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MetaARIMA: Configuration-Level Transfer Learning for ARIMA Models

Vitor Cerqueira, Ricardo Inácio, Carlos Soares

arXiv:2610.34171v1stat.MLcs.LG

TL;DR

ARIMA configuration is usually performed independently for each series, without carrying forward knowledge from earlier experiments. MetaARIMA learns a policy from historical experiments to recommend promising configurations for new series while preserving local ARIMA estimation. It outperforms traditional approaches across benchmark datasets and remains competitive with recent TSFMs.

  • Problem

    ARIMA configuration remains series-by-series and memoryless, while automated choices often rely on heuristic in-sample fit criteria.

    Source: §1 · p. 2

  • Method

    MetaARIMA metalearns from historical feature-performance experiments to recommend top-quantile ARIMA candidates, then uses diversity-aware selection and successive halving for local evaluation.

    Source: §1 · p. 2

  • Results

    MetaARIMA consistently outperforms traditional approaches such as AutoARIMA and AutoETS across diverse benchmark datasets, and remains competitive with recent state-of-the-art TSFMs.

    Source: §6 · p. 25

  • Takeaways & Limitations

    The configuration policy lets ARIMA benefit from accumulated historical experiments while preserving its interpretability and local estimation properties.

    Source: §1 · p. 2

    Transferability may depend on source-target similarity; substantially different domains may degrade recommendations, while representative target-domain data for retraining or fine-tuning may mitigate this.

    Source: §5.2 · p. 24

Abstract

from arXiv · show

Time Series Foundation Models have demonstrated that pretraining on diverse datasets enables effective transfer to new forecasting tasks. Classical methods like ARIMA, however, remain configured and trained independently for each series, discarding knowledge from previous experiments. Consequently, selecting and training an ARIMA configuration remains challenging and often relies on heuristic approaches based on in-sample goodnessof-fit measures. We propose MetaARIMA, a pretrained configuration policy based on metalearning that brings transfer learning to classical statistical forecasting at the configuration level rather than the model level. The policy learns from historical experiments which ARIMA configurations achieve top-quantile performance, and recommends promising candidates for new series while preserving interpretability and local estimation. At inference, it selects a diverse set of candidates via maximal marginal relevance and efficiently identifies the final configuration using successive halving. Experiments in a transfer learning setting, training on M4 and evaluating on M1, M3, and Tourism, show that MetaARIMA outperforms AutoARIMA and other classical methods while being more dataefficient. In a comparison with recent zero-shot foundation models, MetaARIMA remains competitive with Chronos2, Moirai2, and TimesFM. The experiments are publicly available at https://github.com/vcerqueira/experiments-metaarima.

1 Introduction

MetaARIMA transfers historical configuration knowledge to classical ARIMA by learning which specifications are promising for new series, while retaining local estimation and interpretability. It outperforms AutoARIMA and other classical methods across benchmarks and remains competitive with recent time-series foundation models.

1 Introduction

  • The policy transfers knowledge at the configuration level: it maps time-series characteristics to promising ARIMA specifications rather than pretraining the forecaster itself.This preserves ARIMA’s local estimation and interpretability while drawing on historical experiments.Source: §1 · pp. 2–3
  • Metalearning targets configurations likely to fall within a top performance quantile, rather than predicting one winner when leading candidates may differ only marginally.The meta-dataset pairs time-series features with configuration performance.Source: §1 · p. 2
  • PCA compresses binary top-quantile indicators into principal components, reducing the dimensionality of the configuration-scoring problem.Predicted components are mapped back to configuration scores.Source: §1 · p. 2
  • At inference, maximal marginal relevance selects diverse promising candidates, and successive halving evaluates them on progressively larger data subsets until one remains.The paper defines an ARIMA configuration by its model orders, including seasonal orders when applicable.Source: §1 · pp. 2–3
  • MetaARIMA consistently outperforms AutoARIMA and other classical methods across M1, M3, and Tourism, and remains competitive with recent TSFMs.The configuration policy is trained on M4; the final ARIMA models retain local estimation and interpretability.Source: §1 · p. 3

2 Background

The background establishes how forecasting series and ARIMA configuration are framed, reviews feature extraction and metalearning, and positions configuration-level transfer between memoryless local methods and global neural forecasters.

