Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/284809 
Year of Publication: 
2021
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 43 [Issue:] 2 [Publisher:] John Wiley & Sons, Ltd [Place:] Oxford, UK [Year:] 2021 [Pages:] 285-311
Publisher: 
John Wiley & Sons, Ltd, Oxford, UK
Abstract: 
Vector‐valued‐60 extensions of univariate generalized binary auto‐regressive (gbAR) processes are proposed that enable the joint modeling of serial and cross‐sectional‐50 dependence of multi‐variate binary data. The resulting class of generalized binary vector auto‐regressive (gbVAR) models is parsimonious, nicely interpretable and allows also to model negative dependence. We provide stationarity conditions and derive moving‐average‐type representations that allow to prove geometric mixing properties. Furthermore, we derive general stochastic properties of gbVAR processes, including formulae for transition probabilities. In particular, classical Yule–Walker equations hold that facilitate parameter estimation in gbVAR models. In simulations, we investigate the estimation performance, and for illustration, we apply gbVAR models to particulate matter (PM10, ‘fine dust’) alarm data observed at six monitoring stations in Stuttgart, Germany.
Subjects: 
Binary data
mixing properties
multi‐variate time series
stationarity conditions
transition probabilities
Yule–Walker equations
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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