SimpleTM

The repo is the official implementation for the paper: [ICLR '25] SimpleTM: A Simple Baseline For Multivariate Time Series Forcasting.

Introduction

We propose SimpleTM, a simple yet effective architecture that uniquely integrates classical signal processing ideas with a slightly modified attention mechanism.

We show that even a single-layer configuration can effectively capture intricate dependencies in multivariate time-series data, while maintaining minimal model complexity and parameter requirements. This streamlined construction achieves a performance profile surpassing (or on par with) most existing baselines across nearly all publicly available benchmarks.

Table 6: Complete results of the long-term forecasting task, with an input length of 96 for all tasks. The reported metrics include the averaged Mean Squared Error (MSE) and Mean Absolute Error (MAE) across four prediction horizons, where lower values indicate better model performance.

Dataset	Horizon	SimpleTM (Ours)		TimeMixer (2024)		iTransformer (2024)		CrossGNN (2024)		RLinear (2023)		PatchTST (2023)		Crossformer (2023)		TiDE (2023)		TimesNet (2023)		DLinear (2023)		SCINet (2022)		FEDformer (2022)		Stationary (2022)		Autoformer (2021)
		MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTm1	96	0.321	0.361	0.328	0.363	0.334	0.368	0.335	0.373	0.355	0.376	0.329	0.367	0.404	0.426	0.364	0.387	0.338	0.375	0.345	0.372	0.418	0.438	0.379	0.419	0.386	0.398	0.505	0.475
	192	0.360	0.380	0.364	0.384	0.377	0.391	0.372	0.390	0.391	0.392	0.367	0.385	0.450	0.451	0.398	0.404	0.374	0.387	0.380	0.389	0.439	0.450	0.426	0.441	0.459	0.444	0.553	0.496
	336	0.390	0.404	0.390	0.404	0.426	0.420	0.403	0.411	0.424	0.415	0.399	0.410	0.532	0.515	0.428	0.425	0.410	0.411	0.413	0.413	0.490	0.485	0.445	0.459	0.495	0.464	0.621	0.537
	720	0.454	0.438	0.458	0.445	0.491	0.459	0.461	0.442	0.487	0.450	0.454	0.439	0.666	0.589	0.487	0.461	0.478	0.450	0.474	0.453	0.595	0.550	0.543	0.490	0.585	0.516	0.671	0.561
	Avg	0.381	0.396	0.385	0.399	0.407	0.410	0.393	0.404	0.414	0.407	0.387	0.400	0.513	0.496	0.419	0.419	0.400	0.406	0.403	0.407	0.485	0.481	0.448	0.452	0.481	0.456	0.588	0.517
ETTm2	96	0.173	0.257	0.176	0.259	0.180	0.264	0.176	0.266	0.182	0.265	0.175	0.259	0.287	0.366	0.207	0.305	0.187	0.267	0.193	0.292	0.286	0.377	0.203	0.287	0.192	0.274	0.255	0.339
	192	0.238	0.299	0.242	0.303	0.250	0.309	0.240	0.307	0.246	0.304	0.241	0.302	0.414	0.492	0.290	0.364	0.249	0.309	0.284	0.362	0.399	0.445	0.269	0.328	0.280	0.339	0.281	0.340
	336	0.296	0.338	0.304	0.342	0.311	0.348	0.304	0.345	0.307	0.342	0.305	0.343	0.597	0.542	0.377	0.422	0.321	0.351	0.369	0.427	0.637	0.591	0.325	0.366	0.334	0.361	0.339	0.372
