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

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

Strong Performance

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.

4

Step 1 Data Sourcing ~200

A Large Scale ~2 M ~16 B ~142 B

datasets

files

Step 2 Data Processing

Various Domains

Impute Missing Values

Environment

timesteps timepoints

Finance

Handle Outliers

Energy

Various Sources

Industry

…

kaggle

Join Relevant Time Series

Traffic Others

Type string float

Variable timestamp pressure

Type string float

Variable timestamp

Type string

humidity pressure

float float

Enhance Data Quality

Address Data Scarce

Step 3 Schema Unification

Step 4 Metadata Construction

Step 5 Dataset Refinement

NUSITS/

Basic Information [Target] [Covariate] [Domain] [Frequency] [Quality] [Statistics]

Consistency Checks yyyy-mm-dd yyyy-mm-dd Timestamp yyyy/mm/dd

Dataset_n/

Dataset_1/ 0.parquet 1.parquet

… n.parquet

𝒙𝒙𝟏𝟏 𝒙𝒙𝟐𝟐

Variable timestamp humidity

…

𝒄𝒄𝟏𝟏 Time 10:00 11:00

… 𝒄𝒄𝟐𝟐 Humidity 60% 55%

0.parquet 1.parquet

… n.parquet 𝒄𝒄𝟑𝟑 Pressure 1013.2 1012.9

…

Facilitate Pretraining and Evaluation

…

Source Dataset Link + BibTeX Citation

Cross-Domain Rebalancing

License Fully Open

+

Statistical Analyses

Specific Type

Ensure Traceability and Reproducibility

Ensure Reliability and Usability

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

6

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

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Figure 3: Training and ID loss curves of four TSFMs on different training corpora of the first epoch.

model, we compare ID results within each model across different pretraining corpora and training progress, rather than directly comparing results across models. Figures 3 and 4 present the training and ID loss curves of four investigated TSFMs during pretraining. Both TimesFM-2.5 and Moirai-2.0 converge within 1 epoch, as shown in Figure 3. In contrast, we observe that the training loss curves of both Chronos-2 and GTT indicate a downward trend within the first epoch. However, the ID loss curves become relatively stable by the end of the second epoch, as shown in Figure 4. Specifically, the ID loss curves of Chronos-2 decrease by less than 0.03 over the final quarter of the second epoch, while that of GTT decreases by less than 0.01. Moreover, we find that the second epoch does not consistently lead to better OOD benchmark performance than the first epoch, and even results in severe performance degradation in some cases, suggesting that additional training does not necessarily provide substantial OOD benefits, as detailed in Appendix B.2. Thus, we conclude that Chronos-2 and GTT also converge after 2 epochs. Summing up the training dynamics of both univariate and multivariate models, we observe that the RM corpus does not achieve the lowest ID loss among the single-source corpora in most cases, which suggests that realworld multivariate data do not necessarily make pretraining easier in terms of convergence or ID loss. This may be associated with more complex real-world patterns and richer cross-variable dependencies in the RM corpus,

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3.3. Out-of-Distribution Forecasting This subsection provides an overall comparison of the OOD performance of TSFMs pretrained with different training corpora. To provide a unified OOD comparison across univariate and multivariate TSFMs, we evaluate all models on both the univariate and multivariate subsets of the benchmarks. For univariate TSFMs, evaluation on the multivariate subsets follows the same decomposition strategy as in Subsection 3.1 and processes each variable independently, without using covariates or cross-variable dependencies. We count the average ranks across seven training corpora according to the OOD MASE scores of four TSFMs. Figure 5 reports the average ranks of seven corpora, where a lower rank indicates better forecasting performance that corresponds to the investigated corpus. It is observed that the RU corpus ranks last among all training corpora, suggesting the univariate dataset is less effective for pretraining TSFMs than the multivariate dataset. Furthermore, the RM corpus consistently outranks the SM corpus under both single-source-corpus and two-source-corpus pretraining. Specifically, the RM corpus achieves a better rank than the SM corpus, and the RU+RM corpus further outranks the RU+SM corpus. These results suggest that the real-world multivariate corpus is more advantageous for 10

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pretraining TSFMs than the synthetic multivariate corpus. Finally, the RU+SM+RM corpus achieves the best average rank, and the top three training corpora all contain the RM corpus. The comparisons indicate that incorporating a real-world multivariate corpus can further improve the performance of TSFMs. We further examine the detailed results on each TSFM and OOD benchmark subset. Figure 6 displays the MASE results on all datasets and subset benchmarks for the TSFMs. We have the following observations and conclusions. (1) We observe that the RU corpus performs worse than the other training corpora in most cases, indicating that using the univariate dataset alone is insufficient to achieve strong OOD performance in our experiments. (2) The relative performance between the SM corpus and the RM corpus varies across models and benchmarks. For Chronos-2, the SM corpus outperforms the RM corpus, and the RU+SM corpus outperforms the RU+RM corpus. For GTT, the SM corpus outperforms the RM corpus in most cases, while the RU+SM corpus and the RU+RM corpus show comparable performance. For Moirai-2.0 and TimesFM-2.5, the RM

11

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Figure 7: Forecasts generated by Chronos-2 models which are pretrained on the SM corpus and the RM corpus for two fev-bench tasks: (a) the electricity price forecasting task across the Pennsylvania, New Jersey, and Maryland zones and (b) the electricity load forecasting task from the ENTSO-E Transparency Platform. The forecasting horizon starts at the gray dashed vertical line, while the shaded area denotes the central 80% prediction interval around the median forecast. For visualization, each target and covariate series is normalized, and the early part of the context window is truncated to improve visibility.

corpus generally outperforms the SM corpus, and the RU+RM corpus outperforms the RU+SM corpus. These results indicate that neither the SM corpus nor the RM corpus is uniformly superior to the other, and both corpora have their respective strengths. (3) The RU+SM+RM corpus achieves the lowest MASE across most settings and reduces average MASE by 4.476% compared with the currently widely used RU+SM corpus. Based on this, we recommend the RU+SM+RM corpus as the preferred pretraining corpus for building stronger multivariate TSFMs. Detailed MASE and WQL results for the OOD benchmarks can be accessed from Appendix B.1.

