Inference for Network Count Time Series with the R Package PNAR

TL;DR

This paper presents the R package PNAR for flexible inference on network count time series, enabling nonlinear modeling, testing, and simulation, demonstrated through influenza case data in Germany.

Contribution

The paper introduces new computational tools and algorithms for fitting and testing nonlinear network count time series models in R, including copula Poisson simulation.

Findings

Successful modeling of weekly influenza cases in Germany

Development of fast algorithms for linearity testing

Implementation of nonlinear network autoregressive models

Abstract

We introduce a new R package useful for inference about network count time series. Such data are frequently encountered in statistics and they are usually treated as multivariate time series. Their statistical analysis is based on linear or log linear models. Nonlinear models, which have been applied successfully in several research areas, have been neglected from such applications mainly because of their computational complexity. We provide R users the flexibility to fit and study nonlinear network count time series models which include either a drift in the intercept or a regime switching mechanism. We develop several computational tools including estimation of various count Network Autoregressive models and fast computational algorithms for testing linearity in standard cases and when non-identifiable parameters hamper the analysis. Finally, we introduce a copula Poisson algorithm for simulating multivariate network count time series. We illustrate the methodology by modeling weekly number of influenza cases in Germany.