Data-Driven Spatial Weight Matrices for Space-Time Autoregressive Models: A Similarity-Based Framework with an Application to Global Temperature Dynamics

<title>Abstract</title> <p>Spatial autoregressive models commonly rely on geographical contiguity or physical distance to specify spatial dependence among observational units. Although these approaches are computationally convenient and widely adopted, they implicitly assume that geographical proximity provides an adequate representation of the dependence structure. However, similar dynamics could depend on various factors, not necessarily linked to the neighbouring. This paper proposes a data-driven framework for constructing spatial weight matrices based on statistical similarity rather than geographical proximity. The proposed approach combines similarity measures and clustering techniques to derive alternative spatial weight matrices that are subsequently incorporated into Space--Time Autoregressive models. Analyzing temperature dynamics, three complementary similarity criteria are considered, capturing long-term warming rates, annual temperature variations, and the persistence of patterns. These criteria generate alternative representations of spatial dependence that reflect the intrinsic behaviour of the observed time series. The methodology is illustrated using annual temperature observations collected for 168 countries over the period 1901--2022. The empirical analysis compares the proposed similarity-based STAR models with the conventional contiguity-based specification through both in-sample fitting and out-of-sample forecasting. Results show that similarity-based spatial weight matrices improve model performance, with the Hamming-distance specification providing the highest forecasting accuracy. Beyond the climate application considered here, the proposed framework provides a general strategy for defining spatial dependence in situations where statistical similarity offers a more informative description of interactions than geographical neighbourhood. The methodology can therefore be naturally extended to a wide range of spatio-temporal problems in environmental sciences, socio-economics, epidemiology and other application domains.</p>