3.4. Case Studies To visualize the advantage of real-world multivariate data in learning complex cross-variable dependencies, we compare the forecasts produced by the Chronos-2 model pretrained on the SM corpus and the RM corpus with respect to two representative samples, which cover simple and complex cross-variable dependencies, respectively. Figure 7(a) shows a price forecasting task across the Pennsylvania, New Jersey, and Maryland zones. In this task, the next-day electricity price is forecasted using covariates of system load forecasts and zonal COMED load forecasts. The target and the two covariates exhibit highly similar trends, indicating that the cross-variable dependencies are relatively clear and easy to capture. For this case, the models pretrained on the SM corpus and on the RM corpus achieve comparable MASE, suggesting that both real-world multivariate data and synthetic multivariate data are sufficient for learning relatively simple cross-variable dependencies. Figure 7(b) shows an hourly electricity load forecasting task from the ENTSO-E Transparency Platform. In this 12

task, electricity load is forecasted using covariates of diffuse horizontal radiation, direct horizontal radiation, and temperature. Unlike the previous case, the target and covariates do not follow highly similar trends and show more complex cross-variable dependencies. In this setting, the model pretrained on the RM corpus obtains a much lower MASE than that pretrained on the SM corpus, with 0.2134 for RM and 0.7697 for SM. This suggests that real-world multivariate data provides stronger support for learning complex cross-variable dependencies and improves forecasting accuracy in such challenging settings.

4. Conclusions

In this paper, we proposed the RMISC corpus for supporting pretraining and benchmarking TSFMs with largescale and real-world multivariate time series. In systematic comparisons with real-world univariate and synthetic multivariate corpora, we confirmed that the RMISC corpus provides valuable multivariate information from realistic contexts and can effectively complement existing pretraining data. In particular, the combination of realworld univariate data, synthetic multivariate data, and RMISC leads to more robust zero-shot generalization than the currently widely used pretraining corpus. These results suggest that our proposed RMISC corpus provides an effective data foundation for building multivariate TSFMs.

Acknowledgements

This research was supported by the Nanjing University-Siemens Joint Research Center for Industrial AI, Jiangsu Science and Technology Project (BG2024031).

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[95] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. London smart meters dataset (with missing values). Zenodo, 2020. [96] Dong Wang, Junbo Zhang, Wei Cao, Jian Li, and Yu Zheng. When will you arrive? Estimating travel time based on deep neural networks. In Proceedings of the 2018 AAAI Conference on Artificial Intelligence, pages 2500–2507, 2018. [97] Mohammad Malekzadeh, Richard G. Clegg, Andrea Cavallaro, and Hamed Haddadi. Mobile sensor data anonymization. In Proceedings of the 2019 International Conference on Internet of Things Design and Implementation, pages 49–58, 2019. [98] Jingyuan Wang, Jiawei Jiang, Wenjun Jiang, Chao Li, and Wayne Xin Zhao. LibCity: An open library for traffic prediction. In Proceedings of the 29th International Conference on Advances in Geographic Information Systems, page 145–148, 2021. [99] Wilhelm Kirchgässner, Oliver Wallscheid, and Joachim Böcker. Electric motor temperature. Kaggle, 2021. [100] Rodrigo de Medrano and Jose L Aznarte. A spatio-temporal attention-based spot-forecasting framework for urban traffic prediction. Applied Soft Computing, 96, 2020. [101] Jessica Granderson, Guanjing Lin, Ari Harding, Piljae Im, and Yan Chen. Dataset for building fault detection and diagnostics algorithm creation and performance testing. Figshare, 2020. [102] Stefan Pfenninger and Iain Staffell. Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data. Energy, 114:1251–1265, 2016. [103] Iain Staffell and Stefan Pfenninger. Using bias-corrected reanalysis to simulate current and future wind power output. Energy, 114:1224–1239, 2016. [104] Narjes Davari, Bruno Veloso, Rita Ribeiro, and Joao Gama. MetroPT-3 dataset. UCI Machine Learning Repository, 2021. [105] Subutai Ahmad, Alexander Lavin, Scott Purdy, and Zuha Agha. Unsupervised real-time anomaly detection for streaming data. Neurocomputing, 2017. [106] Oliver Ruhnau, Lion Hirth, and Aaron Praktiknjo. Time series of heat demand and heat pump efficiency for energy system modeling. Scientific Data, 6:189, 2019. [107] John Hogue. Metro interstate traffic volume. UCI Machine Learning Repository, 2019. [108] Attila Reiss. PAMAP2 physical activity monitoring. UCI Machine Learning Repository, 2012.

