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… 
Multivariate time series models for mixed data
TLDR
It is proved that autoregressive parameters can be consistently estimated equation-by-equation using a pseudo-maximum likelihood method, leading to a fast implementation even when the number of time series is large, and consistency results when a parametric copula model is fitted to the time series.
Observation-driven models for discrete-valued time series
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
Testing Linearity for Network Autoregressive Models
A quasi-score linearity test for continuous and count network autoregressive models is developed. We establish the asymptotic distribution of the test when the network dimension is fixed or
Flexible bivariate Poisson integer-valued GARCH model
Integer-valued time series models have been widely used, especially integer-valued autoregressive models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models.
Multivariate Count Data Models for Time Series Forecasting
TLDR
This paper reviews two models from these classes: the log-linear multivariate conditional intensity model and the non-linear state-space model for count data and discusses the pros and cons of inference for both models in detail.
Periodically stationary multivariate autoregressive models
TLDR
An iterative algorithm is developed to obtain unconditional means, variances and auto-/cross-covariances for models with higher order lags and applies it to a dataset on norovirus gastroenteritis in two German states.
Bivariate integer-autoregressive process with an application to mutual fund flows
Density power divergence for general integer-valued time series with multivariate exogenous covariate
In this article, we study a robust estimation method for a general class of integer-valued time series models. The conditional distribution of the process belongs to a broad class of distribution
Robust Estimation for Bivariate Poisson INGARCH Models
TLDR
This work considers a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator, and demonstrates the proposed estimator is consistent and asymptotically normal under certain regularity conditions.
...
...

References

SHOWING 1-10 OF 77 REFERENCES
Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model
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
Log-linear Poisson autoregression
On Composite Likelihood Estimation of a Multivariate INAR(1) Model
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
Poisson Autoregression ( Complete Version )
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
TLDR
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
TLDR
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
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
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
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
...
...