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Summary A broad but parametrically simple model for a stationary sequence of dependent discrete random variables is given and several submodels are discussed. The structure of the model is specified by the marginal distribution of the random variables and several other parameters. The sequence of random variables is formed by a probabilistic linear combination of i.i.d. discrete random variables and is in general not Markovian. Second-order joint moments and spectra are obtained for the model, as well as some properties for the lengths of runs. The special case of a process in which the variables take on only two values is considered; this binary process is useful as a model for the counting process in a discrete-time point process.
Jacobs et al. (1978) studied this question.