SearchCast: Preprocessing-Optimized Ridge Forecasting

• SearchCast is a time-series forecasting pipeline that leverages Ridge regression’s closed-form solution to optimize preprocessing and expose dataset structure.
• It jointly tunes lookback, normalization, regularization, and augmentation, showing that well-chosen preprocessing can close accuracy gaps seen in larger models.
• Interactive diagnostics in SearchCast reveal seasonal anchors and data heterogeneity, making forecasting decisions transparent and interpretable.

SearchCast is a time-series forecasting pipeline built around a single, transparent model—Ridge regression—whose closed-form solution is used to shift model selection effort from enlarging the predictor to tuning preprocessing choices. In this formulation, lookback length, normalization scope, regularization, and augmentation are treated as the primary search dimensions, and the resulting hyperparameter surface is used not only to optimize forecasting accuracy but also to diagnose dataset structure. On eight standard long-horizon benchmarks, the reported optimized models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks (Huang et al., 25 Jun 2026).

1. Conceptual framing

SearchCast takes the position that much of the accuracy gap in time-series forecasting can be closed at lower cost by tuning preprocessing rather than by scaling model capacity. The pipeline therefore uses Ridge regression as the testbed, specifically because it has a closed-form solution and interpretable weights, allowing the optimal hyperparameters to be read directly from search outcomes. The system searches jointly over context length, local normalization, regularization, and augmentation, and evaluates these choices over series, horizons, or grouped subsets thereof (Huang et al., 25 Jun 2026).

This design places SearchCast within a line of forecasting research that has increasingly emphasized larger architectures, including specialized transformers and general-purpose foundation models, but it inverts the usual premise that capacity is the main driver of performance. Its central claim is not that nonlinear models are unnecessary in every setting, but that a substantial fraction of the performance differential can be explained by under-optimized preprocessing. A plausible implication is that part of what larger forecasters appear to learn as internal representation may, in some datasets, correspond to structure that can be exposed explicitly through search over data transformations and context selection.

2. Ridge-regression forecasting formulation

The core prediction problem is defined as follows: given an $L$-step context $x\in\mathbb R^L$ and forecast horizon $H$, SearchCast predicts the next $H$ values by

$$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$

Training uses $N$ sliding windows $X\in\mathbb R^{L\times N}$ and $Y\in\mathbb R^{H\times N}$, with Ridge regression

$$W^*=\arg\min_W \|Y - W\,X\|_F^2 + \alpha\,\|W\|_F^2,$$

whose closed-form solution is

$W^* \;=\; Y\,X^\top\,(X\,X^\top + \alpha I)^{-1}.$

In the univariate one-step case, this reduces to

$x\in\mathbb R^L$0

Each row of $x\in\mathbb R^L$1 is interpreted as an impulse response over the past $x\in\mathbb R^L$2 lags: large-magnitude weights at lag $x\in\mathbb R^L$3 indicate that $x\in\mathbb R^L$4 is informative for forecasting, while small or zero weights indicate that the lag contributes little (Huang et al., 25 Jun 2026).

This formulation is technically important because it makes the forecasting model itself fixed and analytically tractable. SearchCast therefore relocates most of the effective model design into the data interface: how much history is retained, how the context is normalized, how strongly the estimator is regularized, and whether perturbative augmentation improves generalization. The transparency of $x\in\mathbb R^L$5 also supports direct inspection of seasonal anchors and lag structure, which larger black-box models would typically absorb into less legible learned parameters.

3. Search space and grouped optimization

SearchCast exposes four preprocessing axes and tunes them with Optuna over each series and horizon, or over groups of them. The search dimensions are summarized below.

Axis	Search space	Reported behavior
Context lookback $x\in\mathbb R^L$6	$x\in\mathbb R^L$7 (log-uniform)	Optimal $x\in\mathbb R^L$8 is series-specific and often non-monotonic in $x\in\mathbb R^L$9
Normalization	Global mean/std or local trailing window $H$0, $H$1	Local standardization is almost always preferred
Regularization $H$2	21 values, $H$3 (log-uniform)	Chosen per trial by cross-validation
Augmentation	None; time-domain Gaussian noise; frequency-domain Gaussian perturbation	Chosen in 60%–70% of best trials

For context length, SearchCast models the optimal lookback by a power law,

$H$4

The fitted exponents vary substantially by dataset: ETTm2 has $H$5; ETTh1 and ETTh2 have $H$6–$H$7; Weather and Electricity satisfy $H$8; Exchange and Traffic have $H$9. These values directly challenge the common heuristic that longer horizons necessarily require longer histories (Huang et al., 25 Jun 2026).

