RMISC: A Large-scale Real-world Multivariate Corpus for Time Series Foundation Models Qian Sun1,2,4,* Yong-Ming Tian1,2,4,* Jia-Wei Huang1,2,4 3,4 Cheng Feng Shao-Qun Zhang1,2,4, B 1 State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China 2 School of Intelligent Science and Technology, Nanjing University, Suzhou, China 3 Siemens Data and AI Research, Beijing, China 4 Nanjing University – Siemens Joint Research Center on Industrial AI, Suzhou, China
arXiv:2607.06504v1 [cs.AI] 7 Jul 2026
Abstract
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. Key words: multivariate time series forecasting, time series foundation model, real-world time series corpus, covariates, out-of-distribution generalization
1. Introduction
Recent advances in Time Series Foundation Models (TSFMs) have significantly remodeled the paradigm of time series analysis [1]. Fed into large-scale and heterogeneous time series corpora, TSFMs can be directly compatible with diverse forecasting tasks, frequency distributions, and data modalities [2] with remarkable zero-shot generalization capabilities, thus moving beyond traditional statistical methods [3, 4] and deep learning
Preprint
July 8, 2026
Univariate
Univariate Time Series
Univariate Models
Forecasting Results
𝐲𝐲𝟏𝟏
𝒙𝒙𝟏𝟏: Target
𝒙𝒙𝟐𝟐: Target
Plenty of Real-World Data
Patching
Time Attention
Input Embedding
Multivariate Models
𝐲𝐲𝟏𝟏,𝟐𝟐
𝒙𝒙𝟏𝟏,𝟐𝟐 : Target 2
𝐲𝐲𝟏𝟏,𝟑𝟑
𝒙𝒙𝟏𝟏,𝟑𝟑 : Covariate
𝒚𝒚𝟐𝟐,𝟏𝟏
𝒙𝒙𝟐𝟐,𝟏𝟏: Target 1
𝒚𝒚𝟐𝟐,𝟐𝟐
𝒙𝒙𝟐𝟐,𝟐𝟐 : Target 2
Limited to Synthetic Data
Forecasting Results
𝐲𝐲𝟏𝟏,𝟏𝟏
𝒙𝒙𝟏𝟏,𝟏𝟏: Target 1
𝒙𝒙𝟐𝟐,𝟑𝟑 : Covariate
𝐲𝐲𝟐𝟐
Limited Performance
Target-Covariate Modeling
Target-Covariate Structuring
Multivariate Time Series
Multivariate
Input Embedding
Time Attention Group Attention
Patching
𝒚𝒚𝟐𝟐,𝟑𝟑
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Figure 1: The modeling workflow of univariate and multivariate time series foundation models on corpora.
models [5, 6, 7] that repeatedly train task-specific models for individual time series [8, 9]. In recent years, developers have widely applied TSFM to various fields, such as industrial sensing [10], financial assessment [11], healthcare monitoring [12], climate modeling [13], energy management [14], and traffic prediction [15]. Capturing the cross-variable information is one of the fundamental topics in the development of TSFMs [16, 17], the modeling workflow of which is illustrated in Figure 1. Intuitively, real-world time series are rarely observed in isolation; one target variable is usually accompanied by multiple related covariates, and its temporal dynamics are often shaped by complex cross-variable dependencies [18]. For instance, temperature changes in weather forecasts are affected by rainfall and wind speed. Thus, covariate modeling in multivariate TSFMs contributes to more accurate forecasts as auxiliary covariates and cross-variable dependencies provide complementary signals beyond the target history alone [9, 18, 19]. However, current multivariate TSFMs are predominantly pretrained on multivariate synthetic data [16, 20]; despite the ease of use and scalability, there still exists a gap between synthetic and real-world time series in terms of capturing complex temporal dynamics and cross-variable relationships [20, 21]. This raises a key question: Whether and to what extent do the leading TSFMs trained with the real-world corpus perform better than those trained with synthetic data?