21

[109] Ricardo Emanuel Vaz Vargas, Celso José Munaro, Patrick Marques Ciarelli, André Gonçalves Medeiros, Bruno Guberfain do Amaral, Daniel Centurion Barrionuevo, Jean Carlos Dias de Araújo, Jorge Lins Ribeiro, and Lucas Pierezan Magalhães. A realistic and public dataset with rare undesirable real events in oil wells. Journal of Petroleum Science and Engineering, 181, 2019. [110] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Pablo Montero-Manso, and Rob Hyndman. Dominick dataset. Zenodo, 2020. [111] Guokun Lai, Weicheng Chang, Yiming Yang, and Hanxiao Liu. Modeling long-and short-term temporal patterns with deep neural networks. In Proceedings of the 41st International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 95–104, 2018. [112] Kyle Hundman, Valentino Constantinou, Christopher Laporte, Ian Colwell, and Tom Soderstrom. Detecting spacecraft anomalies using LSTMs and nonparametric dynamic thresholding. arXiv preprint arXiv:1802.04431, 2018. [113] Christoph Bergmeir, Quang Bui, Frits de Nijs, and Peter Stuckey. Residential power and battery data. Zenodo, 2023. [114] Corporación Favorita, Inversion, Julia Elliott, and Mark McDonald. Corporación Favorita grocery sales forecasting. Kaggle, 2017. [115] Binbing Liao, Jingqing Zhang, Chao Wu, Douglas McIlwraith, Tong Chen, Shengwen Yang, Yike Guo, and Fei Wu. Deep sequence learning with auxiliary information for traffic prediction. In Proceedings of the 24th ACM International Conference on Knowledge Discovery and Data Mining, pages 537–546, 2018. [116] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Rideshare dataset without missing values. Zenodo, 2021. [117] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Solar dataset (10 minutes observations). Zenodo, 2020. [118] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Mahdi Abolghasemi, Rob Hyndman, and Pablo Montero-Manso. Solar power dataset (4 seconds observations). Zenodo, 2020. [119] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Pablo Montero-Manso, and Rob Hyndman. FRED-MD dataset. Zenodo, 2020. [120] Jing Yuan, Yu Zheng, Xing Xie, and Guangzhong Sun. Driving with knowledge from the physical world. In Proceedings of the 17th International Conference on Knowledge Discovery and Data Mining, 2011.

22

[121] Jing Yuan, Yu Zheng, Chengyang Zhang, Wenlei Xie, Xing Xie, Guangzhong Sun, and Yan Huang. TDrive: Driving directions based on taxi trajectories. In Proceedings of the 18th International Conference on Advances in Geographic Information Systems, pages 99–108, 2010. [122] Paolo Mancuso, Veronica Piccialli, and Antonio M. Sudoso. Hierarchical sales data of an Italian grocery store. Mendeley Data, 2021. [123] Eamonn Keogh, Li Wei, Xiaopeng Xi, Sang-Hee Lee, and Michail Vlachos. LB Keogh supports exact indexing of shapes under rotation invariance with arbitrary representations and distance measures. In Proceedings of the 32nd International Conference on Very Large Data Bases, pages 882–893, 2006. [124] Abdulwahed Salam and Abdelaaziz El Hibaoui. Power consumption of Tetouan city. UCI Machine Learning Repository, 2018. [125] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Traffic hourly dataset. Zenodo, 2020. [126] Jack Kelly and William Knottenbelt. The UK-DALE dataset: Domestic appliance-level electricity demand and whole-house demand from five UK homes. Scientific Data, 2(150007), 2015. [127] Addison Howard, Spyros Makridakis, and Vangelis. M5 forecasting – accuracy. Kaggle, 2020. [128] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Kaggle Wikipedia web traffic daily dataset (without missing values). Zenodo, 2020. [129] Haoxin Liu, Shangqing Xu, Zhiyuan Zhao, Lingkai Kong, Harshavardhan Kamarthi, Aditya B. Sasanur, Megha Sharma, Jiaming Cui, Qingsong Wen, Chao Zhang, and B. Aditya Prakash. Time-MMD: A new multi-domain multimodal dataset for time series analysis. arXiv preprint arXiv:2406.08627, 2024. [130] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Kaggle Wikipedia web traffic weekly dataset. Zenodo, 2020. [131] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. US births dataset. Zenodo, 2020. [132] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Mahdi Abolghasemi, Rob Hyndman, and Pablo Montero-Manso. Wind farms dataset (without missing values). Zenodo, 2020. [133] Benjamin Blankertz, Guido Dornhege, Matthias Krauledat, Klaus-Robert Müller, and Gabriel Curio. The non-invasive Berlin brain-computer interface: Fast acquisition of effective performance in untrained subjects. NeuroImage, 37(2):539–550, 2007. [134] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. Vehicle trips dataset with missing values. Zenodo, 2021. 23

[135] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Mahdi Abolghasemi, Rob Hyndman, and Pablo Montero-Manso. Wind power dataset (4 seconds observations). Zenodo, 2020. [136] Rakshitha Godahewa, Christoph Bergmeir, Geoff Webb, Rob Hyndman, and Pablo Montero-Manso. NN5 daily dataset (with missing values). Zenodo, 2020. [137] Clemens Brunner, Robert Leeb, Gernot Müller-Putz, Alois Schlögl, and Gert Pfurtscheller. BCI competition 2008–Graz data set A. Institute for Knowledge Discovery (Laboratory of Brain-computer Interfaces), Graz University of Technology, 16(1-6):34, 2008. [138] Jennifer R. Kwapisz, Gary M. Weiss, and Samuel A. Moore. Activity recognition using cell phone accelerometers. In Proceedings of the 4th International Workshop on Knowledge Discovery from Sensor Data, 2010. [139] Gary M. Weiss and Jeffrey W. Lockhart. The impact of personalization on smartphone-based activity recognition. In Proceedings of the 2012 AAAI Workshop on Activity Context Representation: Techniques and Languages, 2012. [140] Song Chen. Beijing multi-site air quality. UCI Machine Learning Repository, 2017. [141] Robert Leeb, Clemens Brunner, G Müller-Putz, Alois Schlögl, and GJGUOT Pfurtscheller. BCI competition 2008–Graz data set B. Graz University of Technology, Austria, 16:1–6, 2008. [142] Mohamed-Ali Tnani, Michael Feil, and Klaus Diepold. Smart data collection system for brownfield CNC milling machines: A new benchmark dataset for data-driven machine monitoring. Procedia CIRP, 107: 131–136, 2022. [143] Louis Korczowski, Ekaterina Ostaschenko, Anton Andreev, Grégoire Cattan, Pedro Luis Coelho Rodrigues, Violette Gautheret, and Marco Congedo. Brain invaders solo versus collaboration: Multi-user P300-based brain-computer interface dataset(bi2014b). Zenodo, 2019. [144] Iman Sharafaldin, Arash Habibi Lashkari, and Ali A. Ghorbani. Toward generating a New intrusion detection dataset and intrusion traffic characterization. In Proceedings of the 4th International Conference on Information Systems Security and Privacy, 2018. [145] Mauro Giuffrè and Dennis L Shung. Harnessing the power of synthetic data in healthcare: Innovation, application, and privacy. NPJ Digital Medicine, 6(1):186, 2023.

