# Exploring Over-stationarization in Deep Learning-based Bus/Tram Arrival Time Prediction: Analysis and Non-stationary Effect Recovery

arXiv: https://arxiv.org/abs/2509.06979 · HTML: https://mlsanity.com/paper/2509.06979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [A Tutorial on Learning With Bayesian Networks](https://mlsanity.com/paper/2002.00269/) (2020)
- [ArrivalNet: Predicting City-wide Bus/Tram Arrival Time with Two-dimensional Temporal Variation Modeling](https://mlsanity.com/paper/2410.14742/) (2024)

## Abstract (arXiv)

Arrival time prediction (ATP) of public transport vehicles is essential in improving passenger experience and supporting traffic management. Deep learning has demonstrated outstanding performance in ATP due to its ability to model non-linear and temporal dynamics. In the multi-step ATP, non-stationary data will degrade the model performance due to the variation in variables' joint distribution along the temporal direction. Previous studies mainly applied normalization to eliminate the non-stationarity in time series, thereby achieving better predictability. However, the normalization may obscure useful characteristics inherent in non-stationarity, which is known as the over-stationarization. In this work, to trade off predictability and non-stationarity, a new approach for multi-step ATP, named non-stationary ATP ( NSATP), is proposed. The method consists of two stages: series stationarization and non-stationarity effect recovery. The first stage aims at improving the predictability. As for the latter, NSATP extends a state-of-the-art method from one-dimensional to two dimensional based models to capture the hidden periodicity in time series and designs a compensation module of over-stationarization by learning scaling and shifting factors from raw data. 125 days' public transport operational data of Dresden is collected for validation. Experimental results show that compared to baseline methods, the proposed NSATP can reduce RMSE, MAE, and MAPE by 2.37%, 1.22%, and 2.26% for trams and by 1.72%, 0.60%, and 1.17% for buses, respectively.