On Some Spatial Considerations of the Tabulated (Categorical) Stationary Series (Natural Modelling; Probability Restrictions; Markovian Dependence)

A spatial model for the strictly stationary series that have been discretized into a specified number of categories, is presented: special emphasis is concentrated on the finite two-sided Markovian structure. The new suggestion puts forward an all-random model, relying on a collection of unobserved series, with variables that are defined on different sample spaces. Imitating the linear ARMA series (that employ the spectral densities though), symmetry restrictions (via Bernoulli variables) and time reversal are explored and succeed to a certain extent. Subject to an, applicable to any distribution, assignment of variables’ values into (k + 1) ranges, and to the selection of the serial order p and q, the general Table Auto-Linear Moving-Average (k, p, q) equation provides for the spatial, all-moments stationary as well as infinite homogeneous Markovian, dependence.

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The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.