24

Appendix This appendix provides the supplementary materials for our work “RMISC: A Large-scale Real-world Multivariate Corpus for Time Series Foundation Models”.

A. Characteristics of the RMISC Corpus

A.1. Full properties of the RMISC Corpus Table 3 summarizes the datasets and key properties of RMISC, including domain, frequency, dimensionality, scale, and original source. Table 3: Datasets and key properties of RMISC. “Freq.” denotes the sampling frequency (ms = millisecond, s = second, min = minute, h = hour, d = day, m = month, y = year, “-” signifies multiple values or unknown frequency); “Dim.” represents the average dimension of the dataset; “Time Steps” represents the number of time steps within the dataset; “Obs.” refers to the total count of time points; and “Source” denotes the original paper or resource of the dataset. Dataset

Domain

Freq.

Dim.

Time Steps

Obs.

Source

ACSF1

Energy

-

1

0.29 M

0.29 M

[39, 40]

ApplianceEnergy

Energy

10min

26

0.02 M

0.51 M

[45]

AustralianElectricityDemand

Energy

30min

5

0.23 M

1.15 M

[46]

AzurePublicDatasetV1

Energy

5min

3

1020.38 M

3060.08 M

[47]

AzurePublicDatasetV2

Energy

5min

3

1656.28 M

4968.71 M

BDG2-Bear

Energy

h

1

1.42 M

1.42 M

[49, 41]

[47]

BDG2-Fox

Energy

h

1

2.29 M

2.29 M

[49, 41]

BDG2-Panther

Energy

h

1

0.89 M

0.89 M

[49, 41]

BDG2-Rat

Energy

h

1

4.60 M

4.60 M

[49, 41]

BatteryRUL

Energy

-

9

0.02 M

0.14 M

Kaggle2

BritainCoal

Energy

-

10

0.80 M

7.96 M

Data.World3

BuildingsBenchComAmy

Energy

h

148

20.59 M

3040.60 M

[62]

BuildingsBenchComTmy

Energy

h

147

20.59 M

3026.98 M

[62]

BuildingsBenchRealCSV

Energy

h

2

22.25 M

39.64 M

[62]

BuildingsBenchResAmy

Energy

h

235

20.46 M

4815.70 M

[62]

BuildingsBenchResTmy

Energy

h

235

20.46 M

4815.72 M

[62]

Bull

Energy

-

1

0.50 M

0.50 M

[41]

Computers

Energy

2min

1

0.36 M

0.36 M

TSC.4

ERCOT

Energy

h

8

0.17 M

1.39 M

ERCOT5

ETT

Energy

15min

7

0.17 M

1.22 M

[79]

Continued on next page

2 https://www.kaggle.com/ 3 https://data.world/ 4 https://www.timeseriesclassification.com/ 5 https://www.ercot.com/

25

Table 3 – continued from previous page Dataset

Domain

Freq.

Dim.

Time Steps

Obs.

Source

ETTMulti

Energy

15min

7

0.17 M

1.22 M

[79]

Electricity

Energy

-

321

0.03 M

8.44 M

[84]

ElectricityHourly

Energy

h

321

0.03 M

8.44 M

[87]

GFC2012

Energy

h

1

0.50 M

0.50 M

[41, 82] [26, 41]

Hog

Energy

h

1

0.37 M

0.37 M

HouseholdPower

Energy

h

7

2.08 M

14.53 M

[91]

Ideal

Energy

h

1

1.25 M

1.25 M

[26, 41]

LondonSmartMeters

Energy

30min

1

71.93 M

71.93 M

[95]

OPSD

Energy

h

8

2.86 M

22.90 M

OPSD6

OPSD-Household

Energy

15min

7

7.12 M

47.88 M

OPSD

OPSD-PV-Wind

Energy

h

4

12.62 M

48.74 M

[102, 103]

OPSD-When2Heat

Energy

h

22

2.09 M

45.61 M

[106]

OilWell

Energy

-

5

50.91 M

244.53 M

[109]

Pvdaq

Energy

15min

2

3.97 M

8.21 M

OEDI7

ResidentialPower

Energy

min

2

262.85 M

525.09 M

[113]

ShellHackathon

Energy

-

15

0.53 M

7.91 M

Kaggle

Solar10Minutes

Energy

10min

137

0.05 M

7.20 M

[117]

Solar4Seconds

Energy

4s

1

7.40 M

7.40 M

[118]

