||Monte Carlo methods for dynamical systems
||Winther, Ole (Intelligent Signal Processing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||Monte Carlo methods are statistical methods that can be used to give approximate answers
to questions such as finding the distribution or expectation of a stochastic variable
through simulation. Two of the most widely used Monte Carlo methods are Markov
Chain Monte Carlo (MCMC) and particle filtering. In the thesis, a thorough review
of the theoretical properties of these two Monte Carlo methods is given. After having
established the theoretical foundation for the algorithms, the algorithms are used to do
inference in a Stochastic Volatility (SV) model.
For both the methods, the importance of choosing a good proposal distribution is emphasized,
and it is shown that the choice of proposal density can have a marked effect
on the performance of the algorithm. Several novel methods for choosing a good importance
density are proposed and implemented.
The standard SV model is extended in two ways. The first way it is extended is by
letting the volatility process be modeled by an autoregressive process of arbitrary order
p. The filtering and predictive properties of the MCMC method is investigated through
simulation of this extended SV model. The second way the standard SV model is extended
is by allowing the model parameters to vary over time. The particle filtering
algorithm is tested on synthetic data generated from this model. However, for the particle
filtering algorithm, the main focus will be on illustrating some of the problems
related to the algorithm, along with their solution.
Finally, the MCMC method is used to estimate parameters and volatility for two selected
financial time series.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2009-04-14
Update date: 2010-08-25