MetaARIMA: Configuration-Level Transfer Learning for ARIMA Models

Vitor Cerqueira; Ricardo Inácio; Carlos Soares

stat.MLOct 25, 2026

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

Abstract

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

\mathcal{Y}

is summarised into a feature set

\mathcal{M}

. A set of ARIMA configurations (e.g. ARIMA(0,0,0)) is evaluated on each series in

\mathcal{Y}

, resulting in error estimates

\mathcal{E}

. The error scores

\mathcal{E}

are processed according to a quantile-based binarization that identifies series-wise top configurations (

\mathcal{T}

), a representation that is then compacted using PCA (

\mathcal{Z}

). A correlation analysis is also conducted using

\mathcal{E}

to identify redundant configurations.

Figure 2: Workflow for the inference stage of MetaARIMA . The query time series

Y_{query}

is converted to meta-features

M_{query}

; the meta-model outputs predictions in PCA space, which are inverted to obtain scores

\hat{T}_{query}

. MMR, using

\hat{T}_{query}

and the stored error correlations, selects a diverse subset of configurations; successive halving and AICc on

Y_{query}

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

\mathcal{A}

Notation	Value	Description
Development stage
$\tau$	0.25	Quantile threshold
$n_{pc}$	50 (15 yearly)	# principal components
$l$	42	# meta-features
Inference stage
$\lambda$	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

\lambda

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

Panel of Figure 10 — Figure 10: Forecasts of MetaARIMA and Chronos2 for four time series from the M3-M dataset illustrating contrasting performance scenarios.

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Inspired by recent breakthroughs in large language models for natural language processing, foundation models have emerged as a promising paradigm for zero-shot time series forecasting, enabling accurate predictions on datasets never seen during pre-training. Ranging from tens to hundreds of millions of parameters, these models are pre-trained on vast and diverse collections of time series, learning generalizable representations that support both point and probabilistic forecasting. This approach alleviates the need for dataset-specific model design and manual tuning, offering a unified solution across forecasting problems. In this work, we review the main architectures, pre-training strategies, and optimization methods underpinning these models. We further investigate post-pre-training fine-tuning of selected foundation models to enhance their performance on specific datasets. Our empirical results demonstrate that this step consistently improves forecasting accuracy over the zero-shot baseline.

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