SolarEnergy

Energy

10min

137

0.05 M

7.20 M

[111]

TetuanPowerConsumption

Energy

10min

8

0.05 M

0.42 M

[124]

UK-DALE

Energy

-

2

30.20 M

65.60 M

[126]

WindElec

Energy

15min

13

0.23 M

3.01 M

DCIC8

WindFarms

Energy

min

295

0.07 M

19.26 M

[132]

WindPower4secs

Energy

4s

1

7.40 M

7.40 M

[135]

BeijingAirQuality

Environment

h

8

0.42 M

3.16 M

[140]

BeutenbergWeather

Environment

-

20

0.89 M

17.88 M

Kaggle

CMIP6-2000-PartI

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2000-PartII

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2000-PartIII

Environment

6h

1

1056.49 M

1056.49 M

[41, 42]

CMIP6-2005-PartI

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2005-PartII

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2005-PartIII

Environment

6h

1

1056.49 M

1056.49 M

[41, 42]

CMIP6-2010-PartI

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2010-PartII

Environment

6h

1

1056.50 M

1056.50 M

[41, 42]

CMIP6-2010-PartIII

Environment

6h

1

1056.49 M

1056.49 M

[41, 42]

ERA5HourlySingleLevels

Environment

h

15

30.86 M

462.92 M

[50]

GasSensorTemperature

Environment

-

20

3.84 M

76.86 M

[53]

GlobalClimateChange

Environment

m

2

2.81 M

5.63 M

Data.World

KDDCup2018

Environment

h

50

0.01 M

0.54 M

[56]

OikolabWeather

Environment

h

8

0.10 M

0.80 M

[57]

PM25FiveCities

Environment

h

10

0.11 M

1.15 M

[59]

Subseasonal

Environment

d

60

93.79 M

5668.67 M

[63]

TemperatureRain

Environment

d

1614

0.0007 M

1.17 M

[65]

Tigge

Environment

6h

194

0.11 M

21.01 M

[67]

USAirPollution

Environment

-

14

1.75 M

24.45 M

Data.World

Weather

Environment

d

1

14.72 M

14.72 M

[71]

Continued on next page

6 https://data.open-power-system-data.org/ 7 https://data.openei.org/ 8 https://www.dcic-china.com/competitions/10098/datasets

26

Table 3 – continued from previous page Dataset

Domain

Freq.

Dim.

Time Steps

Obs.

Source

WeatherBench5-625deg

Environment

h

61

684.84375 M

43783.91 M

[67]

WeatherTest

Environment

-

21

0.05 M

1.11 M

MPIB9

XiamenAirQuality

Environment

h

6

1.54 M

9.10 M

DataCastle10

AMarketChina

Finance

-

6

0.62 M

3.71 M

[80]

AMarketChinaKnownOpen

Finance

-

6

0.62 M

3.71 M

[80]

AliCar

Finance

-

2

0.005 M

0.01 M

Aliyun11

Bitcoin

Finance

d

645

0.004 M

2.83 M

Kaggle

Bizitobs application

Finance

10s

1

0.01 M

0.02 M

[35, 89]

Bizitobs l2c H

Finance

h

1

0.00 M

0.02 M

[35, 89]

CSI500

Finance

min

7

91.96 M

643.70 M

CSI12

CausalEffects

Finance

-

100

0.001 M

0.11 M

Data.World

ChinaMinuteStock

Finance

min

13

498.52 M

6480.79 M

Hugging Face13

Cif2016-12

Finance

m

1

0.006 M

0.006 M

[26, 41]

Cif2016-6

Finance

m

1

0.0006 M

0.0006 M

[26, 41]

Cryptocurrency

Finance

-

5

1.97 M

9.87 M

Kaggle

CryptocurrencyKnownOpen

Finance

-

5

1.97 M

9.87 M

Kaggle

Dominick

Finance

-

1298

0.0004 M

0.51 M

[110]

ExchangeRate

Finance

-

8

0.01 M

0.06 M

[111]

FavoritaSales

Finance

d

28

15.85 M

448.49 M

[114]

FavoritaTransactions

Finance

d

3

0.08 M

0.25 M

[114]

FavoritaTransactionsKnownOil

Finance

d

3

0.08 M

0.25 M

[114]

FredMD

Finance

m

110

0.0007 M

0.08 M

[119]

HierachicalSales

Finance

d

234

0.002 M

0.42 M

[122]

KaggleTS

Finance

-

6

0.01 M

0.05 M

Kaggle

M5

Finance

-

318

0.37 M

116.21 M

[127]

NIFTYStock

Finance

-

9

0.47 M

4.24 M

Kaggle

NIFTYStockKnownOpen

Finance

-

9

0.47 M

4.24 M

Kaggle

NN5Daily

Finance

d

114

0.0008 M

0.09 M

[136]

Restaurant

Finance

-

1

0.03 M

0.03 M

[41]

Rohlik orders 1D

Finance

d

7

0.01 M

0.01 M

[34]

Rohlik orders 1W

Finance

w

7

0.00 M

0.00 M

[34]

Rossmann 1D

Finance

d

1115

1.05 M

1.05 M

[34]

Rossmann 1W

Finance

w

1115

0.15 M

0.15 M

[34]

SP500

Finance

-

5

0.60 M

3.01 M

[43]

SP500KnownOpen

Finance

-

5

0.60 M

3.01 M

StockFactorsCleaned

Finance

m

70

16.20 M

1133.71 M

StockMarketData

Finance

-

70

0.01 M

0.69 M

TourismMonthly

Finance

m

1

0.10 M

0.10 M

[41]

TushareETFDaily

Finance

d

10

2.44 M

24.36 M

Tushare14

[43] Hugging Face Kaggle

TushareIndexDaily

Finance

d

11

2.64 M

26.40 M

Tushare

TushareStockDaily

Finance

d

11

14.16 M

155.79 M

Tushare

TushareStockDailyMetrics

Finance

d

14

14.03 M

196.43 M

Tushare

TushareStockWeekly

Finance

w

11

2.97 M

32.64 M

Tushare

Continued on next page

9 https://www.bgc-jena.mpg.de/wetter/ 10 https://challenge.datacastle.cn/v3/cmptDetail.html?id=950 11 https://tianchi.aliyun.com/competition/entrance/231641/information 12 https://www.csindex.com.cn 13 https://huggingface.co/ 14 https://tushare.pro/

27

Table 3 – continued from previous page Dataset

Domain

Freq.

