  Time series imputation is one of the most fundamental tasks for time series.
Real-world time series datasets are frequently incomplete (or irregular with
missing observations), in which case imputation is strongly required. Many
different time series imputation methods have been proposed. Recent
self-attention-based methods show the state-of-the-art imputation performance.
However, it has been overlooked for a long time to design an imputation method
based on continuous-time recurrent neural networks (RNNs), i.e., neural
controlled differential equations (NCDEs). To this end, we redesign time series
(variational) autoencoders based on NCDEs. Our method, called continuous-time
autoencoder (CTA), encodes an input time series sample into a continuous hidden
path (rather than a hidden vector) and decodes it to reconstruct and impute the
input. In our experiments with 4 datasets and 19 baselines, our method shows
the best imputation performance in almost all cases.
