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Predictive likelihood for coherent forecasting of count time series
Author(s) -
Mukhopadhyay Siuli,
Sathish Vurukonda
Publication year - 2019
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.2566
Subject(s) - autoregressive model , robustness (evolution) , series (stratigraphy) , computer science , likelihood function , econometrics , time series , probabilistic forecasting , poisson distribution , statistics , mathematics , maximum likelihood , data mining , artificial intelligence , machine learning , paleontology , biochemistry , chemistry , biology , probabilistic logic , gene
A new forecasting method based on the concept of the profile predictive likelihood function is proposed for discrete‐valued processes. In particular, generalized autoregressive moving average (GARMA) models for Poisson distributed data are explored in detail. Highest density regions are used to construct forecasting regions. The proposed forecast estimates and regions are coherent. Large‐sample results are derived for the forecasting distribution. Numerical studies using simulations and two real data sets are used to establish the performance of the proposed forecasting method. Robustness of the proposed method to possible misspecifications in the model is also studied.