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The predictive distributions of thinning‐based count processes
Author(s) -
Lu Yang
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12438
Subject(s) - thinning , term (time) , computer science , mathematics , taylor series , algorithm , mathematical optimization , mathematical analysis , physics , quantum mechanics , biology , ecology
This paper shows that the term structure of conditional (i.e. predictive) distributions allows for closed form expression in a large family of (possibly higher order or infinite order) thinning‐based count processes such as INAR( p ), INARCH( p ), NBAR( p ), and INGARCH(1,1). Such predictive distributions are currently often deemed intractable by the literature and existing approximation methods are usually time consuming and induce approximation errors. In this paper, we propose a Taylor's expansion algorithm for these predictive distributions, which is both exact and fast. Through extensive simulation exercises, we demonstrate its advantages with respect to existing methods in terms of the computational gain and/or precision.