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We consider network autoregressive models for count data with a non‐random neighborhood structure. The main methodological contribution is the development of conditions that guarantee stability and valid statistical inference for such models. We consider both cases of fixed and increasing network dimension and we show that quasi‐likelihood inference provides consistent and asymptotically normally distributed estimators. The article is complemented by simulation results and a data example. [ABSTRACT FROM AUTHOR]

We study the dynamic price competition of hotels in Venice using publicly available data scraped from an online travel agency. This study poses two main challenges. First, the time series of prices recorded for each hotel encompasses a twofold time frame. For every single asking price for an overnight stay on a specific day, there is a corresponding time series of asking prices along the booking window on the online platforms. Second, the competition relations between different hoteliers is clearly unknown and needs to be discovered using a suitable methodology. We address these problems by proposing a novel Network Autoregressive model which is able to handle the peculiar threefold data structure of the data set with time-varying coefficients over the booking window. This approach allows us to uncover the competition network of the market players by employing a quick data-driven algorithm. Independent, mixed, and leader–follower relationships are detected, revealing the competitive dynamics of the destination, useful to managers and stakeholders. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]