Tsururu: A Python-based Time Series Forecasting Strategies Library

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1 Introduction

A fundamental task in time series analysis is forecasting, which involves predicting future values Xt+1:H over a horizon H at timestep t, given the historical data X1:t and known covariates Z1:H for all time points [Salinas et al., 2020; Kim et al., 2024]. Later in this paper, we consider multivariate data comprising multiple time series within the dataset.

To advance forecasting capabilities, various libraries have been developed to benchmark state-of-the-art (SoTA) models, including tslib [Wang et al., 2024], neuralforecast [Olivares et al., 2022], uni2ts [Aksu et al., 2024] (for in-context learning models), pytorch-forecasting [Beitner, 2020] (has earlier deep learning models), BasicTS [Shao et al., 2024]. However, they are suboptimal for real-world scenarios. They often rely on fixed forecasting strategies, offer constrained support for exogenous variables, and face difficulties in the usage of custom datasets. These factors limit their suitability for industrial scenarios. A potential solution is a time series library that seamlessly handles diverse datasets, including nonaligned ones or those with exogenous features.

Indeed, some of the issues above are partially covered in existing practically oriented time series libraries. Almost all such libraries use global approach [Januschowski et al., 2020; Montero-Manso and Hyndman, 2021] (useful for non-aligned series) and support exogenous variables: Darts [Herzen et al., 2022], sktime [Kir´aly et al., 2025], gluonts [Alexandrov et al., 2020], tslearn [Tavenard et al., 2020], skforecast [Amat Rodrigo and Escobar Ortiz, 2024], AutoTS [Catlin, 2021] (global for aligned time series only), ETNA [Alekseev et al., 2021], mlforecast [Morales, 2021]. However, some of them could not use exogenous features as input, like tslearn [Tavenard et al., 2020], and tsspiral [Cerliani, 2023] or work only in the multivariate setting, such as tsai [Oguiza, 2023].

Nevertheless, the full predictive potential of time series models remains unexplored, as the impact of forecasting strategies [Taieb, 2014] has received limited attention. Classical time series forecasting is based either on a recursive strategy [Gustin et al., 2018] or a multi-input-multi-output (MIMO) strategy [Bontempi, 2008; Bontempi and Taieb, 2011; Kline, 2004]. Recent research claimed that the question of which strategy to use is still open [Green et al., 2024]. Notably, most state-of-the-art neural networks are trained using the MIMO strategy. However, incorporating additional forecasting strategies demonstrates that MIMO is not always optimal (see Section 3). Only Darts, sktime, skforecast and tspiral have at least three strategies. Nevertheless, they offer only a narrow pool of preprocessing methods. For example, none of them is integrated with the LastKnownNormalizer - subtraction or division on the last element in available history. Our experiments show that this rarely used preprocessing enhances forecasting performance significantly (see Section 3).

Given the weaknesses of existing time series libraries, this paper introduces Tsururu (Fig. 1), the modular framework for both practitioners and researchers that makes combinable global/multivariate approaches, different forecasting strategies, and models. This flexibility connects state-of-the-art research with real-world business applications.

2 Framework Design

The Tsururu architecture (Fig. 1) facilitates the comparison of configurations and the development of task-specific forecasting systems, incorporating strategies with support for exogenous variables.

Multi-series prediction strategies. Tsururu supports both Global and Multivariate approaches for all models for handling multiple time series [Januschowski et al., 2020; Montero-Manso and Hyndman, 2021]. The Global approach fits a single model to all time series, treating them as independent, while the Multivariate approach allows the model to capture dependencies between them. Moreover, each deep learning model in Tsururu supports Channel Independence

(CI) and Channel Mixing (CM) modes [Han et al., 2024]. The last one controls the interaction between series in the multivariate setting.

Multi-step-ahead prediction strategies. Different strategies can be applied to multi-step forecasting. Recursive (Rec) [Weigend, 2018] trains a single model to predict the next point (MH = 1), iteratively extending predictions across the forecast horizon and using previous predictions to update the features in the test data. MH denotes the model horizon, i.e., the number of points which the model outputs in a single step. Tsururu also supports the hybrid Recursive-MIMO (Rec-MIMO) strategy (MH > 1), which follows the recursive strategy but generates multiple-step predictions at each iteration instead of a single point. Direct (Dir) [Weigend, 2018] uses separate models for each prediction step with model horizon length, constructing the full forecast horizon. MIMO [Bontempi, 2008] trains a single model to simultaneously predict the entire forecast horizon (MH = H). FlatWideMIMO (FWM) uses a single model to predict a specific point in the forecasting vector, with the horizon index explicitly provided as an input feature. While rarely used, this strategy can be effective.

