forecasting
State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China · School of Intelligent Science and Technology, Nanjing University, Suzhou, China · Nanjing University – Siemens Joint Research Center on Industrial AI, Suzhou, China +1
Does Synthetic Data Help? Empirical Evidence from Deep Learning Time Series Forecasters
May 7, 2026Hugo Cazaux, Eyjólfur Ingi Ásgeirsson, Hlynur StefánssonSynthetic Data Augmentation Synthetic Data Generation
Department of Engineering Reykjavík University Iceland, Menntavegur 1, 102
Mix, Don't Pick: Why Synthetic Corpus Composition Matters for Time Series Foundation Model Pretraining
Jun 6, 2026Aaryan Nagpal, Debdeep Sanyal, Murari Mandal +2Synthetic Data Pretraining Time Series Forecasting
Birla AI Labs, Mumbai, India · KIIT, Bhubaneswar, India · BITS Pilani, Pilani, India

Jul 7, 2026J/K move · Enter open · S save

RMISC: A Large-scale Real-world Multivariate Corpus for Time Series Foundation Models

Qian Sun, Yong-Ming Tian, Jia-Wei Huang, Cheng Feng+1

State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China · School of Intelligent Science and Technology, Nanjing University, Suzhou, China · Nanjing University – Siemens Joint Research Center on Industrial AI, Suzhou, China+1

Synthetic Data Pretraining Multivariate Time Series Forecasting Zero-Shot Time Series Forecasting Time-Series Foundation Models

Open paper AskPDF arXiv

Recent years have witnessed the emergence of multivariate modeling using time series foundation models (TSFMs), which achieve advanced zero-shot generalization. Modern multivariate TSFMs are predominantly pretrained on multivariate synthetic data, which is easier to scale but may fail to capture the complex temporal dynamics and cross-variable relationships present in real-world time series. This raises a key question: Whether and to what extent the leading TSFMs trained with the real-world corpus perform better than those trained with synthetic data? To answer this, we establish the RMISC corpus, a considerably large-scale, high-quality, openly accessible, real-world, and multivariate time series archive that contains around 200 datasets and 142 billion time points across diverse domains. Furthermore, we pretrain four advanced TSFMs on univariate, synthetic multivariate, and real-world multivariate data and evaluate their zero-shot generalization capabilities on standard in-distribution and out-of-distribution benchmarks. Experimental results show that incorporating real-world multivariate data predominantly improves the generalization performance for both univariate and multivariate TSFMs. These results provide a deeper understanding of how real-world multivariate data contributes to the development of stronger TSFMs.

Abstract

Explore similar work

RMISC: A Large-scale Real-world Multivariate Corpus for Time Series Foundation Models

Does Synthetic Data Help? Empirical Evidence from Deep Learning Time Series Forecasters

Mix, Don't Pick: Why Synthetic Corpus Composition Matters for Time Series Foundation Model Pretraining