1.1. Related Studies Due to the absence of covariate modeling, the generalization of univariate TSFM remains limited. Recent TSFMs have begun to explicitly incorporate multivariate modeling, involving Chronos-2 [16], COSMIC [22], 2
Toto [23], GTT [24], TabPFN-TS [25], and Moirai-1 [26]. Among them, Chronos-2, pretrained on hundreds of millions of multivariate time series data, achieves substantial improvements over univariate TSFMs [16, 26]. Nevertheless, existing real-world multivariate time series datasets still fall short in terms of quantity and quality, challenging the training and evaluation of large-scale multivariate TSFMs [20]. As an alternative, synthetic time series data has been increasingly explored and used primarily for training multivariate TSFMs [16], which are easier to obtain at scale. Various synthetic time series generation methods have been explored, ranging from classical statistical models and simulation-based approaches to deep generative models such as GANs, VAEs, and diffusion models [27, 28, 29]. For example, the Chronos family uses synthetic time series generated by AR and ETS models, TSI, and KernelSynth [30, 31, 32, 33]. Despite the scalability and flexibility of synthetic time series data, it is often constrained by the assumptions of the generation process and may fail to faithfully preserve real-world complex patterns and complex cross-variable dependencies [20]. Recent evidence further shows that TSFMs pretrained on synthetic multivariate datasets and performing well on standard benchmarks may still struggle with realworld temporal dynamics [21]. Recent TSFMs have incorporated real-world time series into model development [26, 23], and dedicated benchmarks have also been introduced to evaluate models under realistic multivariate forecasting scenarios [34, 35, 36]; however, existing real-world multivariate time series datasets remain limited in quantity and quality, insufficient to fully support the pretraining of large-scale multivariate TSFMs [37]. Moreover, it is also necessary to build a testbed from multivariate real-world time series data, used to comprehensively evaluate the pretraining and downstream performance of multivariate TSFMs [34].
1.2. Our Contributions In this paper, we provide comprehensive investigations on the effects of multivariate TSFMs trained with synthetic and realistic time series data. We establish the Real-world Multivariate tIme Series Corpus (RMISC), which is a considerably large-scale, high-quality, openly accessible, real-world, and multivariate time series archive, as summarized in Table 3. The RMISC corpus contains around 200 datasets and 142 billion time points, collected from real-world scenarios with open and legal licenses, and supports pretraining and benchmarking of multivariate TSFMs. Furthermore, we empirically compare the convergence and generalization of four advanced TSFMs pretrained on univariate, synthetic multivariate, and real-world multivariate data that corresponds to our proposed RMISC corpus. Specifically, the conducted TSFMs involve Chronos-2 [16], GTT [24], Moirai-2.0 [26], and TimesFM2.5 [38], where the former two are multivariate TSFMs while the latter two are univariate ones. In-distribution performance is measured on in-distribution evaluation sets, while the zero-shot generalization capability is measured on standard out-of-distribution benchmarks that consist of GIFT-Eval [35] and fev-bench [34]. As a 3
Table 1: A compact summary of RMISC datasets, where “Obs.” refers to the total count of time points. Dataset
Domain
Obs. Dataset
Domain
Obs. Dataset
Domain
Obs. Dataset
Domain