2.1 Univariate Time Series Forecasting

  • A univariate series contains one real-valued observation per time step, and forecasting predicts the next h values; local models fit each series separately, while MetaARIMA adds global information to configuration.A collection comprises multiple univariate series, while the final ARIMA models remain locally fitted.Source: §2.1 · pp. 3–4

2.2 ARIMA

  • ARIMA configuration selects model orders; Box-Jenkins requires expert iteration, while AutoARIMA uses tests and stepwise search guided by in-sample criteria that can yield suboptimal choices.Out-of-sample evaluation better reflects future accuracy, but exhaustive search can be computationally prohibitive; these approaches also lack memory of prior series.Source: §2.2 · pp. 4–5

2.3 Time Series Feature Extraction

  • Feature extraction maps series of varying lengths and structures to common descriptive attributes, such as trend, seasonality, and spectral characteristics.The cited tsfeatures package provides 42 interpretable features.Source: §2.3 · p. 5

2.4 Metalearning for Algorithm Selection

  • Metalearning uses historical instance-feature and algorithm-performance pairs to recommend options for new problems; prior time-series applications include forecast weighting and multi-step forecasting.Using this approach to select ARIMA orders from historical configuration performance had not been explored.Source: §2.4 · pp. 5–6

2.5 Research Gap and Positioning

  • MetaARIMA occupies a middle ground: unlike memoryless local configuration or global TSFMs that replace statistical models, it transfers historical knowledge through a policy while retaining locally fitted, interpretable ARIMA.The policy maps series features to promising specifications and is pretrained on M4.Source: §2.5 · p. 6

3 MetaARIMA

MetaARIMA transfers historical ARIMA-configuration experience by training a policy that maps time-series features to promising configurations. It combines top-quantile targets, dimensionality reduction, diversity-aware shortlisting, and successive halving for final selection.

3.1 Problem Formulation

  • MetaARIMA frames ARIMA configuration as metalearning: a policy maps time-series features to promising configurations using historical experiments.The policy is trained once on a source collection and applied to new series without retraining.Source: §3 · p. 6, §3.1 · p. 7

3.2 Development stage

  • The development workflow extracts features, evaluates configurations, computes error correlations, binarizes errors into top-quantile targets, compresses them with PCA, and trains a regressor.The feature and target representations are paired to train the policy that predicts configuration performance patterns.Source: §3.2 · p. 8, Figure 1 · p. 8

3.2.1 Performance estimation

  • Out-of-sample errors across configurations form the performance targets, while their cross-series Pearson correlations identify configurations that tend to succeed or fail together.The stored correlations later help favor candidates with low correlation to those already selected.Source: §3.2.1 · p. 8

3.2.2 Meta-feature extraction

  • Meta-features map series of differing lengths and scales to fixed-length numerical vectors that the shared meta-model can compare and process.The feature set can capture trend, seasonality, stationarity, autocorrelation, and entropy.Source: §3.2.2 · p. 9

3.2.3 Quantile-based target representation and dimensionality reduction

  • Top-quantile membership represents multiple near-best configurations per series, avoiding a single-winner target when several configurations perform comparably.PCA compresses the correlated binary labels into a low-dimensional representation for a multi-target regressor, which predicts scores used to rank configurations.Source: §3.2.3 · pp. 9–10

3.3 Inference stage

  • At inference, the policy extracts query-series features, predicts in PCA space, and inverts that representation to score each configuration.The scores are interpreted as estimates of top-quantile membership for the query series.Source: §3.3 · p. 10, Figure 2 · p. 10

