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Copula approach to fitting bivariate time series

Wang, Jun LU (2023) In Master's Theses in Mathematical Sciences MASM02 20231
Mathematical Statistics
Abstract (Swedish)
We apply the GARCH-copula method to estimate Value at Risk (VaR) for
European and Stockholm stock indices. First, marginal distributions are
estimated by the ARMA-GARCH model with normal, Student-t, and skewed t
distributions. Then we investigate the tails of innovations of
ARMA-GARCH models using the Peaks over thresholds method and find that
the distributions of stock returns are asymmetric with heavier left tails
than right. In order to analyze the dependence between the time series,
we try elliptical copulas (Gaussian, t) and Archimedean copulas (Gumbel,
Frank, and Clayton) to model the dependence structure between two time
series' returns. Parameter estimation is based on the so-called
inference for margins, which... (More)
We apply the GARCH-copula method to estimate Value at Risk (VaR) for
European and Stockholm stock indices. First, marginal distributions are
estimated by the ARMA-GARCH model with normal, Student-t, and skewed t
distributions. Then we investigate the tails of innovations of
ARMA-GARCH models using the Peaks over thresholds method and find that
the distributions of stock returns are asymmetric with heavier left tails
than right. In order to analyze the dependence between the time series,
we try elliptical copulas (Gaussian, t) and Archimedean copulas (Gumbel,
Frank, and Clayton) to model the dependence structure between two time
series' returns. Parameter estimation is based on the so-called
inference for margins, which is a two-step method. Moreover, we adopt
backtesting to test the goodness-of-fit of different copulas using
Monte-Carlo simulations.

Our empirical results show that ARMA(1,1)-GARCH(1,1)-t distribution is
proven to be the best fits for margins and Student's t copula gives the
highest log-likelihood of the model and best VaR estimation. (Less)
Please use this url to cite or link to this publication:
author
Wang, Jun LU
supervisor
organization
course
MASM02 20231
year
type
H2 - Master's Degree (Two Years)
subject
keywords
VaR, Copula, ARMA-GARCH, Extreme Value Theory, GPD, Hill estimator
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMS-3122-2023
ISSN
1404-6342
other publication id
2023:E56
language
English
id
9128552
date added to LUP
2023-06-21 13:19:39
date last changed
2023-07-03 14:05:45
@misc{9128552,
  abstract     = {{We apply the GARCH-copula method to estimate Value at Risk (VaR) for 
European and Stockholm stock indices. First, marginal distributions are 
estimated by the ARMA-GARCH model with normal, Student-t, and skewed t 
distributions. Then we investigate the tails of innovations of 
ARMA-GARCH models using the Peaks over thresholds method and find that 
the distributions of stock returns are asymmetric with heavier left tails 
than right. In order to analyze the dependence between the time series, 
we try elliptical copulas (Gaussian, t) and Archimedean copulas (Gumbel, 
Frank, and Clayton) to model the dependence structure between two time 
series' returns. Parameter estimation is based on the so-called 
inference for margins, which is a two-step method. Moreover, we adopt 
backtesting to test the goodness-of-fit of different copulas using 
Monte-Carlo simulations.

Our empirical results show that ARMA(1,1)-GARCH(1,1)-t distribution is 
proven to be the best fits for margins and Student's t copula gives the 
highest log-likelihood of the model and best VaR estimation.}},
  author       = {{Wang, Jun}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Copula approach to fitting bivariate time series}},
  year         = {{2023}},
}