ACSF1[39, 40] Energy 0.29 M CMIP6-2005-PartII[41, 42] Environment 1056.50 M SP500KnownOpen[43] Finance 3.01 M CSTSNonnormalTrain[44] Others Environment 1056.49 M StockFactorsCleaned Finance 1133.71 M CSTSNormalTest[44] Others ApplianceEnergy[45] Energy 0.51 M CMIP6-2005-PartIII[41, 42] AustralianElectricityDemand[46] Energy 1.15 M CMIP6-2010-PartI[41, 42] Environment 1056.50 M StockMarketData Finance 0.69 M CSTSNormalTrain[44] Others AzurePublicDatasetV1[47] Energy 3060.08 M CMIP6-2010-PartII[41, 42] Environment 1056.50 M TourismMonthly[41] Finance 0.10 M Car[48] Others Environment 1056.49 M TushareETFDaily Finance 24.36 M CinCECGTorso Others AzurePublicDatasetV2[47] Energy 4968.71 M CMIP6-2010-PartIII[41, 42] BDG2-Bear[49, 41] Energy 1.42 M ERA5HourlySingleLevels[50] Environment 462.92 M TushareIndexDaily Finance 26.40 M Covid[51, 52] Others BDG2-Fox[49, 41] Energy 2.29 M GasSensorTemperature[53] Environment 76.86 M TushareStockDaily Finance 155.79 M CovidDeaths[54] Others Environment 5.63 M TushareStockDailyMetrics Finance 196.43 M CovidMobility[55] Others BDG2-Panther[49, 41] Energy 0.89 M GlobalClimateChange BDG2-Rat[49, 41] Energy 4.60 M KDDCup2018[56] Environment 0.54 M TushareStockWeekly Finance 32.64 M Darts Others BatteryRUL Energy 0.14 M OikolabWeather[57] Environment 0.80 M UKEconomy Finance 0.40 M EMG4Gestures[58] Others BritainCoal Energy 7.96 M PM25FiveCities[59] Environment 1.15 M WeeklyFuelPricesItaly Finance 0.02 M EbayServer[60, 61] Others BuildingsBenchComAmy[62] Energy 3040.60 M Subseasonal[63] Environment 5668.67 M WeeklyRoadFuelPrices Finance 0.002 M EigenWorms[64] Others BuildingsBenchComTmy[62] Energy 3026.98 M TemperatureRain[65] Environment 1.17 M BTS[66] Industry 95.87 M FordA Others BuildingsBenchRealCSV[62] Energy 39.64 M Tigge[67] Environment 21.01 M Behavior-1k[68] Industry 37682.52 M Gait[69] Others BuildingsBenchResAmy[62] Energy 4815.70 M USAirPollution Environment 24.45 M FrothFlotation Industry 0.04 M HAR70Plus[70] Others BuildingsBenchResTmy[62] Energy 4815.72 M Weather[71] Environment 14.72 M GasPipeline[72] Industry 1.38 M HARTH[73] Others Environment 43783.91 M GasSensorDynamic[74] Industry 37.75 M HetergeneousHAR[75] Others Bull[41] Energy 0.50 M WeatherBench5-625deg[67] Computers Energy 0.36 M WeatherTest Environment 1.11 M LBNL[76] Industry 122.27 M HungarianChickenpoxCases[77] Others ERCOT Energy 1.39 M XiamenAirQuality Environment 9.10 M OccupancyDetection[78] Industry 0.12 M Illness Others Finance 3.71 M PUMP Industry 9.69 M IndoorLocalisation[81] Others ETT[79] Energy 1.22 M AMarketChina[80] ETTMulti[79] Energy 1.22 M AMarketChinaKnownOpen[80] Finance 3.71 M ProEnFo[82] Industry 5.31 M InlineSkate[83] Others Electricity[84] Energy 8.44 M AliCar Finance 0.01 M RoomOccupancy[85] Industry 0.17 M KeplerLightCurves[86] Others Finance 2.83 M SWAT[88] Industry 7.93 M LargeST Others ElectricityHourly[87] Energy 8.44 M Bitcoin GFC2012[41, 82] Energy 0.50 M Bizitobs application[35, 89] Finance 0.02 M ServerMachineDataset[90] Industry 21.99 M M3 Others Hog[26, 41] Energy 0.37 M Bizitobs l2c H[35, 89] Finance 0.02 M SmellSensor Industry 402.56 M M4 Others HouseholdPower[91] Energy 14.53 M CSI500 Finance 643.70 M WADI Industry 23.96 M MelbournePedestrianCounts[92] Others Ideal[26, 41] Energy 1.25 M CausalEffects Finance 0.11 M BeijingSubway[93] Traffic 2.98 M MiniApp[94] Others LondonSmartMeters[95] Energy 71.93 M ChinaMinuteStock Finance 6480.79 M ChengduTaxi[96] Traffic 2.85 M MotionSense[97] Others OPSD Energy 22.90 M Cif2016-12[26, 41] Finance 0.006 M LoopSeattleLA[98] Traffic 15.89 M MotorTemperature[99] Others Finance 0.0006 M Mdense[100] Traffic 0.02 M MZVAV[101] Others OPSD-Household Energy 47.88 M Cif2016-6[26, 41] OPSD-PV-Wind[102, 103] Energy 48.74 M Cryptocurrency Finance 9.87 M Metropt3[104] Traffic 15.73 M NAB[105] Others OPSD-When2Heat[106] Energy 45.61 M CryptocurrencyKnownOpen Finance 9.87 M MetroTraffic[107] Traffic 0.24 M PAMAP2[108] Others Finance 0.51 M PEMS-Bay-METRO-LA[15] Traffic 24.03 M Rebound Others OilWell[109] Energy 244.53 M Dominick[110] Pvdaq Energy 8.21 M ExchangeRate[111] Finance 0.06 M PEMSCalifornia[98] Traffic 38.22 M Satellite[112] Others