Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/311693 
Year of Publication: 
2025
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2025-004/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
This paper presents a novel copula-based autoregressive framework for multilayer arrays of integer-valued time series with tensor structure. It complements recent advances in tensor time series that predominantly focus on real-valued data and overlook the unique properties of integer-valued time series, such as discreteness and non-negativity. Our approach incorporates feedback effects for the time-varying parameters that describe the counts' temporal dynamics and introduces new identification constraints for parameter estimation. We provide an asymptotic theory for a Two-Stage Maximum Likelihood Estimator (2SMLE) tailored to the new tensor model. The estimator tackles the model's multidimensionality and interdependence challenges for large-scale count datasets, while at the same time addressing computational challenges inherent to copula parameter estimation. In this way it significantly advances the modeling of count tensors. An application to crime time series demonstrates the practical utility of the proposed methodology.
Subjects: 
INGARCH
tensor autoregression
parameter identification
quasi-likelihood
two-stage estimator
Document Type: 
Working Paper

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