3.3.1 Diverse candidate selection via MMR

  • MMR selects a diverse shortlist by balancing each candidate’s predicted score against its maximum correlation with configurations already selected.The trade-off parameter λ controls relevance versus diversity.Source: §3.3.1 · pp. 10–11

3.3.2 Efficient final selection via successive halving

  • Successive halving evaluates shortlisted configurations on progressively larger recent-data windows, eliminating the worst-performing half at each round using AICc.The survivor is selected and fit using the complete training data.Source: §3.3.2 · p. 11

4 Experiments

The experiments assess whether ARIMA configuration can be treated as algorithm selection and solved effectively through metalearning. They also compare performance, test sensitivity to design choices and frequencies, and evaluate MetaARIMA against zero-shot forecasting foundation models.

Research questions

  • RQ1 asks whether ARIMA configuration can be formulated as algorithm selection and whether metalearning can provide an effective and efficient solution.The evaluation includes benchmarking and ablation studies.Source: §4 · p. 12
  • RQ2 compares metalearning-based ARIMA configuration with state-of-the-art alternatives and standard classical forecasting methods.The benchmark includes established classical methods.Source: §4 · p. 12
  • RQ3 examines sensitivity to individual components, hyperparameters, and time-series frequencies.The experiments analyze how parameter values affect overall performance.Source: §4 · p. 12
  • RQ4 compares MetaARIMA with recent zero-shot time-series foundation models.The evaluation includes comparisons with recent zero-shot forecasting models.Source: §4 · p. 12

4.1 Experimental Setup

The experimental setup trains frequency-specific policies on M4 and tests their transfer to M1, M3, and Tourism. It specifies the ARIMA configuration space, training targets, and inference procedure.

4.1.1 Data

  • The benchmarks comprise M1, M3, Tourism, and M4, retaining monthly, quarterly, and yearly series.The transfer evaluation trains each frequency-specific meta-model on the corresponding M4 data and applies it to same-frequency series from M1, M3, and Tourism without retraining or fine-tuning.Source: §4.1.1 · p. 12, Table 1 · p. 13
  • Forecast horizons are 12 steps for monthly series, 8 for quarterly series, and 6 for yearly series.The setup uses distinct horizons by sampling frequency.Source: §4.1.1 · p. 13

4.1.2 Methods

  • The ARIMA configuration space contains 400 candidates for seasonal series and 50 for yearly, non-seasonal series.Yearly configurations fix P = D = Q = 0.Source: §4.1.2 · p. 13, Table 2 · p. 13
  • On M4, the method extracts 42 features, binarizes errors at the top 25% quantile, compresses targets to 50 PCA components (15 for yearly), and trains a CatBoost multi-target regressor.For a target series, MMR selects 25 candidates; successive halving uses AICc, starts at a 4m-observation window, and doubles the window while eliminating the worst half until one remains.Source: §4.1.2 · pp. 13–14

Development stage

The listed experimental settings include a 0.25 quantile threshold, 50 principal components (15 for yearly series), and 42 meta-features.

Development stage

  • The experimental settings use τ = 0.25, npc = 50 (15 for yearly series), and l = 42 meta-features.These values denote the quantile threshold, number of principal components, and number of meta-features, respectively.Source: Development stage · p. 14

Inference stage

The inference stage sets the candidate-search and baseline configuration; evaluation applies frequency-specific policies to held-out target series without retraining or fine-tuning.