ResidentialPower[113] Energy 525.09 M FavoritaSales[114] Finance 448.49 M QtrafficSpeed[115] Traffic 528.77 M SmartMeterAus30m Others ShellHackathon Energy 7.91 M FavoritaTransactions[114] Finance 0.25 M Rideshare[116] Traffic 0.38 M SmartMeterAus60m Others Solar10Minutes[117] Energy 7.20 M FavoritaTransactionsKnownOil[114] Finance 0.25 M SHandHZMetro[98] Traffic 20.38 M SmartMeterUK30m Others Solar4Seconds[118] Energy 7.40 M FredMD[119] Finance 0.08 M T-Drive[120, 121] Traffic 52.99 M SmartMeterUK60m Others SolarEnergy[111] Energy 7.20 M HierachicalSales[122] Finance 0.42 M Traffic[111] Traffic 15.12 M StarLightCurves[123] Others TetuanPowerConsumption[124] Energy 0.42 M KaggleTS Finance 0.05 M TrafficHourly[125] Traffic 15.12 M Sunspots Others UK-DALE[126] Energy 65.60 M M5[127] Finance 116.21 M WikiTrafficDaily[128] Traffic 304.48 M TimeMMD[129] Others WindElec Energy 3.01 M NIFTYStock Finance 4.24 M WikiTrafficWeekly[130] Traffic 16.39 M USBirths[131] Others Finance 4.24 M BCI Competetion IV 1[133] Others 177.37 M VehicleTrips[134] Others WindFarms[132] Energy 19.26 M NIFTYStockKnownOpen WindPower4secs[135] Energy 7.40 M NN5Daily[136] Finance 0.09 M BCI Competetion IV 2a[137] Others 143.09 M WISDM V1[138, 139] Others BeijingAirQuality[140] Environment 3.16 M Restaurant[41] Finance 0.03 M BCI Competetion IV 2b[141] Others 25.37 M WISDM V2[138, 139] Others BeutenbergWeather Environment 17.88 M Rohlik orders 1D[34] Finance 0.01 M BooksPerPerson Others 0.01 M WISDM V3[138, 139] Others CMIP6-2000-PartI[41, 42] Environment 1056.50 M Rohlik orders 1W[34] Finance 0.00 M BoschCNC[142] Others 102.20 M Worms Others CMIP6-2000-PartII[41, 42] Environment 1056.50 M Rossmann 1D[34] Finance 1.05 M BrainInvadersBi2014b[143] Others 573.90 M CMIP6-2000-PartIII[41, 42] Environment 1056.49 M Rossmann 1W[34] Finance 0.15 M CSE-CIC-IDS2018[144] Others 1266.17 M CMIP6-2005-PartI[41, 42] Environment 1056.50 M SP500[43] Finance 3.01 M CSTSNonnormalTest[44] Others 151.83 M
Obs. 151.68 M 151.83 M 151.68 M 0.07 M 2.33 M 0.01 M 0.05 M 0.09 M 0.71 M 38.14 M 3.44 M 27.95 M 2.46 M 1.27 M 15.82 M 27.75 M 98.90 M 0.01 M 0.01 M 1.88 M 1.22 M 5.89 M 4439.10 M 0.23 M 19.65 M 3.13 M 0.34 M 7.42 M 15.97 M 6.83 M 0.32 M 111.72 M 120.02 M 2.91 M 1034.22 M 345.93 M 500.65 M 167.62 M 9.46 M 0.003 M 0.10 M 0.01 M 0.0008 M 3.95 M 10.25 M 38.88 M 0.23 M
result, adding real-world multivariate data consistently leads to stronger and more robust performance in outof-distribution generalization. Specifically, we draw the following conclusions from our experiments: (1) The performance of TSFMs pretrained with multivariate time series consistently outperforms that of univariate data, highlighting the importance of modeling cross-variable dependencies; (2) Replacing synthetic multivariate data with real-world multivariate data yields improvements in both in-distribution and out-of-distribution generalization, potentially benefiting from more realistic temporal dynamics and richer cross-variable dependencies; (3) TSFMs pretrained with a balanced combination of real-world univariate data, synthetic multivariate data, and real-world multivariate data achieve the best overall performance, which we adopt as our final recommended pretraining recipe. The rest of this paper is organized as follows. Section 2 introduces the proposed RMISC corpus and its key properties. Section 3 conducts experiments to investigate how real-world multivariate data affects the performance of pretrained TSFMs. Section 4 concludes this work.
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Step 1 Data Sourcing ~200
A Large Scale ~2 M ~16 B ~142 B
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Impute Missing Values
Environment
timesteps timepoints
Finance
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Energy
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Industry
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kaggle
