Tsururu: Modular Forecasting Strategy Library

• Tsururu is a Python library for multi-step, multivariate forecasting that combines global and multivariate training regimes with varied forecasting strategies.
• It features a unified, modular pipeline that decouples preprocessing, strategy logic, and model training to bridge advanced research and practical applications.
• Empirical studies on ILI data demonstrate that optimal combinations of preprocessing, strategy, and regime choices can significantly enhance forecast precision.

Searching arXiv for the cited Tsururu paper and closely related forecasting-strategy work. Tsururu (“つるる”) is a Python library for flexible, multi-step, multivariate time-series forecasting that was introduced to address underexplored questions of selecting an optimal approach for training forecasting models (Kostromina et al., 19 Sep 2025). It is positioned as a bridge between SoTA research and industry by enabling flexible combinations of global and multivariate approaches, five distinct multi-step-ahead forecasting strategies, and seamless integration with various forecasting models (Kostromina et al., 19 Sep 2025). Its stated emphasis is not solely on new architectures, but on the combinatorial design space formed by preprocessing, regime selection, strategy choice, and model integration.

1. Motivation and problem setting

Tsururu was developed against the observation that classical and modern time-series forecasting libraries, including Darts, sktime, GluonTS, and NeuralForecast, often lock users into a single “global” or “local” regime, a narrow choice of multi-step forecasting strategies, and limited support for non-aligned series or arbitrary exogenous covariates (Kostromina et al., 19 Sep 2025). The library’s motivation is therefore methodological as much as software-oriented: recent research is cited as showing that the choice of multi-step strategy—recursive, direct, MIMO, hybrid, and related variants—can materially affect accuracy (Kostromina et al., 19 Sep 2025).

The scope of the library is defined by three practical requirements. First, it provides a unified, modular pipeline that lets users mix and match global versus multivariate training regimes, arbitrary sets of preprocessing transforms, five forecasting strategies, and any model exposed through a simple adapter interface (Kostromina et al., 19 Sep 2025). Second, it provides out-of-the-box support for non-aligned series, exogenous features, and backtesting or rolling validations (Kostromina et al., 19 Sep 2025). Third, it is explicitly aimed at both researchers, who require fair benchmarking of SoTA models and strategies, and industry practitioners, who require stability, custom data handling, and flexible forecasting strategies (Kostromina et al., 19 Sep 2025).

A plausible implication is that Tsururu treats forecasting strategy as a first-class experimental variable rather than as a fixed implementation detail. This distinguishes its framing from libraries centered primarily on model families.

2. Architecture and pipeline design

The library is organized as a modular dataflow in which preprocessing, feature construction, strategy logic, regime selection, and training are separated into explicit components (Kostromina et al., 19 Sep 2025). The main pipeline components can be summarized as follows.

Component	Function	Examples stated in the source
Series-to-Series transforms	Transform raw series before windowing	imputations, StandardScaler, DifferenceNormalizer, LastKnownNormalizer, date-time/categorical encoders
Series-to-Features	Generate input histories	lagged windows of length $w$
Features-to-Features	Transform window-level features	LKN
Strategy & Regime modules	Apply forecasting logic and choose training regime	recursive, direct, MIMO; global vs. multivariate
Trainer	Manage evaluation and optimization workflow	cross-validation splits, early stopping, backtesting, rolling forecasts

Within this architecture, models are decoupled from raw temporal structure. Preprocessing, strategy logic, and the global or multivariate regime transform raw series into a wide-matrix $X$ and targets $y$, after which models interact with the data through a common scikit-learn-style interface, namely fit(X, y) and predict(X) (Kostromina et al., 19 Sep 2025). This design permits the same forecasting workflow to be used with both classical ML and deep learning models.

The architecture also formalizes two distinct training regimes. In the global regime, each series is treated as an independent sample and one shared model is trained across all series (Kostromina et al., 19 Sep 2025). In the multivariate regime, one model is trained on the full vector of series at once (Kostromina et al., 19 Sep 2025). The multivariate regime is further divided into Channel-Independent (CI), where each channel is processed with shared weights but no mixing, and Channel-Mixing (CM), where the model is allowed to attend or convolve across channels (Kostromina et al., 19 Sep 2025).

This decomposition matters because it isolates modeling assumptions. Global training assumes parameter sharing across series without necessarily modeling inter-series interactions directly, whereas multivariate CM explicitly permits cross-channel dependence. The source does not claim one regime is universally superior; instead, it presents regime choice as contingent on data characteristics and empirical validation (Kostromina et al., 19 Sep 2025).

