Observation-driven models for discrete-valued time series
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Published version
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Author(s)
Armillotta, Mirko
Luati, Alessandra
Lupparelli, Monia
Type
Journal Article
Abstract
Statistical inference for discrete-valued time series has not been developed like traditional methods for time series generated by continuous random variables. Some relevant models exist, but the lack of a homogenous framework raises some critical issues. For instance, it is not trivial to explore whether models are nested and it is quite arduous to derive stochastic properties which simultaneously hold across different specifications. In this paper, inference for a general class of first order observation-driven models for discrete-valued processes is developed. Stochastic properties such as stationarity and ergodicity are derived under easy-to-check conditions, which can be directly applied to all the models encompassed in the class and for every distribution which satisfies mild moment conditions. Consistency and asymptotic normality of quasi-maximum likelihood estimators are established, with the focus on the exponential family. Finite sample properties and the use of information criteria for model selection are investigated throughout Monte Carlo studies. An empirical application to count data is discussed, concerning a test-bed time series on the spread of an infection.
Date Issued
2022-03-02
Date Acceptance
2022-03-01
Citation
Electronic Journal of Statistics, 2022, 16 (1), pp.1393-1433
ISSN
1935-7524
Publisher
Institute of Mathematical Statistics
Start Page
1393
End Page
1433
Journal / Book Title
Electronic Journal of Statistics
Volume
16
Issue
1
Copyright Statement
© 2022 The Author(s). This work is licensed with a CC BY 4.0 International licence.
License URL
Identifier
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000825293500024&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Count data
generalized ARMA models
likelihood inference
link-function
REGRESSION
ERGODICITY
Publication Status
Published
Date Publish Online
2022-03-02