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Traffic Others
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Basic Information [Target] [Covariate] [Domain] [Frequency] [Quality] [Statistics]
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License Fully Open
+
Statistical Analyses
Specific Type
Ensure Traceability and Reproducibility
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Figure 2: The overall construction pipeline of the RMISC corpus.
2. RMISC Corpus
In this section, we formally introduce the RMISC corpus for both pretraining and benchmarking of multivariate TSFMs. The RMISC corpus is collected from real-world scenarios with open and legal licenses and preserves rich multivariate information with explicit target-covariate annotations. Thus, this corpus can support pretraining and evaluation of multivariate TSFMs under realistic forecasting scenarios where prediction targets, auxiliary covariates, and complex cross-variable dependencies are jointly considered. Table 1 summarizes the RMISC corpus in terms of dataset name, domain, and total number of observations, and the more detailed information of the RMISC corpus can be accessed from Appendix A.1. Constructing the RMISC corpus requires substantial data curation and engineering efforts beyond simple aggregation. Figure 2 illustrates the overall construction pipeline of the RMISC corpus, involving five key stages, i.e., data sourcing, data processing, schema unification, metadata construction, and dataset refinement. Stage 1: Data Sourcing. We first collect a large amount of real-world multivariate time series data from diverse sources and domains. Specifically, the resulting RMISC corpus consists of around 200 sub-datasets, 2 million time-series files, 16 billion timesteps, and 142 billion time points, spanning major real-world domains including energy, finance, environment, industry, traffic, etc. Stage 2: Data Processing. Real-world time series data is often noisy and has incomplete information across sources [3, 31]. This step adapts systematic data processing, including handling missing values and outliers, 5
joining correlated time series from multiple files, and transforming raw inputs into consistent time series representations, for enhancing the quality of the collected data. Stage 3: Schema Unification. To facilitate large-scale TSFM pretraining and evaluation, we organize the RMISC corpus in a hierarchical structure, where each subdataset is stored in an independent folder. Within each subdataset, time series data are sequentially partitioned into ordered Parquet files with consistent indexing. Stage 4: Metadata Construction. To ensure data traceability and facilitate reproducible research, we design a standardized metadata and provenance system. Each sub-dataset is associated with a metadata file that records prediction targets, covariates, domain, temporal frequency, and other dataset-level statistics. Since RMISC is fully open-source and curated from publicly available real-world multivariate time series datasets, the metadata additionally records the original data source and license information for each sub-dataset. Furthermore, BibTeX citation files are provided whenever formal references are available. Stage 5: Dataset Refinement. This step performs overall refinement and validation to further improve the overall reliability and usability of the RMISC corpus. Specifically, we conduct consistency checks across datasets, such as timestamp format standardization. Besides, we perform statistical analyses to assess dataset quality, with detailed results provided in Appendix A.2. Note that real-world time series data are inherently unevenly distributed across domains, as privacy-sensitive or commercially valuable sectors such as healthcare and finance often impose stricter constraints on data sharing, licensing, and redistribution [145]. To