3. Formal taxonomy of forecasting strategies

A central contribution of Tsururu is a formal taxonomy of five multi-step forecasting strategies (Kostromina et al., 19 Sep 2025). Let $X_t \in \mathbb{R}^d$ denote the $d$-dimensional observation at time $t$, let $w$ denote the input window length, and let $H$ denote the forecast horizon. The “wide” input sample at time $t$ is defined as

$$x_t = [X_{t-w+1}, \ldots, X_t] \in \mathbb{R}^{w \cdot d},$$

and a multi-step strategy implements a mapping

$X$0

The distinction among strategies lies not in the codomain alone, but in how training targets and inference recursion are structured (Kostromina et al., 19 Sep 2025).

The Recursive strategy corresponds to iterated one-step forecasting with model horizon $X$1 and a single-step predictor $X$2 (Kostromina et al., 19 Sep 2025). At inference time, predictions are fed back into the input window:

$X$3

Its loss is

$X$4

where $X$5 is, for example, MSE or MAE (Kostromina et al., 19 Sep 2025).

The Direct strategy also uses $X$6, but trains separate models $X$7 for each horizon step $X$8 (Kostromina et al., 19 Sep 2025). Inference is non-recursive, with $X$9, and the loss aggregates horizon-specific predictors:

$y$0

The Recursive-MIMO strategy, identified as a hybrid Rec-MIMO approach, uses $y$1 with $y$2 dividing $y$3, and the paper notes $y$4 as typical in its experiments (Kostromina et al., 19 Sep 2025). A multi-output model $y$5 predicts blocks of steps, and the block forecasts are then applied recursively by sliding the window forward using predictions (Kostromina et al., 19 Sep 2025). Its loss is

$y$6

The MIMO strategy sets $y$7, producing the full forecast horizon in one shot via a single model $y$8 (Kostromina et al., 19 Sep 2025). Inference is simply

$y$9

with loss

$X_t \in \mathbb{R}^d$0

The fifth strategy, FlatWideMIMO, is described as rarely used (Kostromina et al., 19 Sep 2025). It keeps $X_t \in \mathbb{R}^d$1 but appends the horizon index $X_t \in \mathbb{R}^d$2 as an extra feature, using a predictor $X_t \in \mathbb{R}^d$3 (Kostromina et al., 19 Sep 2025). During training, each $X_t \in \mathbb{R}^d$4 is replicated $X_t \in \mathbb{R}^d$5 times with the horizon-index feature and supervised against $X_t \in \mathbb{R}^d$6, yielding

$X_t \in \mathbb{R}^d$7

This taxonomy is significant because it makes explicit that “multi-step forecasting” is not a single protocol. The source further states that the choice among recursive, direct, MIMO, and hybrid variants can materially affect accuracy (Kostromina et al., 19 Sep 2025). A plausible implication is that benchmark comparisons across forecasting models are incomplete when strategy choice is held fixed.

4. Model integration and software interface

Tsururu abstracts forecasting algorithms behind an adapter interface designed to accommodate both classical statistical or machine-learning models and PyTorch-based neural architectures (Kostromina et al., 19 Sep 2025). All models are expected to support

$d$6

with preprocessing, strategy logic, and regime selection performed upstream (Kostromina et al., 19 Sep 2025).

The library explicitly lists support for classical ML models such as CatBoost and SketchBoost, described as fast gradient-boosted trees for multi-output, and deep-learning models including DLinear, CycleNet, TimesNet, PatchTST, and GPT4TS (Kostromina et al., 19 Sep 2025). Example adapters are stated to exist for ARIMA via statsmodels, Prophet, Scikit-Learn regressors, and PyTorch-based SoTA networks (Kostromina et al., 19 Sep 2025).

Adding a new model requires a thin wrapper that ingests the wide matrix $X_t \in \mathbb{R}^d$8, calls the underlying library such as CatBoost or PyTorch with hyperparameters passed through its constructor or **cfg, and returns $X_t \in \mathbb{R}^d$9 of shape $d$0 (Kostromina et al., 19 Sep 2025). This formulation reduces the integration problem to a shape-compatible supervised-learning interface.

The significance of this design lies in interoperability. Rather than requiring a model to natively implement every forecasting regime or preprocessing variant, Tsururu relocates those responsibilities to the pipeline. This suggests a separation between temporal problem construction and function approximation: strategy modules define the supervised task, while adapters define the learner.

5. Usage patterns and experimental workflow

The source provides a minimal end-to-end workflow centered on TimeSeriesDataset, ForecastingPipeline, strategy and regime objects, model objects, and a Trainer (Kostromina et al., 19 Sep 2025). The example constructs a dataset from a pandas DataFrame with series_id, time, value, and optional exogenous variables; sets horizon=24 and history=96; specifies exogenous_cols=['temp','promo']; and assembles a pipeline with StandardScaler, LastKnownNormalizer, RecursiveStrategy(mh=6), GlobalRegime(), and SketchBoostRegressor (Kostromina et al., 19 Sep 2025). The Trainer is then configured with cross_validation_splits=3 and backtest_windows=2, followed by fit and predict, and evaluation with mean_absolute_error (Kostromina et al., 19 Sep 2025).

