Echo State Networks for Spatio-Temporal Area-Level Data

TL;DR

This work addresses forecasting spatio-temporal area-level data by enhancing Echo State Networks (ESNs) with spatial structure through an areal input embedding, yielding AESN. By embedding neighborhood information at the input via an areal random representation and leveraging ensemble forecasting for uncertainty, AESN preserves ESN efficiency while significantly improving forecast accuracy over standard ESNs, EOF-augmented ESNs, and dynamic linear models. The approach is demonstrated on Eurostat tourism occupancy data, where AESN better captures both temporal nonlinear dynamics and spatial dependencies, delivering accurate short- and long-horizon forecasts and calibrated predictive intervals. The method offers practical benefits for policy and regional planning by providing reliable spatio-temporal forecasts with efficient training and robust uncertainty quantification.

Abstract

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts.

Figures (4)

• Figure 1: Night spent in thousands at tourist accommodations for NUTS level 2 regions in EU on January 2020. The mid-south region tends to attract a higher number of tourists, whereas the eastern and northern regions generally experience lower tourist activity.
• Figure 2: Time series plots of night spent in thousands at tourist accommodations at selected locations. All four locations reveal some seasonality, an increasing trend, and other nonlinear characteristics.
• Figure 3: Out-of-sample 12-month forecasts for night spent in thousands at tourist accommodations at four selected locations from January 2023 to December 2023, based on the 12-step forecast of the AESN model. For locations with strong seasonality, the AESN model accurately captures the trend of higher tourism activity during the summer and lower activity in other seasons.
• Figure 4: Spatial maps of AESN forecasts for nights spent in thousands at tourist accommodations, based on the 12-step ahead forecast of the AESN model. The AESN model effectively captures the spatial pattern of higher tourism in the mid-south regions. Additionally, it accurately reflects the seasonal trend, with tourism activity increasing from low in spring to high in summer and then declining again in winter.