	720	0.393	0.395	0.393	0.397	0.412	0.407	0.406	0.400	0.407	0.398	0.402	0.400	1.730	1.042	0.558	0.524	0.408	0.403	0.554	0.522	0.960	0.735	0.421	0.415	0.417	0.413	0.433	0.432
	Avg	0.275	0.322	0.278	0.325	0.288	0.332	0.282	0.330	0.286	0.327	0.281	0.326	0.757	0.610	0.358	0.404	0.291	0.333	0.350	0.401	0.571	0.537	0.305	0.349	0.306	0.347	0.327	0.371
ETTh1	96	0.366	0.392	0.381	0.401	0.386	0.405	0.382	0.398	0.386	0.395	0.414	0.419	0.423	0.448	0.479	0.464	0.384	0.402	0.386	0.400	0.654	0.599	0.376	0.419	0.513	0.491	0.449	0.459
	192	0.422	0.421	0.440	0.433	0.441	0.436	0.427	0.425	0.437	0.424	0.460	0.445	0.471	0.474	0.525	0.492	0.436	0.429	0.437	0.432	0.719	0.631	0.420	0.448	0.534	0.504	0.500	0.482
	336	0.440	0.438	0.501	0.462	0.487	0.458	0.465	0.445	0.479	0.446	0.501	0.466	0.570	0.546	0.565	0.515	0.491	0.469	0.481	0.459	0.778	0.659	0.459	0.465	0.588	0.535	0.521	0.496
	720	0.463	0.462	0.501	0.482	0.503	0.491	0.472	0.468	0.481	0.470	0.500	0.488	0.653	0.621	0.594	0.558	0.521	0.500	0.519	0.516	0.836	0.699	0.506	0.507	0.643	0.616	0.514	0.512
	Avg	0.422	0.428	0.458	0.445	0.454	0.447	0.437	0.434	0.446	0.434	0.469	0.454	0.529	0.522	0.541	0.507	0.458	0.450	0.456	0.452	0.747	0.647	0.440	0.460	0.570	0.537	0.496	0.487
ETTh2	96	0.281	0.338	0.292	0.343	0.297	0.349	0.309	0.359	0.288	0.338	0.302	0.348	0.745	0.584	0.400	0.440	0.340	0.374	0.333	0.387	0.707	0.621	0.358	0.397	0.476	0.458	0.346	0.388
	192	0.355	0.387	0.374	0.395	0.380	0.400	0.390	0.406	0.374	0.390	0.388	0.400	0.877	0.656	0.528	0.509	0.402	0.414	0.477	0.476	0.860	0.689	0.429	0.439	0.512	0.493	0.456	0.452
	336	0.365	0.401	0.428	0.433	0.428	0.432	0.426	0.444	0.415	0.426	0.426	0.433	1.043	0.731	0.643	0.571	0.452	0.452	0.594	0.541	1.000	0.744	0.496	0.487	0.552	0.551	0.482	0.486
	720	0.413	0.436	0.454	0.458	0.427	0.445	0.445	0.444	0.420	0.440	0.431	0.446	1.104	0.763	0.874	0.679	0.462	0.468	0.831	0.657	1.249	0.838	0.463	0.474	0.562	0.560	0.515	0.511
	Avg	0.353	0.391	0.384	0.407	0.383	0.407	0.393	0.413	0.374	0.398	0.387	0.407	0.942	0.684	0.611	0.550	0.414	0.427	0.559	0.515	0.954	0.723	0.437	0.449	0.526	0.516	0.450	0.459
ECL	96	0.141	0.235	0.153	0.244	0.148	0.240	0.173	0.275	0.201	0.281	0.181	0.270	0.219	0.314	0.237	0.329	0.168	0.272	0.197	0.282	0.247	0.345	0.193	0.308	0.169	0.273	0.201	0.317
	192	0.151	0.247	0.166	0.256	0.162	0.253	0.195	0.288	0.201	0.283	0.188	0.274	0.231	0.322	0.236	0.330	0.184	0.289	0.196	0.285	0.257	0.355	0.201	0.315	0.182	0.286	0.222	0.334
	336	0.173	0.267	0.184	0.275	0.178	0.269	0.206	0.300	0.215	0.298	0.204	0.293	0.246	0.337	0.249	0.344	0.198	0.300	0.209	0.301	0.269	0.369	0.214	0.329	0.200	0.304	0.231	0.338
	720	0.201	0.293	0.226	0.313	0.225	0.317	0.231	0.335	0.257	0.331	0.246	0.324	0.280	0.363	0.284	0.373	0.220	0.320	0.245	0.333	0.299	0.390	0.246	0.355	0.222	0.321	0.254	0.361
