  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.
