  In this work, we tackle two widespread challenges in real applications for
time-series forecasting that have been largely understudied: distribution
shifts and missing data. We propose SpectraNet, a novel multivariate
time-series forecasting model that dynamically infers a latent space spectral
decomposition to capture current temporal dynamics and correlations on the
recent observed history. A Convolution Neural Network maps the learned
representation by sequentially mixing its components and refining the output.
Our proposed approach can simultaneously produce forecasts and interpolate past
observations and can, therefore, greatly simplify production systems by
unifying imputation and forecasting tasks into a single model. SpectraNet
achieves SoTA performance simultaneously on both tasks on five benchmark
datasets, compared to forecasting and imputation models, with up to 92% fewer
parameters and comparable training times. On settings with up to 80% missing
data, SpectraNet has average performance improvements of almost 50% over the
second-best alternative. Our code is available at
https://github.com/cchallu/spectranet.
