Discovering patterns in categorical time series using IFS
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Statistical analysis of discrete-valued time series using categorical ARMA models
Computational Statistics & Data Analysis
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The NDARMA model is a discrete counterpart to the usual ARMA model, which can be applied to purely categorical processes. NDARMA processes are shown to be @f-mixing, so it is possible to find asymptotic expressions for the distribution of several types of statistics. Such asymptotic properties are useful for hypothesis testing or other inferential procedures. This is exemplified by considering the Gini index and the entropy as measures of marginal dispersion, the Pearson statistic for checking the goodness-of-fit with regard to a hypothetical marginal distribution, and several measures of signed or unsigned serial dependence. For each of these cases, the obtained asymptotic approximations are also compared to the empirically observed behavior in time series of finite length. Practical applications are illustrated by a real-data example.