Dim.

Time Steps

Obs.

Source

UKEconomy

Finance

-

1

0.39 M

0.40 M

Data.World

WeeklyFuelPricesItaly

Finance

w

4

0.005 M

0.02 M

Data.World

WeeklyRoadFuelPrices

Finance

w

2

0.0009 M

0.002 M

Data.World

BTS

Industry

-

1495

0.06 M

95.87 M

[66]

Behavior-1k

Industry

-

446

84.40 M

37682.52 M

[68]

FrothFlotation

Industry

-

12

0.003 M

0.04 M

Kaggle

GasPipeline

Industry

-

10

0.14 M

1.38 M

[72]

GasSensorDynamic

Industry

-

18

2.10 M

37.75 M

[74]

LBNL

Industry

min

61

1.99 M

122.27 M

[76]

OccupancyDetection

Industry

-

6

0.02 M

0.12 M

[78]

PUMP

Industry

-

44

0.22 M

9.69 M

Kaggle

ProEnFo

Industry

h

23

0.23 M

5.31 M

[82]

RoomOccupancy

Industry

30s

17

0.01 M

0.17 M

[85]

SWAT

Industry

5s

42

0.19 M

7.93 M

[88]

ServerMachineDataset

Industry

-

31

0.71 M

21.99 M

[90]

SmellSensor

Industry

m

19

21.19 M

402.56 M

Hugging Face

WADI

Industry

5s

93

0.26 M

23.96 M

Kaggle

BeijingSubway

Traffic

30min

276

0.01 M

2.98 M

[93]

ChengduTaxi

Traffic

-

4

0.71 M

2.85 M

[96]

LoopSeattleLA

Traffic

5min

258

0.06 M

15.89 M

[98]

Mdense

Traffic

-

1

0.02 M

0.02 M

[100]

Metropt3

Traffic

-

15

1.05 M

15.73 M

[104]

MetroTraffic

Traffic

-

5

0.05 M

0.24 M

[107]

PEMS-Bay-METRO-LA

Traffic

5min

278

0.09 M

24.03 M

[15]

PEMSCalifornia

Traffic

-

361

0.11 M

38.22 M

[98]

QtrafficSpeed

Traffic

-

2

264.39 M

528.77 M

[115] [116]

Rideshare

Traffic

h

1969

0.0002 M

0.38 M

SHandHZMetro

Traffic

15min

241

0.08 M

20.38 M

[98]

T-Drive

Traffic

10min

3

17.66 M

52.99 M

[120, 121]

Traffic

Traffic

h

862

0.02 M

15.12 M

[111]

TrafficHourly

Traffic

h

862

0.02 M

15.12 M

[125]

WikiTrafficDaily

Traffic

d

1

304.48 M

304.48 M

[128]

WikiTrafficWeekly

Traffic

w

1

16.39 M

16.39 M

[130]

BCI Competetion IV 1

Others

10ms

59

3.01 M

177.37 M

[133]

BCI Competetion IV 2a

Others

4ms

19

7.39 M

143.09 M

[137]

BCI Competetion IV 2b

Others

4ms

3

8.46 M

25.37 M

[141]

BooksPerPerson

Others

-

1

0.01 M

0.01 M

Data.World

BoschCNC

Others

500us

3

34.07 M

102.20 M

[142]

BrainInvadersBi2014b

Others

2ms

33

17.39 M

573.90 M

[143]

CSE-CIC-IDS2018

Others

-

78

16.23 M

1266.17 M

[144]

CSTSNonnormalTest

Others

s

4

37.96 M

151.83 M

[44]

CSTSNonnormalTrain

Others

s

4

37.92 M

151.68 M

[44]

CSTSNormalTest

Others

s

4

37.96 M

151.83 M

[44]

CSTSNormalTrain

Others

s

4

37.92 M

151.68 M

[44]

Car

Others

-

1

0.07 M

0.07 M

[48]

CinCECGTorso

Others

-

1

2.33 M

2.33 M

TSC.

Covid

Others

-

7

0.001 M

0.01 M

[51, 52]

CovidDeaths

Others

-

236

0.0002 M

0.05 M

[54]

CovidMobility

Others

d

218

0.0004 M

0.09 M

[55]

Continued on next page

28

Table 3 – continued from previous page Dataset

Domain

Freq.

Dim.

Time Steps

Obs.

Source

Darts

Others

-

15

0.05 M

0.71 M

Darts15

EMG4Gestures

Others

-

9

4.24 M

38.14 M

[58]

EbayServer

Others

-

26

0.13 M

3.44 M

[60, 61]

EigenWorms

Others

-

6

4.66 M

27.95 M

[64]

FordA

Others

-

1

2.46 M

2.46 M

TSC.

