Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.697779
Title: Gaussian copula modelling for integer-valued time series
Author: Lennon, Hannah
ISNI:       0000 0004 5993 9960
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2016
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Abstract:
This thesis is concerned with the modelling of integer-valued 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 autoregressive-moving 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 well-established methods in time series analysis can be used. Still the computation of the log-likelihood 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 Expectation-Maximisation (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 rejection-acceptance step. This is shown to work well for large N. Finally we write the model in an R-vine copula representation and use a sequential algorithm for the computation of the log-likelihood. We evaluate the score and Hessian of the log-likelihood 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.
Supervisor: Yuan, Jingsong ; Pan, Jianxin Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.697779  DOI: Not available
Keywords: Vine Copulas ; Time Series ; ARMA ; Maximum Likelihood Estimation ; Expectation-Maximization Algorithm ; Approximate Bayesian Computation
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