# Evaluation of deep learning models for multi-step ahead time series prediction

arXiv: https://arxiv.org/abs/2103.14250 · HTML: https://mlsanity.com/paper/2103.14250/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 108 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Named Entity Recognition with Bidirectional LSTM-CNNs](https://mlsanity.com/paper/1511.08308/) (2015)
- [Multi-Step-Ahead Time Series Prediction using Multiple-Output Support Vector Regression](https://mlsanity.com/paper/1401.2504/) (2014)
- [Predictive State Recurrent Neural Networks](https://mlsanity.com/paper/1705.09353/) (2017)
- [Langevin-gradient parallel tempering for Bayesian neural learning](https://mlsanity.com/paper/1811.04343/) (2018)
- [Co-evolutionary multi-task learning for dynamic time series prediction](https://mlsanity.com/paper/1703.01887/) (2017)

## Built on by (most cited first, 25 of 25)

- [Multi-Modal Deep Learning for Credit Rating Prediction Using Text and Numerical Data Streams](https://mlsanity.com/paper/2304.10740/) (2023)
- [Bayesian neural networks via MCMC: a Python-based tutorial](https://mlsanity.com/paper/2304.02595/) (2023)
- [Time-Series Classification for Dynamic Strategies in Multi-Step Forecasting](https://mlsanity.com/paper/2402.08373/) (2024)
- [Learning with Imperfect Models: When Multi-step Prediction Mitigates Compounding Error](https://mlsanity.com/paper/2504.01766/) (2025)
- [A case study of spatiotemporal forecasting techniques for weather forecasting](https://mlsanity.com/paper/2209.14782/) (2022)
- [A Self-organizing Interval Type-2 Fuzzy Neural Network for Multi-Step Time Series Prediction](https://mlsanity.com/paper/2407.08010/) (2024)
- [Stratify: Unifying Multi-Step Forecasting Strategies](https://mlsanity.com/paper/2412.20510/) (2024)
- [Review of deep learning models for crypto price prediction: implementation and evaluation](https://mlsanity.com/paper/2405.11431/) (2024)
- [Recursive deep learning framework for forecasting the decadal world economic outlook](https://mlsanity.com/paper/2301.10874/) (2023)
- [Blockchain Transaction Fee Forecasting: A Comparison of Machine Learning Methods](https://mlsanity.com/paper/2305.08105/) (2023)
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- [Multi-timestep models for Model-based Reinforcement Learning](https://mlsanity.com/paper/2310.05672/) (2023)
- [A Multi-step Loss Function for Robust Learning of the Dynamics in Model-based Reinforcement Learning](https://mlsanity.com/paper/2402.03146/) (2024)
- [Accelerating Flood Warnings by 10 Hours: The Power of River Network Topology in AI-enhanced Flood Forecasting](https://mlsanity.com/paper/2410.05536/) (2024)
- [A Generative Model Based Honeypot for Industrial OPC UA Communication](https://mlsanity.com/paper/2410.21574/) (2024)
- [Quantile deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2411.15674/) (2024)
- [MAIDS: Malicious Agent Identification-based Data Security Model for Cloud Environments](https://mlsanity.com/paper/2412.14490/) (2024)
- [Spatiotemporal deep learning models for detection of rapid intensification in cyclones](https://mlsanity.com/paper/2506.08397/) (2025)
- [MUSTACHE: Multi-Step-Ahead Predictions for Cache Eviction](https://mlsanity.com/paper/2211.02177/) (2022)
- [RACH Traffic Prediction in Massive Machine Type Communications](https://mlsanity.com/paper/2405.05235/) (2024)
- [Differential Machine Learning for Time Series Prediction](https://mlsanity.com/paper/2503.03302/) (2025)
- [Yet Unnoticed in LSTM: Binary Tree Based Input Reordering, Weight Regularization, and Gate Nonlinearization](https://mlsanity.com/paper/2509.00087/) (2025)
- [Improving accuracy in short mortality rate series: Exploring Multi-step Forecasting Approaches in Hybrid Systems](https://mlsanity.com/paper/2509.22395/) (2025)
- [Extreme value forecasting using relevance-based data augmentation with deep learning models](https://mlsanity.com/paper/2510.02407/) (2025)
- [QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification](https://mlsanity.com/paper/2510.05453/) (2025)

## Abstract (arXiv)

Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and hence it is important to evaluate their strengths and weaknesses. In this paper, we present an evaluation study that compares the performance of deep learning models for multi-step ahead time series prediction. The deep learning methods comprise simple recurrent neural networks, long short-term memory (LSTM) networks, bidirectional LSTM networks, encoder-decoder LSTM networks, and convolutional neural networks. We provide a further comparison with simple neural networks that use stochastic gradient descent and adaptive moment estimation (Adam) for training. We focus on univariate time series for multi-step-ahead prediction from benchmark time-series datasets and provide a further comparison of the results with related methods from the literature. The results show that the bidirectional and encoder-decoder LSTM network provides the best performance in accuracy for the given time series problems.