address cross-domain imbalance, we construct a balanced version of RMISC by selecting a compact yet domain-balanced subset from the full corpus. The balanced version contains approximately 15 billion time points and follows the same standardized organization as the full dataset. Together, these five stages ensure that the RMISC corpus is not only a large-scale collection of heterogeneous time series, but also a fully curated, standardized, and benchmark-ready corpus for multivariate TSFM research. Developers can access both the full and balanced versions of RMISC at Hugging Face1 .
3. Experiments
In this section, we empirically demonstrate the effectiveness of the proposed RMISC corpus. The experiments are performed to answer the question: Whether and to what extent do the leading TSFMs pretrained on the RMISC corpus perform better than those pretrained on univariate and synthetic multivariate data in terms of convergence, in-distribution (ID), and out-of-distribution (OOD) performance? 1 https://huggingface.co/datasets/nju-zhangsq/RMISC
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Table 2: Configurations of model architecture and pretraining, where dmodel , dff , and dkv denote the embedding dimension, hidden dimension of feed-forward networks, and key-value dimension, respectively. Model
Model Architecture Configuration
Model Pretraining Configuration
Modeling Type
Layers
dmodel
Heads
dff
dkv
Size
Learning Rate
Batch Size
Optimizer
Chronos-2
Multivariate
12
768
12
3072
64
∼120M
1e-4
64
AdamW
GTT
Multivariate
8
512
12
3072
64
∼70M
1e-4
32
AdamW
Moirai-2.0
Univariate
12
768
12
3072
64
∼120M
1e-3
256
AdamW
TimesFM-2.5
Univariate
10
1024
16
1024
64
∼70M
1e-4
768
AdamW
3.1. Configurations Datasets. Here, we investigate three types of time series corpora, that is, a real-world univariate corpus, a synthetic multivariate corpus, and our proposed RMISC. The Real-world Univariate corpus, denoted as the RU corpus, is derived from the Chronos-2 training corpus. It consists of real-world univariate time series selected from the training corpora of Chronos [30] and GIFT-Eval [35], comprising approximately 55B univariate time points. The Synthetic Multivariate corpus, denoted as the SM corpus, is constructed following the synthetic data construction pipeline of Chronos-2 and comprises approximately 150B time points. Since the exact synthetic multivariate corpus used in Chronos-2 is not publicly released, we reproduce this pipeline to construct our own synthetic multivariate time series dataset. Specifically, we first generate base univariate time series using autoregressive (AR) models, exponential smoothing (ETS) models, TSI, and KernelSynth [30, 31, 32, 33]. We then apply multivariatizers to these base time series, introducing contemporaneous and sequential dependencies to obtain multivariate time series that form the SM corpus. The proposed RMISC corpus serves as the Realworld Multivariate corpus, denoted as the RM corpus. For each corpus, we randomly sample 20M instances for pretraining using an 80% rule. Specifically, for subdatasets with more than 10 time-series files, we apply a file-level split, where all time steps from the first 80% of time-series files are used for training. For the remaining subdatasets, where a file-level split would be less reliable due to the limited number of files, we apply a temporal split, using the first 80% of time steps in each time series for training. Based on the sampled RU, SM, and RM corpora, we construct seven training corpora corresponding to all non-empty subsets of the three sources, including three single-source corpora, three two-source combinations, and one three-source combination. Models. We consider four representative TSFMs, including Chronos-2 [16], GTT [24], Moirai-2.0 [26], and TimesFM-2.5 [38]. Chronos-2 and GTT are multivariate TSFMs trained with multivariate inputs and can explicitly incorporate covariates, whereas Moirai-2.0 and TimesFM-2.5 follow a univariate modeling paradigm. For the multivariate models, target variables and covariates are provided according to their native multivariate input formats. For the univariate models, each multivariate time series is decomposed into multiple univariate series, which are then treated as independent training instances, neglecting the corresponding covariates and 7