	Avg	0.166	0.260	0.178	0.270	0.201	0.300	0.219	0.298	0.205	0.290	0.244	0.334	0.251	0.344	0.192	0.295	0.212	0.300	0.268	0.365	0.214	0.327	0.193	0.296	0.227	0.338
Weather	96	0.162	0.207	0.165	0.212	0.174	0.214	0.159	0.218	0.192	0.232	0.177	0.218	0.158	0.230	0.202	0.261	0.172	0.220	0.196	0.255	0.221	0.306	0.217	0.296	0.173	0.223	0.266	0.336
	192	0.208	0.248	0.209	0.253	0.221	0.254	0.211	0.266	0.240	0.271	0.225	0.259	0.206	0.277	0.242	0.298	0.219	0.261	0.237	0.296	0.261	0.340	0.276	0.336	0.245	0.285	0.307	0.367
	336	0.263	0.290	0.264	0.293	0.278	0.296	0.267	0.310	0.292	0.307	0.278	0.297	0.272	0.335	0.287	0.335	0.280	0.306	0.283	0.335	0.309	0.378	0.339	0.380	0.321	0.338	0.359	0.395
	720	0.340	0.341	0.342	0.345	0.358	0.347	0.352	0.362	0.364	0.353	0.354	0.348	0.398	0.418	0.351	0.386	0.365	0.359	0.345	0.381	0.377	0.427	0.403	0.428	0.414	0.410	0.419	0.428
	Avg	0.243	0.271	0.245	0.276	0.258	0.278	0.247	0.289	0.272	0.291	0.259	0.281	0.259	0.315	0.271	0.320	0.259	0.287	0.265	0.317	0.292	0.363	0.309	0.360	0.288	0.314	0.338	0.382
Traffic	96	0.410	0.274	0.464	0.289	0.395	0.268	0.570	0.310	0.649	0.389	0.462	0.295	0.522	0.290	0.805	0.493	0.593	0.321	0.650	0.396	0.788	0.499	0.587	0.366	0.612	0.338	0.613	0.388
	192	0.430	0.280	0.477	0.292	0.417	0.276	0.577	0.321	0.601	0.366	0.466	0.296	0.530	0.293	0.756	0.474	0.617	0.336	0.598	0.370	0.789	0.505	0.604	0.373	0.613	0.340	0.616	0.382
	336	0.449	0.290	0.500	0.305	0.433	0.283	0.588	0.324	0.609	0.369	0.482	0.304	0.558	0.305	0.762	0.477	0.629	0.336	0.605	0.373	0.797	0.508	0.621	0.383	0.618	0.328	0.622	0.337
	720	0.486	0.309	0.548	0.313	0.467	0.302	0.597	0.337	0.647	0.387	0.514	0.322	0.589	0.328	0.719	0.449	0.640	0.350	0.645	0.394	0.841	0.523	0.626	0.382	0.653	0.355	0.660	0.408
	Avg	0.444	0.289	0.497	0.300	0.428	0.282	0.583	0.323	0.626	0.378	0.481	0.304	0.550	0.304	0.760	0.473	0.620	0.336	0.625	0.383	0.804	0.509	0.610	0.376	0.624	0.340	0.628	0.379
Solar-Energy	96	0.163	0.232	0.215	0.294	0.203	0.237	0.222	0.301	0.322	0.339	0.234	0.286	0.310	0.331	0.312	0.399	0.250	0.292	0.290	0.378	0.237	0.344	0.242	0.342	0.215	0.249	0.884	0.711
	192	0.182	0.247	0.237	0.275	0.233	0.261	0.246	0.307	0.359	0.356	0.267	0.310	0.734	0.725	0.339	0.416	0.296	0.318	0.320	0.398	0.280	0.380	0.285	0.380	0.254	0.272	0.834	0.692
	336	0.193	0.257	0.252	0.298	0.248	0.273	0.263	0.324	0.397	0.369	0.290	0.315	0.750	0.735	0.368	0.430	0.319	0.330	0.353	0.415	0.304	0.389	0.282	0.376	0.290	0.296	0.941	0.723
	720	0.199	0.252	0.244	0.293	0.249	0.275	0.265	0.318	0.397	0.356	0.289	0.317	0.769	0.765	0.370	0.425	0.338	0.337	0.356	0.413	0.308	0.388	0.357	0.427	0.285	0.295	0.882	0.717
	Avg	0.184	0.247	0.237	0.290	0.233	0.262	0.249	0.313	0.369	0.356	0.270	0.307	0.641	0.639	0.347	0.417	0.301	0.319	0.330	0.401	0.282	0.375	0.291	0.381	0.261	0.381	0.885	0.711

