This thesis is concerned with the modelling of integervalued time series. The data naturally occurs in various areas whenever a number of events are observed over time. The model considered in this study consists of a Gaussian copula with autoregressivemoving average (ARMA) dependence and discrete margins that can be specified, unspecified, with or without covariates. It can be interpreted as a 'digitised' ARMA model. An ARMA model is used for the latent process so that wellestablished methods in time series analysis can be used.Still the computation of the loglikelihood poses many problems because it is the sum of 2^N terms involving the Gaussian cumulative distribution function when N is the length of the time series. We consider an Monte Carlo ExpectationMaximisation (MCEM) algorithm for the maximum likelihood estimation of the model which works well for small to moderate N. Then an Approximate Bayesian Computation (ABC) method is developed to take advantage of the fact that data can be simulated easily from an ARMA model and digitised. A spectral comparison method is used in the rejectionacceptance step. This is shown to work well for large N. Finally we write the model in an Rvine copula representation and use a sequential algorithm for the computation of the loglikelihood. We evaluate the score and Hessian of the loglikelihood and give analytic solutions for the standard errors. The proposed methodologies are illustrated using simulation studies and highlight the advantages of incorporating classic ideas from time series analysis into modern methods of model fitting. For illustration we compare the three methods on US polio incidence data (Zeger, 1988) and we discuss their relative merits.
Date of Award  31 Dec 2016 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Jingsong Yuan (Supervisor) & Jianxin Pan (Supervisor) 

 Vine Copulas
 Time Series
 ARMA
 Maximum Likelihood Estimation
 ExpectationMaximization Algorithm
 Approximate Bayesian Computation
Gaussian Copula Modelling for IntegerValued Time Series
Lennon, H. (Author). 31 Dec 2016
Student thesis: Phd