Inference stage

  • Inference settings use λ = 0.75 for the MMR trade-off and k = 25 candidate configurations, with successive halving starting at 4m and using resource multiplier 2 and elimination rate 2.The comparison includes SeasonalNaive, AutoARIMA, fixed ARIMA(2,1,2), and fixed AR(1).Source: Inference stage · pp. 14–15

4.1.3 Evaluation

  • Frequency-specific meta-models trained on M4 are applied directly to matching-frequency M1, M3, and Tourism series without retraining or fine-tuning.Each series uses training data for feature extraction and configuration fitting, with its final h observations held out for testing.Source: §4.1.3 · p. 15
  • Meta-features and ARIMA configuration validation scores use only source-series training and validation segments; target forecasts are scored on held-out tests using seasonal MASE for monthly and quarterly series and non-seasonal MASE for yearly series.The protocol avoids future information in feature extraction and configuration selection.Source: §4.1.3 · p. 15

4.2 Exploratory Analysis of ARIMA Configurations

ARIMA configuration performance varies substantially across series, and the best average-ranked configurations are not simply those with the most parameters.

4.2 Exploratory Analysis of ARIMA Configurations

  • ARIMA(1,1,1)(1,0,0) has the best average rank, while white-noise ARIMA(0,0,0)(0,0,0) has the worst among the 15 best and 15 worst configurations.Figure 3 shows their MASE-based rank distributions across time series.Source: §4.2 · p. 15, Figure 3 · p. 16
  • Even configurations with the best average performance can rank among the worst on some series, and the reverse also occurs.This cross-series variability motivates improving automatic ARIMA configuration.Source: §4.2 · p. 16
  • More parameters show only a slight trend toward better average rank, and the best-performing configurations are not those with the largest parameter counts.Figure 4 plots average rank against total parameters with a LOESS fit.Source: §4.2 · p. 16

4.3 Results

Across classical benchmarks, MetaARIMA generally ranks strongly, especially on seasonal series; ablations and sensitivity analyses identify useful design choices, and inference uses fewer observations than AutoARIMA.

4.3.1 Comparing with Classical Approaches

  • MetaARIMA beats AutoARIMA on 7/9 datasets and is best or second-best on 6/9, with strongest results on seasonal series and AutoTheta ahead on yearly datasets.It is best on all monthly variants and best or second-best on 2/3 quarterly datasets; it still beats AutoARIMA in 2/3 yearly cases.Source: §4.3.1 · p. 16, Table 4 · p. 17

4.3.2 Ablation and Sensitivity Analysis

  • Removing PCA, successive halving, or quantile preprocessing worsens performance; Monte Carlo beats no successive halving but trails the original, while regression variants perform similarly.Multi-target regression is more computationally efficient than fitting a separate model for each principal component.Source: §4.3.2 · pp. 18–19, Figure 5 · p. 18
  • Average MASE rank improves as trials rise from 5 to around 20, is best at 30, then deteriorates; around 20 trials offers a performance-efficiency trade-off.Beyond this range, validation overfitting is a likely explanation for worse generalization.Source: §4.3.2 · p. 19, Figure 6 · p. 19
  • Performance is best around λ = 0.7–0.9: diversity-only selection performs poorly, while performance-only selection near λ = 1.0 is slightly worse than the intermediate balance.Figure 7 examines performance across λ values.Source: §4.3.2 · p. 19, Figure 7 · p. 20
  • Performance remains strong beyond roughly 25–50 principal components, and the default of 50 is a compromise between performance and computational efficiency.Even two components improve performance substantially; the analysis ranges from 2 to 350 components.Source: §4.3.2 · pp. 19–20, Figure 8 · p. 20
  • The best quantile threshold is around 0.5; very low thresholds perform poorly, while thresholds approaching 1.0 dilute the top-configuration supervision signal.Figure 9 evaluates performance across quantile thresholds.Source: §4.3.2 · p. 20, Figure 9 · p. 21

4.3.3 Data Efficiency Analysis

  • MetaARIMA processes 4,847,310 observations versus AutoARIMA’s 14,140,044 on M3-Monthly, a reduction of approximately 65.7% while achieving better forecasting performance.The accounting includes feature extraction and successive-halving evaluation for MetaARIMA, and observations used across AutoARIMA’s visited configurations.Source: §4.3.3 · p. 21

4.4 Comparing with TSFMs

In a zero-shot comparison on monthly datasets, Chronos2 performs best overall, while MetaARIMA remains competitive with the other foundation models and retains a classical ARIMA approach.