Pipeline and Data Transformations. Tsururu's pipeline applies sequential transformations to time series data, categorized into three types: Series-to-Series are used for data preprocessing and feature generation, Series-to-Features build a "wide" series matrix with lagged versions of generated features, Features-to-Features perform window-based processing, such as LastKnownNormalizer (LKN), based on normalizing values by the most recent observed one in available history, i.e. in corresponding row of the "wide" series matrix. Tsururu supports separate transformations for features and targets, allowing more data preparation flexibility.

Models. Tsururu offers classical ML and deep learning models. For ML, it includes boosting methods like CatBoost [Prokhorenkova et al., 2018] and SketchBoost [Iosipoi and Vakhrushev, 2022], with SketchBoost chosen for its speed in GBDT training [Friedman, 2001]. DL models are grouped into linear (DLinear [Zeng et al., 2023], CycleNet [Lin et al., 2024]), CNN-based (TimesNet [Wu et al., 2023]), and Transformer-based (PatchTST [Nie et al., 2023], GPT4TS [Zhou et al., 2023]).

Data flow. In Tsururu, data moves through a structured pipeline. First, time series pass through preprocessing. Next, some relevant features are generated: categorical encodings and datetime features. Once these features are in place, Tsururu operates at the index level, converting "long" into "wide" series through lag transformations. This protocol prevents leakage from future values, supports dynamic feature generation, and reduces memory overhead. Afterward, Tsururu applies the beforehand chosen multi-step forecasting strategy and selects either the Global or Multivariate approach. Window normalization can then be used to rescale each observation in wide data to the most recent known value, thus helping to cope with local shifts in the data distribution. Finally, the prepared dataset and model are passed to the Trainer module. The Trainer is responsible for the training process. It also uses cross validator (CV) to generate validation splits. When multiple splits exist, a separate model is trained for each split, and their predictions are averaged during inference. The validation set can also be used for early stopping. The final model is then validated using backtesting and rolling validation methods to ensure robustness (note that it is not the same as CV in Trainer).

3 Experimental Results

Setup. We examine such models as SketchBoost, DLinear, PatchTST, GPT4TS, and CycleNet, exploring both global and multivariate approaches (with either Channel Independence or Channel Mixing) and forecasting strategies: Recursive (with model horizon MH equal to 1 or 6), MIMO, and FlatWideMIMO. These models are evaluated on the ILI dataset 1 , a challenging weekly time series with annual periodicity and distinct temporal structures, to showcase the library's capabilities and highlight the importance of nondefault model-approach-strategy combinations.

For all settings, we used a cosine-based scheduler for over 50 epochs, with the learning rate set to 0.0001, and performed parameter updates at the end of each batch. We fixed batch size to 32, history to 96, and horizon to 24. The model hyperparameters (i.e., hidden dimension, the number of attention heads, etc.) were left unchanged from their earlier configurations in the initial works [Zhou et al., 2023; Zeng et al., 2023]. In cases where the authors had not tested their models on ILI, we retained the hyperparameters for ETTh1 [Zhou et al., 2021].

1 https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html

Table 1: Comparison of hyperparameters of data manipulation pipeline. For boosting, there is no Multivariate CI mode by construction; only Multivariate CM mode is available. MH stands for the model horizon of the Recursive strategy.

Hyperparam	Value	NN models		Boosting		Overall
		Rank	MedianMAE	Rank	MedianMAE	Rank	MedianMAE
Datetime Features	False True	1.3819 1.6181	1.0087 1.1323	1.3333 1.6667	1.6050 1.6174	1.3743 1.6257	1.0448 1.1785
ID Features	False True	1.7262 1.2738	1.0780 1.0024	1.5714 1.4286	1.6174 1.5898	1.6952 1.3048	1.1319 1.0611
Mode	Global Multivariate CI Multivariate CM	1.5476 2.2619 2.1905	1.0056 1.1217 1.1319	1.0952 NaN 1.9048	1.5648 NaN 1.6248	1.5476 2.2619 2.1905	1.0735 1.1217 1.2129
Prediction Strategy	FlatWideMIMO MIMO Recursive (MH = 1) Recursive (MH = 6)	3.9375 1.7500 2.4167 1.8958	1.3080 1.0280 1.0314 1.0228	2.8889 2.4444 2.7778 1.8889	1.6208 1.6072 1.6066 1.5816	3.7719 1.8596 2.4737 1.8947	1.3543 1.0621 1.0763 1.0541

Results. As shown in Figure 2, LKN significantly outperforms default preprocessing strategies, demonstrating its effectiveness despite not being adopted in common libraries. We use delta-mode normalization (based on subtraction from the current value, the previous one for DifferenceNormalizer (DN), and the most recent one in available history for LKN).

