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Title Monte Carlo methods for dynamical systems
Author Svenstrup, Dan
Supervisor Winther, Ole (Intelligent Signal Processing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2009
Abstract 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.
Imprint Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Series IMM-M.Sc.-2009-21
Original PDF ep09_21.pdf (1.42 MB)
Admin Creation date: 2009-04-14    Update date: 2010-08-25    Source: dtu    ID: 241272    Original MXD