Copula approach to fitting bivariate time series
(2023) In Master's Theses in Mathematical Sciences MASM02 20231Mathematical 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:
http://lup.lub.lu.se/student-papers/record/9128552
- author
- Wang, Jun LU
- supervisor
- organization
- course
- MASM02 20231
- year
- 2023
- 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}}, }