THESIS
2018
iv, 45 pages : illustrations ; 30 cm
Abstract
Modeling financial returns is challenging because the correlations and the variances of
returns are changing and the covariance matrices are high-dimensional. In our paper,
modified Cholesky decomposition is applied to model the correlations between the financial
returns because it enables us to reparametrize the correlations parameters, write down
the new parameters in regression equations and avoid the constraint that the correlation
matrices must positive definite. To implement efficient sampling scheme, hierarchical representation
of Bayesian Lasso is used to shrink coefficients in linear regression formulas
to their prior means because it has a proven track of shrinkage power.
In our paper, several simulation results show the good sampling properties that the iterates
conv...[
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Modeling financial returns is challenging because the correlations and the variances of
returns are changing and the covariance matrices are high-dimensional. In our paper,
modified Cholesky decomposition is applied to model the correlations between the financial
returns because it enables us to reparametrize the correlations parameters, write down
the new parameters in regression equations and avoid the constraint that the correlation
matrices must positive definite. To implement efficient sampling scheme, hierarchical representation
of Bayesian Lasso is used to shrink coefficients in linear regression formulas
to their prior means because it has a proven track of shrinkage power.
In our paper, several simulation results show the good sampling properties that the iterates
converge very fast, there exists one mode for each parameter and the autocorrelation
drops rapidly. The real data sampling, which suggests the same good properties as those
in simulation, captures the changing variances for the five stocks, the changing correlations
between the five stocks and a peak of one stock in variance between 28 Oct, 2008
and 30 Oct, 2008, around the time when the stock had a peak in returns.
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