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QUASI‐LIKELIHOOD INFERENCE FOR NEGATIVE BINOMIAL TIME SERIES MODELS
Author(s) -
Christou Vasiliki,
Fokianos Konstantinos
Publication year - 2014
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12050
Subject(s) - negative binomial distribution , mathematics , count data , quasi likelihood , estimator , series (stratigraphy) , poisson distribution , binomial distribution , beta binomial distribution , multinomial distribution , statistics , inference , econometrics , negative multinomial distribution , computer science , artificial intelligence , paleontology , biology
We study inference and diagnostics for count time series regression models that include a feedback mechanism. In particular, we are interested in negative binomial processes for count time series. We study probabilistic properties and quasi‐likelihood estimation for this class of processes. We show that the resulting estimators are consistent and asymptotically normally distributed. These facts enable us to construct probability integral transformation plots for assessing any assumed distributional assumptions. The key observation in developing the theory is a mean parameterized form of the negative binomial distribution. For transactions data, it is seen that the negative binomial distribution offers a better fit than the Poisson distribution. This is an immediate consequence of the fact that transactions can be represented as a collection of individual activities that correspond to different trading strategies.