Skriti markovski modeli v analizi finančnih časovnih vrst

delo diplomskega seminarja

Martin Praček (Author), Damjan Škulj (Mentor)

Abstract

V moji diplomski nalogi sem se ukvarjal s skritimi markovskimi modeli. Gre za vrsto markovskega modela, kjer ne poznamo stanj, v katerih se model nahaja. Opazujemo lahko le signale, ki o sistemu podajo le posredne informacije. Skozi celotno nalogo predstavim skrite markovske modele, od njihove zgodovine do uporabe v biologiji. Poseben del je posvečen skritim markovskim modelom, ki jih opišemo z Gaussovimi mešanicami. Za te predstavim uporabo Baum-Welchovega in Viterbijevega algoritma. Posvetil sem se tudi časovnim vrstam in njihovim lastnostim. Posebej predstavim finančne časovne vrste in prikažem primer uporabe na le teh. Obenem pa sem opisal še praktični primer, kjer pokažem kako izračunamo prehodno matriko.

Keywords

finančna matematika;skriti markovski modeli;časovne vrste;slučajni procesi;Gaussova mešanica;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FDV - Faculty of Social Sciences
Publisher:	[M. Praček]
UDC:	519.2
COBISS:	18724697
Views:	1739
Downloads:	278
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Hidden Markov Models in Financial Time Series Analysis
Secondary abstract:	For my graduate thesis I researched Hidden Markov Models, a type of Markov Models where states of model are not known. We can only observe signals, that only show indirect information about the system. Through the paper, it presents Hidden Markov Models from their history, to their use in biology. A part of paper is dedicated to Hidden Markov Models described with Gaussian mixtures. For this models, use of Baum-Welch and Viterbi algorithm is shown. There is also a part about time series and their properties. Financial time series are discussed separately and there is an example of application. Also, I included my own example, where I show the method for calculating tranistion matrix.
Secondary keywords:	mathematics;hidden Markov models;time series;stohastic processes;Gaussian mixture;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	28 str.
ID:	11227555