  Multivariate time series forecasting (MTSF) is crucial for decision-making to
precisely forecast the future values/trends, based on the complex relationships
identified from historical observations of multiple sequences. Recently,
Spatial-Temporal Graph Neural Networks (STGNNs) have gradually become the theme
of MTSF model as their powerful capability in mining spatial-temporal
dependencies, but almost of them heavily rely on the assumption of historical
data integrity. In reality, due to factors such as data collector failures and
time-consuming repairment, it is extremely challenging to collect the whole
historical observations without missing any variable. In this case, STGNNs can
only utilize a subset of normal variables and easily suffer from the incorrect
spatial-temporal dependency modeling issue, resulting in the degradation of
their forecasting performance. To address the problem, in this paper, we
propose a novel Graph Interpolation Attention Recursive Network (named GinAR)
to precisely model the spatial-temporal dependencies over the limited collected
data for forecasting. In GinAR, it consists of two key components, that is,
interpolation attention and adaptive graph convolution to take place of the
fully connected layer of simple recursive units, and thus are capable of
recovering all missing variables and reconstructing the correct
spatial-temporal dependencies for recursively modeling of multivariate time
series data, respectively. Extensive experiments conducted on five real-world
datasets demonstrate that GinAR outperforms 11 SOTA baselines, and even when
90% of variables are missing, it can still accurately predict the future values
of all variables.