Get Started

1. Download the Data

All datasets have been preprocessed and are ready for use. You can obtain them from their original sources:

• ETT: https://github.com/zhouhaoyi/ETDataset/tree/main
• Traffic, Electricity, Weather: https://github.com/thuml/Autoformer
• Solar: https://github.com/laiguokun/LSTNet
• PEMS: https://github.com/cure-lab/SCINet

For convenience, we provide a comprehensive package containing all required datasets, available for download from Google Drive. You can place it under the folder ./dataset.

2. Setup Your Environment

Choose one of the following methods to set up your environment:

Option A: Anaconda

Create and activate a Python environment using the provided configuration file environment.yml:

conda env create -f environment.yml -n SimpleTM
conda activate SimpleTM

Option B: Docker

If you prefer Docker, build an image using the provided Dockerfile:

docker build --tag simpletm:latest .

3. Train the Model

Experiment scripts for various benchmarks are provided in the scripts directory. You can reproduce experiment results as follows:

bash ./scripts/multivariate_forecasting/ETT/SimpleTM_h1.sh       # ETTh1
bash ./scripts/multivariate_forecasting/ECL/SimpleTM.sh          # Electricity
bash ./scripts/long_term_forecast/SolarEnergy/SimpleTM.sh        # Solar-Energy
bash ./scripts/long_term_forecast/Weather/SimpleTM.sh            # Weather
bash ./scripts/short_term_forecast/PEMS/SimpleTM_03.sh           # PEMS03

Docker Users

If you're using Docker, run the scripts with the following command structure (example for ETTh1):

docker run --gpus all -it --rm --ipc=host \
    --user $(id -u):$(id -g) \
    -v "$(pwd)":/scratch --workdir /scratch -e HOME=/scratch \
    simpletm:latest \
    bash scripts/multivariate_forecasting/ETT/SimpleTM_h1.sh

Model Efficiency

To provide an efficiency comparison, we evaluated our model against two of the most competitive baselines: the transformer-based iTransformer and linear-based TimeMixer. Our experimental setup used a consistent batch size of 256 across all models and measured four key metrics: total trainable parameters, inference time, GPU memory footprint, and peak memory usage during the backward pass. Results for all baseline models were compiled using PyTorch.

Please note that our default experimental configuration does not employ compilation optimizations. To speed up, enable the --compile flag in the scripts.

Table 13: Comparison of model performance and resource utilization across different datasets. Metrics include Mean Squared Error (MSE), total parameter count, inference time (seconds), GPU memory footprint (MB), and peak memory usage (MB).

Dataset	Model	MSE	Total Params	Inference Time (s)	GPU Mem Footprint (MB)	Peak Mem (MB)
Weather	SimpleTM	0.162	13,472	0.0132	994	181.75
	TimeMixer	0.164	104,433	0.0453	2,954	2,281.38
	iTransformer	0.176	4,833,888	0.0222	1,596	847.62
Solar	SimpleTM	0.163	166,304	0.0455	2,048	1,181.56
	TimeMixer	0.215	13,009,079	0.2644	7,576	6,632.40
	iTransformer	0.203	3,255,904	0.0663	4,022	2,776.50

Acknowledgement

We appreciate the following GitHub repos a lot for their valuable code and efforts.

• Time-Series-Library (https://github.com/thuml/Time-Series-Library)
• iTransformer (https://github.com/thuml/iTransformer)
• TimeMixer (https://github.com/kwuking/TimeMixer)
• Autoformer (https://github.com/thuml/Autoformer)

Citation

If you find this repo helpful, please cite our paper.

@inproceedings{
chen2025simpletm,
title={Simple{TM}: A Simple Baseline for Multivariate Time Series Forecasting},
author={Hui Chen and Viet Luong and Lopamudra Mukherjee and Vikas Singh},
booktitle={The Thirteenth International Conference on Learning Representations},
year={2025},
url={https://openreview.net/forum?id=oANkBaVci5}
}