Table 1 presents the results of an ablation study on hyperparameters of the data manipulation pipeline, analyzing the impact of date and id features inclusion, forecasting mode, and strategy selection on model performance. The id features improved model accuracy, while including date features led to worse performance for both neural networks and GBDT. The Global approach outperformed the multivariate one, achieving the lowest rank and median MAE across all models. The MIMO strategy ranked best for neural networks, while RecMIMO (MH = 6, see Section 2) achieved the lowest median MAE. For GBDT, Rec-MIMO (MH = 6) is the best strategy in rankings and median MAE. Thus, this hybrid approach is rarely used but is a competitive alternative.

Table 2 provides the independent ranking of models based on test and validation MAE. In this evaluation, we also considered an alternative scaling approach using ratio normalization without an initial StandardScaler for boosting models. Our results confirm that GPT4TS outperformed all other models. Notably, the Rec-MIMO strategy with MH = 6 achieved the best overall test MAE. However, on the validation set, the highest-ranked strategy was MIMO. Interestingly, FlatWideMIMO combined with boosting models also ranked among the top strategies, demonstrating that GBDT can be competitive when paired with non-standard multistep-ahead forecasting approaches. The diversity of topranked models and strategies underscores the importance of exploring rarely used model-strategy combinations.

Table 2: Best 10 combinations model-strategy based on MAE on validation and test subsets.

rank	Model	Strategy	MAE (test)	Model	Strategy	MAE (val)
1	GPT4TS	Recursive (MH = 6)	0.7804	GPT4TS	MIMO	0.2713
2	GPT4TS	Recursive (MH = 1)	0.7822	GPT4TS	Recursive (MH = 6)	0.2833
3	PyBoost	FlatWideMIMO	0.7921	GPT4TS	Recursive (MH = 1)	0.2938
4	GPT4TS	MIMO	0.7926	PatchTST	MIMO	0.3005
5	PatchTST	Recursive (MH = 6)	0.8630	PatchTST	Recursive (MH = 6)	0.3050
6	PatchTST	MIMO	0.8769	DLinear	Recursive (MH = 6)	0.3169
7	PatchTST	Recursive (MH = 1)	0.8949	PatchTST	Recursive (MH = 1)	0.3180
8	DLinear	Recursive (MH = 6)	0.9193	DLinear	MIMO	0.3205
9	DLinear	MIMO	0.9220	PyBoost	FlatWideMIMO	0.3239
10	DLinear	Recursive (MH = 1)	0.9314	DLinear	Recursive (MH = 1)	0.3313

Table 3: Original vs. Ours. Metrics for the ILI dataset with a forecasting horizon of 24. Values marked with * indicate that the corresponding metric was not taken from the original paper but computed using the official implementation. Results are presented as mean ± standard deviation, calculated across three seeds.

Model	MAE (Original)	MSE (Original)	MAE (Ours)	MSE (Ours)
DLinear	1.081	2.215	1.037±0.004	2.227±0.010
PatchTST	0.754	1.319	0.716±0.043	1.239±0.103
GPT4TS	0.881	2.063	0.896±0.024	2.028±0.054
TimesNet	0.934	2.317	0.927±0.031	2.033±0.155
CycleNet	1.073*	2.400*	1.051±0.013	2.345±0.049

Reproducibility. To validate the accuracy of our time series library, we reproduce results from previous studies using Tsururu and compare them to the metrics reported in the original papers (Table 3). The close alignment between these metrics demonstrates the fidelity of our implementations.

4 Conclusion

This paper introduces Tsururu, an open-source Python library for ablating all-with-all combinations of preprocessing, time series models, forecasting approaches, and strategies. It can be easily integrated with new SoTA models for fair benchmarking while providing key industrial features, such as exogenous variables and a Global approach to handling non-aligned time series. It also supports channel mixing and channel-independent forecasting, rarely used in existing libraries. Our experiments show the advantages of using rarely employed preprocessing (like LastKnownNormalizer) and combining strategies (like Recursive for PatchTST). Moreover, combining a Recursive strategy with the Global approach makes short time-series forecasting feasible, with extended horizons and support for custom datasets. The extended results for other datasets can be found in our repository. An ability to handle non-aligned series represents our essential advantage of combining regimes and strategies.

Future work includes incorporating Rectify [Taieb, 2014], and DirRec [Sorjamaa and Lendasse, 2006], building a universal neural network constructor, testing patching techniques, and supporting time series with mixed discretization (daily, monthly, weekly, etc.) within multivariate datasets.

Ethical Impact

The framework's methods and specifications do not directly relate to ethical concerns. However, high-stakes domains such as healthcare and finance, where time series are widespread, require careful attention. Before deploying our library in such contexts, a thorough evaluation is essential to ensure it does not support decisions that could negatively impact individuals or organizations.

Acknowledgments

The work of A. Savchenko was supported by a Research Center for Trusted Artificial Intelligence the Ivannikov Institute for System Programming of the Russian Academy of Sciences.

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