This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given covariates, random effects and process history, the observed responses at each time in each series are independent and have an exponential family distribution. We develop maximum likelihood estimation of the mixed effects model using an observation driven generalized linear autoregressive moving average specification for the serial dependence in each series. The paper presents an easily implementable approach which uses existing single time series methods to handle the serial dependence structure in combination with adaptive Gaussian quadrature to approximate the integrals over the regression random effects required for the likelihood and its derivatives. The models and methods presented allow extension of existing mixed model procedures for count data by incorporating serial dependence which can differ in form and strength across the individual series. The structure of the model has some similarities to longitudinal data transition models with random effects. However, in contrast to that setting, where there are many cases and few to moderate observations per case, the time series setting has many observations per series and a few to moderate number of cross sectional time series. The method is illustrated on time series of binary responses to musical features obtained from a panel of listeners.
Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with the dimensionality which necessitates the sparsity assumption in high dimensions. However, it is debatable whether such an assumption is adequate for handling datasets exhibiting strong serial and cross-sectional correlations. We propose a piecewise stationary time series model that simultaneously allows for strong correlations as well as structural changes…
This article presents a new continuous-time modelling framework for multivariate time series of counts which have an infinitely divisible marginal distribution. The model is based on a mixed moving average process driven by Lévy noise - called a trawl process - where the serial correlation and the cross-sectional dependence are modelled independently of each other. Such processes can exhibit short or long memory. We derive a stochastic simulation algorithm and a statistical inference method for such processes. The new methodology is then applied to high frequency financial data, where we inves…
In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis to such observations, we should first embed them in a linear space in which the essential properties of densities are preserved under addition and scalar multiplication. Bayes Hilbert spaces provide one way to achieve this embedding. In this paper we investigate the use of Bayes Hilbert spaces to model cointegrated density-valued linear processes. We develop …
Shape information is of great importance in many applications. For example, the oil-bearing capacity of sand bodies, the subterranean remnants of ancient rivers, is related to their cross-sectional shapes. The analysis of these shapes is therefore of some interest, but current classifications are simplistic and ad hoc. In this paper, we describe the first steps towards a coherent statistical analysis of these shapes by deriving the integrated likelihood for data shapes given class parameters. The result is of interest beyond this particular application.
This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and, in the short memory case, asymptotic normality of this estimator. When the underlying trawl p…
An extension of the RINAR(1) process for modelling discrete-time dependent counting processes is considered. The model RINAR(p) investigated here is a direct and natural extension of the real AR(p) model. Compared to classical INAR(p) models based on the thinning operator, the new models have several advantages: simple innovation structure ; autoregressive coefficients with arbitrary signs ; possible negative values for time series ; possible negative values for the autocorrelation function. The conditions for the stationarity and ergodicity, of the RINAR(p) model, are given. For parameter est…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions. Motivated by such data, we propose an autoregressive model for density time series by exploiting the tangent space structure on the space of distributions that is induced by the Wasserstein metric. The densities themselves are not assumed to have any specific parametric form, leading to flexible forecasting of future unobserved densities. The main estimation targets…
The aim of this work is to develop methods for studying the determinants of marriage incidence using marriage histories collected under two different types of retrospective cross-sectional study designs. These designs are: sampling of ever married women before the cross-section, a prevalent cohort, and sampling of women irrespective of marital status, a general cross-sectional cohort. While retrospective histories from a prevalent cohort do not identify incidence rates without parametric modelling assumptions, the rates can be identified when combined with data from a general cohort. Moreover,…
Mixtures of experts models provide a framework in which covariates may be included in mixture models. This is achieved by modelling the parameters of the mixture model as functions of the concomitant covariates. Given their mixture model foundation, mixtures of experts models possess a diverse range of analytic uses, from clustering observations to capturing parameter heterogeneity in cross-sectional data. This chapter focuses on delineating the mixture of experts modelling framework and demonstrates the utility and flexibility of mixtures of experts models as an analytic tool.
Policy evaluation studies, which intend to assess the effect of an intervention, face some statistical challenges: in real-world settings treatments are not randomly assigned and the analysis might be further complicated by the presence of interference between units. Researchers have started to develop novel methods that allow to manage spillover mechanisms in observational studies; recent works focus primarily on binary treatments. However, many policy evaluation studies deal with more complex interventions. For instance, in political science, evaluating the impact of policies implemented by …
Principal Stratification with Bayesian Additive Regression Trees for Count-Valued Intermediate Variables: Estimating the Effect of Fertility on Women's Employment
In this paper we introduce a multilevel specification with stochastic volatility for repeated cross-sectional data. Modelling the time dynamics in repeated cross sections requires a suitable adaptation of the multilevel framework where the individuals/items are modelled at the first level whereas the time component appears at the second level. We perform maximum likelihood estimation by means of a nonlinear state space approach combined with Gauss-Legendre quadrature methods to approximate the likelihood function. We apply the model to the first database of tribal art items sold in the most im…
Moderation effects and elasticities in compositional regression with a total. Application to Bayesian spatiotemporal modelling of all-cause mortality from environmental stressors
