Abstract
In this note, we introduce a discrete counterpart of the conventional max-autoregressive moving-average process of Davis and Resnick (1989), based on the binomial thinning operator and driven by a sequence of i. i. d. nonnegative integer-valued random variables with a finite range of counts. Basic probabilistic and statistical properties of this new class of models are discussed in detail, namely the existence of a stationary distribution, and how observations’ and innovations’ distributions are related to each other. Furthermore, parameter estimation is also addressed.
Highlights
Modeling the temporal dependence of integer-valued time series defined on a finite range of counts, say {0, 1, . . . , n}, is nowadays a topic of research which is gaining importance in time series analysis
Note that traditional integer-valued ARMA-type models are useless in this context, since such models are defined over unbounded sets
Our aim in this paper is to construct a full integer-valued time series model with finite support, in the sense that the model should include both an autoregressive-type and a moving-average-type component ( a “full” counterpart), and it should certainly contain both a purely autoregressive-type and a purely moving-average-type model as a special case. To this extent we introduce a discrete counterpart of the conventional maxautoregressive moving-average process of Davis & Resnick (1989) which will be referred to as the maximum BARMA (in short max-BARMA(p, q)) model
Summary
Modeling the temporal dependence of integer-valued time series defined on a finite range of counts, say {0, 1, . . . , n}, is nowadays a topic of research which is gaining importance in time series analysis. Our aim in this paper is to construct a full integer-valued time series model with finite support, in the sense that the model should include both an autoregressive-type and a moving-average-type component ( a “full” counterpart), and it should certainly contain both a purely autoregressive-type and a purely moving-average-type model as a special case. To this extent we introduce a discrete counterpart of the conventional maxautoregressive moving-average process of Davis & Resnick (1989) which will be referred to as the maximum BARMA (in short max-BARMA(p, q)) model.
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