Spatio-temporal modelling of economic phenomena in the context of reducing the dimensions of the random field

Motivation: Clear spatial diversity and high variability in time of economic phenomena and the fact that they show dependencies in space and time dimensions, as well as the spatio-temporal dependencies, lead to the consideration of the phenomena in terms of random fields. On the other hand, applying methods and tools from the field of multidimensional stochastic processes called random fields is difficult due to the specificity of the economic data, in particular to a low number of the observations in space. Hence, there arises the problem of the reduction of the dimensions (especially the space dimension) of the random fields which define economic phenomena. Aim: The aim of the paper is to discuss a model that will reflect the structure of spatial connections and dependence in the spatio-temporal process, while reducing the dimension of space as a non-random argument of the random field. As a result, the set of N time series will be analysed. Therefore, we build a multiple-equation model of autoregressive character with a spatial structure of dependence. In the paper we discuss the advantages and cognitive values of such an approach to the study of economic phenomena in spatio-temporal terms. Results: The empirical example concerns the unemployment rate in Poland across provinces (NUTS2) in the period from January 2011 to April 2019. The data create spatio-temporal series which is the realisation of the two-dimensional random field. The model building strategy is based on a vector autoregressive (VAR) specification, where there are as many time series as the provinces. The study shows that the use of the concept of the conditional, with regard to space dimension, random field simplifies the econometric analysis of the spatio-temporal process under consideration without losing the accuracy of the description of his basic properties.