Classical inference for static and dynamic copula models

Abstract

In this thesis, we present a detailed review of copula models including the parameter estimation through likelihood-based methods and Markov chain Monte Carlo (MCMC) techniques and develop several models incorporating copulas to fit financial time series data and psycho-logical clinical data. Firstly, the vine copula model and pair-copula construction for dependent multi-variables are reviewed. An MCMC-based method is applied to estimate the parameters of the vine copula models. Secondly, we assess the value at risk (VaR) of the portfolio and forecast the daily volatility using the multivariate GARCH model with the D-vine copula. The parameters are jointly estimated with our likelihood-based method, and the results are compared with those obtained with the typical two-step estimation procedure. Thirdly, we construct a copula with marginal distributions derived from the multivariate ordered probit model to handle the categorical variables and apply it to psychological clinical data. The parameters are co-estimated with our Metropolis Hasting within Gibbs sampling algorithm. Finally, we propose a novel GAS-copula model that has a similar structure to stochastic volatility models while retaining the computational convenience of observation-driven models. We use it to fit the European and Asian indices, showing that our method is competitive with GARCH models.

Date of Award	1 Jul 2021
Original language	English
Awarding Institution	King's College London
Supervisor	Mike Pitt (Supervisor) & Weining Wang (Supervisor)