This example encodes several methodological commitments. The library treats exogenous variables as native components of the dataset abstraction (Kostromina et al., 19 Sep 2025). It also distinguishes internal cross-validation for early stopping from outer backtesting for performance estimation (Kostromina et al., 19 Sep 2025). The recommendations section reinforces this dual validation protocol by stating that rolling cross-validation should be used for early stopping and backtest windows for realistic error estimates (Kostromina et al., 19 Sep 2025).

The source also recommends including “id” features to help global models distinguish series, while cautioning that adding date or time features hurt performance on ILI in the reported ablation (Kostromina et al., 19 Sep 2025). This is noteworthy because it counters a common assumption that calendar covariates are uniformly beneficial. The statement is dataset-specific in the source and should be interpreted as such.

6. Empirical performance and reported findings

The empirical study reported for Tsururu is conducted on the weekly ILI dataset, described as challenging because of distinct annual seasonality and non-aligned series, with forecast horizon $d$1 and history $d$2 (Kostromina et al., 19 Sep 2025). Within that setup, the source reports several findings.

Preprocessing with LastKnownNormalizer (LKN) + StandardScaler is stated to significantly outperform default scaling or differencing, as shown in a Critical-Difference diagram (Fig. 2) (Kostromina et al., 19 Sep 2025). This places preprocessing choice alongside model and strategy choice as a major determinant of forecasting performance.

For training regimes, the reported median MAE ranking is Global > Multivariate(CI) > Multivariate(CM) (Table 1) (Kostromina et al., 19 Sep 2025). This indicates that, on the weekly ILI benchmark, the global regime was more robust than the two multivariate variants. The recommendations align with this result by stating that the global regime is more robust on non-aligned or short series, while Multivariate CM should be tried if the series truly share dynamics (Kostromina et al., 19 Sep 2025).

For forecasting strategies, the source reports a differentiated pattern by model family (Kostromina et al., 19 Sep 2025). For deep nets such as PatchTST, GPT4TS, and DLinear, MIMO is strongest on validation, but Rec-MIMO (MH = 6) often yields the lowest test MAE (Kostromina et al., 19 Sep 2025). For boosting, specifically SketchBoost, Rec-MIMO (MH = 6) or FlatWideMIMO top-rank over MIMO (Kostromina et al., 19 Sep 2025). The source further states that Direct is generally weaker and that simple recursive forecasting with $d$3 sometimes suffers from error accumulation (Kostromina et al., 19 Sep 2025).

The best reported test result in the model-strategy ranking is MAE = 0.7804, achieved by GPT4TS with Rec-MIMO (MH = 6) (Table 2) (Kostromina et al., 19 Sep 2025). In addition, the reproducibility analysis states that Tsururu reproduces published MAE and MSE within noise bounds, reported as mean $d$4 across seeds (Table 3) (Kostromina et al., 19 Sep 2025).

These findings support the paper’s central claim that there are non-trivial gains from exploring combinations beyond default recursive or MIMO paradigms (Kostromina et al., 19 Sep 2025). At the same time, the results are benchmark-specific. A careful reading suggests that the library is intended to facilitate such comparative evaluation rather than to prescribe a universally dominant strategy.

7. Best practices, limitations, and open directions

The source gives a concise set of operational recommendations. It recommends always experimenting with at least two strategies, specifically MIMO and Rec-MIMO (MH > 1), because simple recursive forecasting with $d$5 or direct forecasting may be suboptimal for long horizons (Kostromina et al., 19 Sep 2025). It recommends using LastKnownNormalizer in addition to standard scaling to handle local distribution shifts (Kostromina et al., 19 Sep 2025). It also states that, for deep learning, MIMO often converges faster, whereas for tree-based models, hybrid Rec-MIMO or FlatWideMIMO can unlock multi-output power (Kostromina et al., 19 Sep 2025).

These recommendations also clarify possible misconceptions. One misconception would be that multivariate channel mixing should dominate global models whenever multiple related series are available. The reported weekly ILI results do not support that as a universal rule, since the median MAE ordering favors the global regime (Kostromina et al., 19 Sep 2025). Another misconception would be that recursive one-step forecasting is a neutral default; the source explicitly notes possible error accumulation and weaker long-horizon behavior relative to hybrid or one-shot alternatives (Kostromina et al., 19 Sep 2025).

The stated roadmap identifies four future directions: additional strategies such as DirRec and Rectify; automatic neural-architecture search / universal constructor; support for mixed-frequency data such as daily plus monthly series in one dataset; and integration with newly published SoTA models through community adapters (Kostromina et al., 19 Sep 2025). These are presented as limitations or future work rather than completed functionality.

Taken together, these points define Tsururu as a forecasting-strategy library as much as a model library. Its main contribution is the exposure of a fully modular combinatorial space of preprocessing, strategies, regimes, and models, coupled with an API intended to make those combinations easy to configure and fair to compare (Kostromina et al., 19 Sep 2025).