  In this paper, we propose an online algorithm mspace for forecasting node
features in temporal graphs, which captures spatial cross-correlation among
different nodes as well as the temporal auto-correlation within a node. The
algorithm can be used for both probabilistic and deterministic multi-step
forecasting, making it applicable for estimation and generation tasks.
Comparative evaluations against various baselines, including temporal graph
neural network (TGNN) models and classical Kalman filters, demonstrate that
mspace performs at par with the state-of-the-art and even surpasses them on
some datasets. Importantly, mspace demonstrates consistent performance across
datasets with varying training sizes, a notable advantage over TGNN models that
require abundant training samples to effectively learn the spatiotemporal
trends in the data. Therefore, employing mspace is advantageous in scenarios
where the training sample availability is limited. Additionally, we establish
theoretical bounds on multi-step forecasting error of mspace and show that it
scales linearly with the number of forecast steps $q$ as $\mathcal{O}(q)$. For
an asymptotically large number of nodes $n$, and timesteps $T$, the
computational complexity of mspace grows linearly with both $n$, and $T$, i.e.,
$\mathcal{O}(nT)$, while its space complexity remains constant
$\mathcal{O}(1)$. We compare the performance of various mspace variants against
ten recent TGNN baselines and two classical baselines, ARIMA and the Kalman
filter across ten real-world datasets. Additionally, we propose a technique to
generate synthetic datasets to aid in evaluating node feature forecasting
methods, with the potential to serve as a benchmark for future research.
Lastly, we have investigate the interpretability of different mspace variants
by analyzing model parameters alongside dataset characteristics to derive model
and data-centric insights.
