Regularising Generalised Linear Mixed Models with an autoregressive random effect

Generalised Network Autoregressive Processes and the GNAR package

This article introduces the GNAR package, which fits, predicts, and simulates from a powerful new class of generalised network autoregressive processes. Such processes consist of a multivariate time series along with a real, or inferred, network that provides information about inter-variable relationships. The GNAR model relates values of a time series for a given variable and time to earlier values of the same variable and of neighbouring variables, with inclusion controlled by the network structure. The GNAR package is designed to fit this new model, while working with standard ts objects an…

Quantifying the economic response to COVID-19 mitigations and death rates via forecasting Purchasing Managers' Indices using Generalised Network Autoregressive models with exogenous variables

Knowledge of the current state of economies, how they respond to COVID-19 mitigations and indicators, and what the future might hold for them is important. We use recently-developed generalised network autoregressive (GNAR) models, using trade-determined networks, to model and forecast the Purchasing Managers' Indices for a number of countries. We use networks that link countries where the links themselves, or their weights, are determined by the degree of export trade between the countries. We extend these models to include node-specific time series exogenous variables (GNARX models), using t…

Modelling Time-Varying Rankings with Autoregressive and Score-Driven Dynamics

We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum likelihood in a straightforward manner. Rankings are modelled using the Plackett-Luce distribution with time-varying worth parameters that follow a mean-reverting time series process. To capture the dependence of the worth parameters on past rankings, we utilise the conditional score in the fashion of the generalised autoregressive score (GAS) models. Simulation e…

具有广义Katz新息的一阶整数值自回归过程

First-order integer-valued autoregressive processes with Generalized Katz innovations

本文提出一种基于广义Katz新息的整数值自回归模型，可灵活处理计数数据的过离散、欠离散、偏态和厚尾，并应用于130个Google趋势序列，揭示气候变化公众关注度的时空异质性。

Modelling the effects of air pollution on health using Bayesian Dynamic Generalised Linear Models

The relationship between short-term exposure to air pollution and mortality or morbidity has been the subject of much recent research, in which the standard method of analysis uses Poisson linear or additive models. In this paper we use a Bayesian dynamic generalised linear model (DGLM) to estimate this relationship, which allows the standard linear or additive model to be extended in two ways: (i) the long-term trend and temporal correlation present in the health data can be modelled by an autoregressive process rather than a smooth function of calendar time; (ii) the effects of air pollution…

纵向网络的广义网络自回归建模及其在美国总统选举中的应用

Generalized network autoregressive modelling of longitudinal networks with application to presidential elections in the USA

本文提出带交互项的 community-α GNAR 模型并给出有限样本误差界，用于分析高维纵向网络，且通过1976–2020年美国各州选举数据揭示任期、2016年变化及红蓝州差异。