Multivariate count autoregression
@article{Doukhan2020MultivariateCA, title={Multivariate count autoregression}, author={Paul Doukhan and Konstantinos Fokianos and Baard Stove and Dag Tj{\o}stheim}, journal={Bernoulli}, year={2020} }
We are studying the problems of modeling and inference for multivariate count time series data with Poisson marginals. The focus is on linear and log-linear models. For studying the properties of such processes we develop a novel conceptual framework which is based on copulas. However, our approach does not impose the copula on a vector of counts; instead the joint distribution is determined by imposing a copula function on a vector of associated continuous random variables. This specific…
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References
SHOWING 1-10 OF 77 REFERENCES
Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model
- Mathematics, Economics
- 2003
This paper introduces and evaluates new models for time series count data. The Autoregressive Conditional Poisson model (ACP) makes it possible to deal with issues of discreteness, overdispersion…
On Composite Likelihood Estimation of a Multivariate INAR(1) Model
- Mathematics
- 2013
In several circumstances the collected data are counts observed in different time points, while the counts at each time point are correlated. Current models are able to account for serial correlation…
On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood
- Mathematics
- 2013
Poisson Autoregression ( Complete Version )
- Mathematics
- 2009
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past…
Stationarity of Count-Valued and Nonlinear Time Series Models
- Computer Science, Mathematics
- 2010
This work provides a formal justification for the use of drift conditions on count-valued observation-driven models, and proves for the first time stationarity and ergodicity of several models, including the class of Generalized Autoregressive Moving Average models.
Some recent theory for autoregressive count time series
- Mathematics, Computer Science
- 2012
It is argued that the developed theory forms a necessary basis for modelling and application of these count time series and is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models.
Theory and Inference for a Class of Observation-driven Models with Application to Time Series of Counts
- Mathematics
- 2012
This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of…
Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models
- Mathematics
- 2017
We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson…
Poisson Autoregression
- Mathematics
- 2009
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its…