For normalization, SearchCast compares train-set global normalization with local normalization over a learned trailing fraction of the context. The standardization rule is

$H$0

A robust alternative based on median and interquartile range was also tested but underperformed mean/std. SearchCast almost always selects local standardization with $H$1, corresponding to the final 0.3%–30% of the context.

Regularization is selected from an inner-loop grid of 21 values over $H$2, with the best value chosen per trial to minimize cross-validation loss at zero extra cost. For augmentation, the search considers no augmentation, time-domain Gaussian noise scaled by $H$3, and frequency-domain Gaussian perturbation of Fourier coefficients, with noise intensity $H$4; augmentation appears in 60%–70% of best trials and is split roughly 50/50 between time and frequency domains.

The pipeline also supports grouped search. Series grouping size $H$5 determines whether hyperparameters are shared across channels, from fully per-series ($H$6) to fully shared ($H$7). Optimal $H$8 varies by dataset: fully shared on ETTh*, per-series on Weather, and intermediate on Electricity. Horizon grouping size $H$9 shares settings across blocks of horizons; the reported choice $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$0 produces negligible degradation, below 0.4%, while drastically reducing the number of runs because nearby horizons vary smoothly in their preferred settings.

4. Empirical regularities and overturned heuristics

The empirical analysis identifies three recurring patterns. First, the relation between lookback and horizon is non-monotonic across datasets. Reported $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$1 values range from $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$2 on ETTm2 to $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$3 on Exchange and Traffic, with Weather and Electricity near zero. This overturns the rule that one should always use more history for longer-horizon forecasts (Huang et al., 25 Jun 2026).

Second, partial-context normalization almost always outperforms normalization over the full lookback. Rather than setting $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$4, SearchCast typically selects a much smaller trailing fraction, indicating that normalization should adapt to the most recent regime rather than average over the entire available history.

Third, substantial cross-series heterogeneity is observed. Some datasets, especially ETT, benefit from fully shared preprocessing, whereas Weather is heterogeneous enough that per-series tuning is optimal, and datasets such as Electricity and Traffic occupy intermediate positions. This suggests that multivariate forecasting datasets cannot be assumed to admit a uniform preprocessing policy even when they are packaged as a single benchmark.

Taken together, these results recast several common forecasting heuristics as dataset-contingent rather than universal. A plausible implication is that benchmark comparisons confound model class with preprocessing defaults more often than is generally acknowledged. SearchCast’s reported results indicate that some apparent gains from larger models may instead reflect their ability to internalize choices about regime adaptation, context truncation, and heterogeneity management that a linear system can match when those choices are searched explicitly.

5. Diagnostic and interpretive interface

SearchCast includes an interactive online demonstration that displays per-series and per-horizon bars of optimal lookback, heatmaps of $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$5 across series-by-horizon grids, and weight-lag plots designed to reveal seasonal anchors (Huang et al., 25 Jun 2026). The interface also allows users to vary $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$6 and $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$7 in order to inspect Pareto curves of accuracy versus grouping size, identify series that disagree with the dominant setting, and drill down into individual series’ hyperparameter choices and weight patterns.

These interface components are not merely presentation tools. They operationalize the paper’s claim that the same pipeline used to optimize forecasts can also expose stationarity, seasonality, and heterogeneity in the data. Because the underlying predictor is Ridge regression, these visualizations remain directly tied to interpretable parameters rather than to latent states or attention maps whose relation to forecasting behavior may be less immediate.

In that sense, SearchCast functions as a dataset explorer as well as a forecaster. The reported hyperparameter surfaces are treated as diagnostic objects: they summarize where recent context matters more than long memory, where normalization must be local rather than global, and where hyperparameter sharing across channels is or is not justified by the data.

6. Access, deployment, and research significance

The project provides a live demonstration and documentation at https://sakanaai.github.io/SearchCast/ and a code repository at https://github.com/SakanaAI/SearchCast, released under the Apache-2.0 license and based on PyTorch, Optuna, and NumPy (Huang et al., 25 Jun 2026). The reported quick start consists of cloning the repository, installing requirements, and running: $$\hat y = W\,x + b,\quad W\in\mathbb R^{H\times L},b\in\mathbb R^H.$$8 Users supply their own multivariate series and forecast horizons; SearchCast then runs the grouped Optuna search, produces summary plots, exports the best Ridge weights, and can optionally serve a Jupyter-widget interface for interactive exploration.

Its broader significance lies in combining low compute cost, analytic solvability, and interpretability with competitive benchmark performance. The reported results show that carefully tuned preprocessing alone can raise linear Ridge regression to a level that matches or surpasses much larger nonlinear learners on many benchmark entries. Equally important, the optimized hyperparameters are used as a diagnostic on the data itself, revealing structures that larger models may absorb silently into learned parameters. This establishes SearchCast as both a forecasting method and an empirical framework for interrogating the structure of time-series datasets.