  The majority of real-world processes are spatiotemporal, and the data
generated by them exhibits both spatial and temporal evolution. Weather is one
of the most essential processes in this domain, and weather forecasting has
become a crucial part of our daily routine. Weather data analysis is considered
the most complex and challenging task. Although numerical weather prediction
models are currently state-of-the-art, they are resource-intensive and
time-consuming. Numerous studies have proposed time series-based models as a
viable alternative to numerical forecasts. Recent research in the area of time
series analysis indicates significant advancements, particularly regarding the
use of state-space-based models (white box) and, more recently, the integration
of machine learning and deep neural network-based models (black box). The most
famous examples of such models are RNNs and transformers. These models have
demonstrated remarkable results in the field of time-series analysis and have
demonstrated effectiveness in modelling temporal correlations. It is crucial to
capture both temporal and spatial correlations for a spatiotemporal process, as
the values at nearby locations and time affect the values of a spatiotemporal
process at a specific point. This self-contained paper explores various
regional data-driven weather forecasting methods, i.e., forecasting over
multiple latitude-longitude points (matrix-shaped spatial grid) to capture
spatiotemporal correlations. The results showed that spatiotemporal prediction
models reduced computational costs while improving accuracy. In particular, the
proposed tensor train dynamic mode decomposition-based forecasting model has
comparable accuracy to the state-of-the-art models without the need for
training. We provide convincing numerical experiments to show that the proposed
approach is practical.
