# Long-Term Missing Value Imputation for Time Series Data Using Deep Neural Networks

arXiv: https://arxiv.org/abs/2202.12441 · HTML: https://mlsanity.com/paper/2202.12441/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 49 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Genetic CNN](https://mlsanity.com/paper/1703.01513/) (2017)
- [NeuralProphet: Explainable Forecasting at Scale](https://mlsanity.com/paper/2111.15397/) (2021)
- [AR-Net: A simple Auto-Regressive Neural Network for time-series](https://mlsanity.com/paper/1911.12436/) (2019)
- [Surrogate Optimization of Deep Neural Networks for Groundwater Predictions](https://mlsanity.com/paper/1908.10947/) (2019)

## Built on by (most cited first, 7 of 7)

- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Risk factor aggregation and stress testing](https://mlsanity.com/paper/2310.04511/) (2023)
- [Missing Data Imputation Based on Dynamically Adaptable Structural Equation Modeling with Self-Attention](https://mlsanity.com/paper/2308.12388/) (2023)
- [Spatiotemporal Transformer for Imputing Sparse Data: A Deep Learning Approach](https://mlsanity.com/paper/2312.00963/) (2023)
- [Imputation of Missing Data in Smooth Pursuit Eye Movements Using a Self-Attention-based Deep Learning Approach](https://mlsanity.com/paper/2506.00545/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Data-driven Lake Water Quality Forecasting for Time Series with Missing Data using Machine Learning](https://mlsanity.com/paper/2601.15503/) (2026)

## Abstract (arXiv)

We present an approach that uses a deep learning model, in particular, a MultiLayer Perceptron (MLP), for estimating the missing values of a variable in multivariate time series data. We focus on filling a long continuous gap (e.g., multiple months of missing daily observations) rather than on individual randomly missing observations. Our proposed gap filling algorithm uses an automated method for determining the optimal MLP model architecture, thus allowing for optimal prediction performance for the given time series. We tested our approach by filling gaps of various lengths (three months to three years) in three environmental datasets with different time series characteristics, namely daily groundwater levels, daily soil moisture, and hourly Net Ecosystem Exchange. We compared the accuracy of the gap-filled values obtained with our approach to the widely-used R-based time series gap filling methods ImputeTS and mtsdi. The results indicate that using an MLP for filling a large gap leads to better results, especially when the data behave nonlinearly. Thus, our approach enables the use of datasets that have a large gap in one variable, which is common in many long-term environmental monitoring observations.