MetaARIMA: Configuration-Level Transfer Learning for ARIMA Models
Authors: Vitor Cerqueira, Ricardo Inácio, Carlos Soares
Organizations: University of Coimbra; CISUC/LASI – Centre for Informatics and Systems of the University of Coimbra; Coimbra, Portugal · Faculty of Engineering, University of Porto; Porto, Portugal · Faculty of Engineering, University of Porto; Laboratory for Artificial Intelligence and Computer Science (LIACC), Portugal; Fraunhofer Portugal AICOS, Portugal; Porto, Portugal
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.
Figures & tables
Figure 1: Workflow for building MetaARIMA . A set of time series Y is summarised into a feature set M . A set of ARIMA configurations (e.g. ARIMA(0,0,0)) is evaluated on each series in Y , resulting in error estimates E . The error scores E are processed according to a quantile-based binarization that identifies series-wise top configurations ( T ), a representation that is then compacted using PCA ( Z ). A correlation analysis is also conducted using E to identify redundant configurations.
Figure 2: Workflow for the inference stage of MetaARIMA . The query time series Yquery is converted to meta-features Mquery ; the meta-model outputs predictions in PCA space, which are inverted to obtain scores T^query . MMR, using T^query and the stored error correlations, selects a diverse subset of configurations; successive halving and AICc on Yquery then choose the single selected configuration.
Frequency
Usage
# time series
# observations
M4
Monthly
Source
48000
11246411
Quarterly
24000
2406108
Yearly
23000
858458
M1
Monthly
Target
617
44892
Quarterly
203
8320
Yearly
181
4515
Table 1: Summary of the datasets: number of time series and number of observations
Parameter
Values
p
{0, 1, 2, 3, 4}
d
{0, 1}
q
{0, 1, 2, 3, 4}
P
{0, 1}
D
{0, 1}
Q
{0, 1}
Table 2: Parameter ranges used to construct the ARIMA configuration space A .
Notation
Value
Description
Development stage
τ
0.25
Quantile threshold
npc
50 (15 yearly)
# principal components
l
42
# meta-features
Inference stage
λ
0.75
MMR trade-off
Table 3: Summary of MetaARIMA parameters, their notation, values used in the experiments, and brief descriptions.
Figure 3: Rank distribution based on MASE of the top 15 and bottom 15 ARIMA configurations across all time series in the datasets. Methods are ordered by average rank.
Figure 4: Scatter plot of the average rank of the ARIMA configurations against the total number of parameters. Each point represents a configuration, with the red line representing the LOESS fit.
MetaARIMA
AutoARIMA
AutoETS
AutoTheta
AR
MA
ARMA
ARIMA
SeasonalNaive
M1-M
0.8709
0.916
0.9055
0.9226
1.5173
2.1584
1.351
1.2628
1.1233
M1-Q
1.7027
1.6878
1.6609
1.6671
2.1007
4.4207
1.9577
1.9702
2.0775
M1-Y
3.8196
3.7911
3.9572
3.6589
5.2963
9.553
4.6296
4.2926
4.8943
M3-M
0.7137
0.7367
0.7233
0.7243
1.1869
2.1853
0.9894
0.9792
1.0018
M3-Q
1.1395
1.233
1.1436
1.1186
1.6895
3.6976
1.5451
1.3932
1.4253
M3-Y
3.0899
3.1313
2.6953
2.6097
3.378
7.5622
3.166
3.281
3.1717
Table 4: Average MASE of each approach in each dataset, and respective average rank
Figure 5: Average rank of different variants of MetaARIMA across all seasonal datasets.
Figure 6: Performance of MetaARIMA across different number of trials.
Figure 7: Performance of MetaARIMA across different values for λ .
Figure 8: Performance of MetaARIMA across different values for the number of principal components.
Figure 9: Performance of MetaARIMA across different values for quantile threshold.
MetaARIMA
AutoARIMA
Chronos2
Moirai2
TimesFM
M1-M
0.871
0.916
0.867
0.882
0.899
M3-M
0.714
0.737
0.693
0.694
0.723
T-M
1.166
1.217
1.166
1.25
1.359
Table 5: Average MASE of each approach across different monthly datasets
Figure 10: Forecasts of MetaARIMA and Chronos2 for four time series from the M3-M dataset illustrating contrasting performance scenarios.
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We study the adaptation of pretrained language models to univariate time-series forecasting through a parameter-efficient transfer learning framework, with the goal of understanding which design choices drive effective cross-modal transfer. While language models operate on discrete textual tokens, time series consist of continuous numerical observations with temporal dependencies. To bridge this modality gap, we project fixed-length time-series patches directly into the embedding space of a pretrained GPT-2 backbone, bypassing textual tokenization and treating the Transformer as a generic sequence encoder. Through controlled ablation studies on seven benchmark datasets spanning energy, weather, traffic, and finance, we analyze the effects of (i)~representation strategy (continuous embeddings versus textual serialisation), (ii)~adaptation regime (frozen backbone versus partial or full fine-tuning), (iii)~architectural components such as adapters, pooling strategies, and prediction heads, and (iv)~input context length. Continuous patch-based embeddings consistently outperform textual prompting and randomly initialised backbones. The adapted pipeline attains MASE within the range of specialised forecasting architectures while updating less than 1% of total model parameters. Results further indicate that freezing the pretrained backbone and training lightweight projection and adapter modules provides a favourable accuracy--efficiency trade-off with stable behaviour across varying context lengths.
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Learning time series foundation models has been shown to be a promising approach for zero-shot time series forecasting across diverse time series domains. Insofar as scaling has been a critical driver of performance of foundation models in other modalities such as language and vision, much recent work on time series foundation modeling has focused on scaling. This has resulted in time series foundation models with hundreds of millions of parameters that are, while performant, inefficient and expensive to use in practice. This paper describes a simple recipe for learning efficient foundation models for zero-shot time series forecasting that are orders of magnitude smaller. We show that large-scale transformers are not necessary: small hybrid models that interleave long convolution and linear RNN layers (in particular DeltaNet layers) can match the performance of larger transformer-based models while being more than a hundred times smaller. We also describe several data augmentation and inference strategies that further improve performance. This recipe results in Reverso, a family of efficient time series foundation models for zero-shot forecasting that significantly push the performance-efficiency Pareto frontier.
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