Gait

Others

-

7

0.18 M

1.27 M

[69]

HAR70Plus

Others

-

7

2.26 M

15.82 M

[70]

HARTH

Others

-

7

3.96 M

27.75 M

[73]

HetergeneousHAR

Others

5ms

7

14.13 M

98.90 M

[75]

HungarianChickenpoxCases

Others

-

19

0.0005 M

0.01 M

[77]

Illness

Others

w

10

0.001 M

0.01 M

FluView16

IndoorLocalisation

Others

100ms

12

0.15 M

1.88 M

[81]

InlineSkate

Others

-

1

1.22 M

1.22 M

[83]

KeplerLightCurves

Others

-

1

5.89 M

5.89 M

[86]

LargeST

Others

5min

125

35.66 M

4439.10 M

Kaggle

M3

Others

-

1

0.23 M

0.23 M

Monash TSF.17

M4

Others

-

1

19.65 M

19.65 M

Monash TSF.

MelbournePedestrianCounts

Others

h

1

3.13 M

3.13 M

[92]

MiniApp

Others

-

26

0.01 M

0.34 M

[94]

MotionSense

Others

-

3

2.47 M

7.42 M

[97]

MotorTemperature

Others

-

12

1.33 M

15.97 M

[99]

MZVAV

Others

-

17

0.40 M

6.83 M

[101] [105]

NAB

Others

-

1

0.32 M

0.32 M

PAMAP2

Others

10ms

41

2.72 M

111.72 M

[108]

Rebound

Others

-

6001

0.02 M

120.02 M

Hugging Face

Satellite

Others

-

15

0.19 M

2.91 M

SmartMeterAus30m

Others

30min

2

344.74 M

1034.22 M

Hugging Face

[112]

SmartMeterAus60m

Others

h

2

172.97 M

345.93 M

Hugging Face

SmartMeterUK30m

Others

30min

2

166.88 M

500.65 M

Hugging Face

SmartMeterUK60m

Others

h

2

83.81 M

167.62 M

Hugging Face

StarLightCurves

Others

-

9.24 K

1.02 K

9.46 M

[123]

Sunspots

Others

-

1

0.003 M

0.003 M

Kaggle

TimeMMD

Others

-

3

0.02 M

0.10 M

[129]

USBirths

Others

-

1

0.01 M

0.01 M

[131]

VehicleTrips

Others

d

4

0.0002 M

0.0008 M

[134]

WISDM V1

Others

50ms

4

0.99 M

3.95 M

[138, 139]

WISDM V2

Others

50ms

4

2.69 M

10.25 M

[138, 139]

WISDM V3

Others

50ms

13

2.99 M

38.88 M

[138, 139]

Worms

Others

-

1

0.23 M

0.23 M

TSC.

A.2. Statistical Analyses This subsection provides additional statistical analyses of the proposed RMISC corpus, further demonstrating its scale, diversity, and quality. 15 https://unit8co.github.io/darts/ 16 https://gis.cdc.gov/grasp/fluview/ 17 https://forecastingdata.org/

29

Datasets

Series 25

Environment

37

Finance Energy

Energy

14

Industry

16

Traffic

382.551K 8.503K 338.143K

Traffic 55

Others 0

45.589K

Finance 44

Industry

1.38793M

Environment

159.956K

Others

6 12 18 24 30 36 42 48 54

10K

Count

Timesteps

1M

Time points 10.3776B Environment

Environment 667.207M

Finance Energy Industry

100K

Total series (log)

Energy

111.516M

24.9652B 38.4116B

Industry 605.128M

Traffic

1.13109B

Others 100M

9.30873B

Finance 3.25753B

Traffic

59.6015B

1B

1.05359B 9.45058B

Others 10B

1B

Total timesteps (log)

10B

Total time points (log)

Figure 8: Domain-wise scale statistics of the proposed dataset.

Figure 8 provides an overview of the scale and domain distribution of the RMISC corpus, covering the number of subdatasets, time series, timesteps, and time points. These statistics demonstrate that RMISC offers large-scale real-world time series data while maintaining broad and relatively balanced coverage across diverse application domains. Figure 9 presents the length-dimensionality landscape of all sub-datasets. The result shows that RMISC covers a wide range of sequence lengths and, more importantly, contains a substantial number of multivariate time series, including many high-dimensional datasets. Figure 10 reports the sampling frequency distribution across different domains. The results show that RMISC covers a broad spectrum of temporal resolutions, ranging from sub-second and minute-level observations to hourly, daily, weekly, monthly, and lower-frequency records. This wide frequency coverage enables RMISC to support time series modeling under diverse temporal granularities. Figure 11 summarizes the data quality distribution across domains. Data quality is assessed from both data-level and source-level perspectives. Specifically, we consider basic validity and usability indicators, such as duplicated or constant segments, abnormal values, and irregular records, as well as source-level factors, including the credibility of the original data platform and the clarity of metadata. The results show that the majority of subdatasets are of high or very high quality, indicating that RMISC provides a reliable foundation for large-scale time series pretraining and evaluation.

30

Average dimensionality: time points / timesteps

Length-Dimensionality Landscape Environment Finance Energy Industry Traffic Others

1K

100

10

1 100

1K

10K

100K

1M

10M

Average sequence length: timesteps / series

Figure 9: Length-dimensionality landscape of all subdatasets.

