What is it about?
A time series model that can clothe any distribution stationary dependence (under categorization of the variables) is presented. This may `fall` into the MC form but also covers the infinite Markovian dependence. Causality is defined and accompanied by a condition. For a causal TARMA process, the conditional probability based on all past variables, is expressed as a (hyperbolic) functional of its lagged probabilities.
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Why is it important?
(i) it is a flexible model due to allowing any (k+1) categories, any q moving-average order (for nonzero q, the infinite MC dependence is achieved) and any p auto-regressive order (for zero p, the finite q-dependence is achieved) (ii) it reveals the form of nonlinear dependence for the probabilities of the process, conditional on all past variables (the `Babushka`) (iii) due to its IID (multivariate) building block, it paves the way for the inference and a non-parametric time series stationarity chi-square test
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This page is a summary of: The table auto-regressive moving-average model for (categorical) stationary series: statistical properties (causality; from the all random to the conditional random), Journal of Nonparametric Statistics, October 2018, Taylor & Francis,
DOI: 10.1080/10485252.2018.1527912.
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