4.4 Comparing with TSFMs

  • Chronos2 performs best across all three monthly datasets; MetaARIMA ties for best or ranks second in two cases, outperforming Moirai2 and TimesFM.Table 5 reports average MASE across M1-M, M3-M, and T-M.Source: §4.4 · p. 21, Table 5 · p. 22
  • MetaARIMA’s competitive results use a lightweight, interpretable ARIMA model rather than a neural architecture with millions of parameters.The comparison applies the foundation models in direct zero-shot settings without fine-tuning or domain-specific adaptation.Source: §4.4 · pp. 21–22
  • Four M3-M forecast examples illustrate contrasting cases, including where each method is more accurate and where their MASE gap is largest in either direction.Figure 10 presents these individual series.Source: §4.4 · p. 22, Figure 10 · p. 22

5 Discussion

MetaARIMA reliably recommends ARIMA configurations, outperforming classical benchmarks and competing with recent foundation models in the reported comparisons. The discussion also identifies limits involving feature representation, upfront historical experiments, yearly series, domain transfer, and parameter choices.

5.1 Research Questions

  • MetaARIMA combines local ARIMA fitting with a learned cross-series mapping to promising configurations, retaining interpretability while trading off global and local approaches.Source: §5.1 · p. 23
  • MetaARIMA consistently outperforms AutoARIMA and other classical benchmarks across datasets, beats Moirai2 and TimesFM, and remains competitive with Chronos2.The authors note that raw scores differ from earlier works because all methods use the statsforecast implementation.Source: §5.1 · p. 23
  • Intermediate MMR settings outperform performance-only selection, supporting diverse candidate shortlists when configuration errors are correlated.The method remains robust across reasonable λ and quantile-threshold ranges.Source: §5.1 · p. 23
  • The current implementation uses 42 hand-crafted tsfeatures descriptors; TSFM embeddings are a proposed alternative whose effect on configuration accuracy remains to be tested.The authors chose tsfeatures to keep the pipeline lightweight and consistent with MetaARIMA’s design philosophy.Source: §5.1 · pp. 23–24

5.2 Limitations

  • MetaARIMA requires historical experiments and performance scores, an upfront computational burden that the authors say may be offset by greater data efficiency and transfer across datasets and frequencies.Source: §5.2 · p. 24
  • For yearly non-seasonal series, AutoETS and AutoTheta outperform MetaARIMA; the authors suggest the smaller configuration space and shorter series may limit available learning signal.Transferability may also depend on source-target similarity; substantially different domains could degrade recommendations, while retraining or fine-tuning on representative target-domain data may mitigate this.Source: §5.2 · p. 24
  • MetaARIMA requires choices for trials, principal components, feature extraction, λ, MMR settings, and quantile threshold, though performance is robust across reasonable parameter ranges.Source: §5.1 · p. 23, §5.2 · p. 24

6 Conclusions

MetaARIMA applies metalearning to transfer historical configuration knowledge to classical ARIMA forecasting while preserving local estimation and interpretability. Experiments report stronger performance than traditional approaches across diverse benchmarks, with competitiveness against state-of-the-art foundation models and greater data efficiency.

6 Conclusions

  • The method pretrains a lightweight controller that maps time-series characteristics to promising ARIMA specifications, using historical configuration experiments while retaining local estimation and interpretability.Source: §6 · pp. 24–25
  • MetaARIMA consistently outperforms traditional approaches such as AutoARIMA and AutoETS across diverse benchmark datasets and remains competitive with state-of-the-art TSFMs.Source: §6 · p. 25
  • The authors report better forecasting accuracy, greater data efficiency, and successful transfer across datasets.Source: §6 · p. 25
  • The authors see potential to improve automatic ARIMA configuration by leveraging historical configuration experiments, potentially strengthening ARIMA’s competitiveness with other approaches.Source: §6 · p. 25
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