Sampling Frequency by Domain Environment Finance

80

Energy Industry

Traffic Others

71

Dataset count

70 60 50

43

40 27

30

22 16

20 10

7

5

0

<=s

min

hour

day

week

>=month

multiple values or unknown

Primary sampling interval

Figure 10: Sampling frequency distribution across domains.

very low

1 4%

0 0%

6 14%

0 0%

0 0%

0 0%

low

1 4%

0 0%

0 0%

0 0%

0 0%

3 5%

medium

3 12%

4 11%

11 25%

7 50%

3 19%

29 53%

high

19 76%

21 57%

22 50%

4 29%

11 69%

14 25%

very high

1 4%

12 32%

5 11%

3 21%

2 12%

9 16%

70 60 50 40 30

t

m

en

En

on vir

Fi

n

c an

e

gy er En

ry st du In

Tr

fi af

s

c

er th

O

Figure 11: Data quality distribution across domains.

31

20 10 0

In-domain percentage

Data Quality Composition by Domain

B. Additional Experimental Results

B.1. Full Benchmark Results after Convergence Table 4 reports the detailed MASE and WQL results on four benchmarks. Table 4: Out-of-distribution benchmark results of different training corpora on (a) Chronos-2, (b) GTT, (c) Moirai-2.0, and (d) TimesFM-2. Best results are highlighted in bold, and second best results are underlined. (a) Chronos-2 Training Corpus

fev-uni

fev-multi

(b) GTT GIFT-uni

GIFT-multi

Training Corpus

MASE WQL MASE WQL MASE WQL MASE WQL

fev-uni

fev-multi

GIFT-uni

GIFT-multi

MASE WQL MASE WQL MASE WQL MASE WQL

RU

2.807 0.188 1.401 0.298 1.069 0.343 1.923 0.322

RU

2.318 0.233 2.334 0.407 1.103 0.372 2.032 0.423

SM

2.214 0.180 1.039 0.227 1.003 0.320 1.597 0.307

SM

3.056 0.259 1.175 0.349 1.116 0.387 1.923 0.435

RM

2.193 0.172 1.082 0.237 1.034 0.331 1.725 0.293

RM

2.598 0.244 1.165 0.322 1.094 0.380 1.953 0.410

RU+SM

1.960 0.162 1.033 0.217 0.937 0.308 1.670 0.306

RU+SM

2.288 0.232 1.143 0.339 1.093 0.377 1.916 0.409

RU+RM

2.290 0.167 1.070 0.234 1.000 0.321 1.716 0.302

RU+RM

2.358 0.234 1.150 0.329 1.099 0.374 1.897 0.413

SM+RM

1.881 0.159 0.972 0.205 1.007 0.327 1.545 3.000

SM+RM

2.283 0.227 1.092 0.304 1.039 0.421 1.900 0.458

RU+SM+RM

1.775 0.154 0.973 0.205 0.973 0.316 1.538 0.299

RU+SM+RM

2.249 0.227 1.084 0.315 1.038 0.362 1.791 0.415

(c) Moirai-2.0 Training Corpus

fev-uni

fev-multi

(d) TimesFM-2.5 GIFT-uni

GIFT-multi

Training Corpus

MASE WQL MASE WQL MASE WQL MASE WQL

fev-uni

fev-multi

GIFT-uni

GIFT-multi

MASE WQL MASE WQL MASE WQL MASE WQL

RU

2.156 0.178 1.095 0.256 1.057 0.344 1.792 0.334

RU

SM

2.598 0.194 1.097 0.240 1.010 0.322 1.623 0.335

SM

2.300 0.203 1.156 0.284 1.109 0.360 2.071 0.390 2.337 0.195 1.084 0.256 1.087 0.354 1.685 0.374

RM

2.120 0.175 1.034 0.225 1.040 0.332 1.601 0.313

RM

2.117 0.192 1.061 0.257 1.134 0.368 1.732 0.392

RU+SM

2.250 0.177 1.041 0.223 0.972 0.316 1.544 0.308

RU+SM

2.161 0.192 1.100 0.255 1.117 0.357 1.749 0.392

RU+RM

2.026 0.169 0.994 0.221 0.988 0.315 1.639 0.321

RU+RM

2.074 0.190 1.046 0.254 1.098 0.361 1.639 0.405

SM+RM

2.308 0.178 1.044 0.212 1.005 0.321 1.528 0.305

SM+RM

2.056 0.186 1.038 0.246 1.065 0.352 1.664 0.423

RU+SM+RM

2.142 0.175 1.016 0.216 0.979 0.321 1.515 0.324

RU+SM+RM

1.980 0.183 1.033 0.241 1.074 0.355 1.623 0.402

B.2. Benchmark MASE Results During Two-Epoch Pretraining Figure 12 reports changes in benchmark MASE scores from the first to the second epoch for Chronos-2 and GTT. For Chronos-2, although most corpora achieve lower MASE scores in the second epoch, the improvements are generally marginal. In addition, several corpora show increased MASE scores in the second epoch, suggesting a potential degradation in OOD generalization. For GTT, increases in MASE scores are more evident, as more corpora show higher MASE scores in the second epoch. Overall, these results suggest that both Chronos-2 and GTT converge by the end of the second epoch.

32

(a) Chronos-2 58 60

50 5860

5850 6050





586050

IHYXQL 

IHYPXOWL









  







 



0$6(

0$6(







  

 

  





(SRFK







     



     



*,)7XQL

0$6(

  





  

 





(SRFK













  















 

 





 

(SRFK



*,)7PXOWL



0$6(







 







 











(SRFK





(b) GTT 58 60

50 5860

5850 6050

586050

IHYXQL 

IHYPXOWL 

 







   









(SRFK









   

 



(SRFK



  













(SRFK





*,)7PXOWL  





 





0$6(

0$6(



  

     







     



*,)7XQL



 







 

    







0$6(

0$6(











 

    



 











(SRFK





Figure 12: The changes in benchmark MASE scores from the first to the second epoch of different training corpora on (a) Chronos-2 and (b) GTT. 33

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