cross-variable dependencies. Specifically, for TimesFM-2.5, although pretraining and validation are conducted in a univariate manner, we use its XReg interface during the downstream OOD benchmark to incorporate available covariates, which adjust the model forecasts using external regressors. Table 2 lists the recommended model settings of the four TSFMs. We conduct separate pretraining runs for each TSFM on the seven training corpora, where the pretraining task is formulated as forecasting future values from historical observations. To focus the comparison on the effect of different training corpora, we keep the overall pretraining protocol consistent with Chronos-2. For each training instance, we randomly crop a context window from the original time series, with the context length ranging from 64 to 1984, and use it to predict the subsequent 64 time steps. This strategy exposes the models to diverse context lengths during pretraining and helps maintain their performance on shorter time series. To ensure consistency of multivariate inputs, we restrict the maximum number of channels for a time series sample to 24, including targets and covariates. To achieve a unified numerical magnitude for time series samples across different datasets, we apply robust instance normalization to each training instance. Specifically, we standardize both the historical context and the prediction window of each variable using the mean and standard deviation computed from the historical context. Then, we apply an inverse hyperbolic sine transformation to reduce the influence of extreme values. Table 2 provides further details of the pretraining settings of the models. Evaluation. Our evaluation includes ID and OOD testing. For ID evaluation, we randomly sample 5M instances from the held-out portion of each corpus as the validation dataset, which corresponds to the remaining 20% after constructing the training split. Since different TSFMs adopt different training objectives, we measure ID performance using the native loss function of each pretrained model. Specifically, Chronos-2 is evaluated with Sum Quantile Loss (SQL), GTT with Huber Loss (HL), Moirai-2.0 with Weighted Quantile Loss (WQL), and TimesFM-2.5 with a combination of HL and WQL. For OOD evaluation, we evaluate the pretrained TSFMs on two widely used time series forecasting benchmarks, that is, GIFT-Eval [35] and fev-bench [34]. To ensure a fair evaluation and avoid potential data leakage, all benchmark datasets overlapping with the pretraining data are excluded, and the remaining are used for OOD evaluation. All models are evaluated directly without dataset-specific fine-tuning; the resulting forecasts reflect the zero-shot OOD generalization capability of the pretrained TSFMs. We also split each benchmark into univariate and multivariate subsets. When the prediction horizons become longer than the native output length of the pretrained models, we employ autoregressive rolling prediction. Following the standard evaluation protocols of these benchmarks, we report mean absolute scaled error (MASE) for point forecasting and WQL for probabilistic forecasting. All experiments are conducted on NVIDIA RTX 5090 × 8 and 6000 Ada × 8.
3.2. In-distribution Forecasting To focus the comparison on the effect of different training corpora, we evaluate the models on the held-out ID set of the same corpus used for pretraining. Since ID evaluation preserves the original training objective of each 8