dc.contributor.advisor | Zucchini, Walter Prof. Dr. | de |
dc.contributor.author | Bulla, Jan | de |
dc.date.accessioned | 2013-01-31T08:21:54Z | de |
dc.date.available | 2013-01-31T08:21:54Z | de |
dc.date.issued | 2006-08-02 | de |
dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-000D-F27C-7 | de |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-3687 | |
dc.identifier.uri | http://dx.doi.org/10.53846/goediss-3687 | |
dc.description.abstract | Hidden Markov Modelle (HMMs) und Hidden
Semi-Markov Modelle (HSMMs) erlauben die Modellierung
verschiedenster univariater und multivariater Zeitreihen. Obgleich
das Interesse an diesem Modelltyp in den vergangenen Jahren stetig
gewachsen ist und zahlreiche wissenschaftliche Beiträge sowohl zu
theoretischen als auch zu praktischen Aspekten veröffentlicht
wurden, verbleiben verschiedene offene Punkte. Wir untersuchen im
Wesentlichen drei Fragestellungen. 1.
Parameterschätzung stationärer HMMs. Die Parameter eines HMM
werden im Allgemeinen durch direkte numerische Maximierung (DNM)
der Likelihoodfunktion oder durch den Expectation-Maximization
(EM)-Algorithmus geschätzt. Wir zeigen, wie der EM-Algorithmus zur
Schätzung stationärer HMMs modifiziert werden kann, analysieren die
Performance eines hybriden Algorithmus und untersuchen die
Überdeckungswahrscheinlichkeiten Bootstrap-basierter
Konfidenzintervalle. 2. Ein Markov-switching
Ansatz zur Modellierung zeitvariabler Betas. Im Rahmen des
Capital Asset Pricing Modells untersuchen wir zwei Markov-switching
Modelle und vergleichen ihre Performance mit der eines bivariaten
t-GARCH(1,1), eines bivariaten Stochastic Volatility Modells sowie
zweier Kalman Filter Modelle. 3. Stilisierte
Fakten zu Tagesrenditen und HSMMs. Die Fähigkeit von HMMs,
mehrere stilisierte Fakten von Tagesrenditen abzubilden, wurde on
Ryden et al. (1998) gezeigt. Wir präsentieren zwei HSMM-basierte
Ansätze zur Modellierung von Tagesrenditen. Wesentliches Resultat
ist die im Vergleich zu HMMs bessere Reproduktion der schwach
abfallenden Autokorrelationsfunktion absoluter Renditen durch ein
HSMM mit negativ-binomialer Verweilzeitverteilung und bedingt
normalverteilen Beobachtungen. | de |
dc.format.mimetype | application/postscript | de |
dc.language.iso | eng | de |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ | de |
dc.title | Application of Hidden Markov and Hidden Semi-Markov Models to Financial Time Series | de |
dc.type | doctoralThesis | de |
dc.title.translated | Application of Hidden Markov and Hidden Semi-Markov Models to Financial Time Series | de |
dc.contributor.referee | Zucchini, Walter Prof. Dr. | de |
dc.date.examination | 2006-07-06 | de |
dc.subject.dnb | 310 Statistik | de |
dc.subject.gok | LM - LZ | de |
dc.description.abstracteng | Hidden Markov Models (HMMs) and Hidden
Semi-Markov Models (HSMMs) provide flexible, general-purpose models
for univariate and multivariate time series. Although interest in
HMMs and HSMMs has continuously increased during the past years,
and numerous articles on theoretical and practical aspects have
been published, several gaps remain. This thesis addresses some of
them, divided into three main topics. 1.
Computational issues in parameter estimation of stationary
HMMs. The parameters of a HMM can be estimated by direct
numerical maximization (DNM) of the log-likelihood function or,
more popularly, using the Expectation-Maximization (EM) algorithm.
We show how the EM algorithm could be modified to fit stationary
HMMs. We propose a hybrid algorithm that is designed to combine the
advantageous features of the EM and DNM algorithms, and compare the
performance of the three algorithms (EM, DNM and the hybrid). We
then describe the results of an experiment to assess the true
coverage probability of bootstrap-based confidence intervals for
the parameters. 2. A Markov switching approach
to model time-varying Beta risk of pan-European Industry
portfolios. The motive to take up this topic was the
development of a joint model for many financial time series. We
study two Markov switching models in a Capital Asset Pricing Model
framework, and compare their forecast performances to three models,
namely a bivariate t-GARCH(1,1) model, two Kalman filter based
approaches and a bivariate stochastic volatility model.
3. Stylized facts of financial time series and
HSMMs. The ability of a HMM to reproduce several stylized
facts of daily return series was illustrated by Ryden et al.
(1998). However, they point out that one stylized fact cannot be
reproduced by a HMM, namely the slowly decaying autocorrelation
function of squared returns. We present two HSMM-based approaches
to model eighteen series of daily sector returns with about 5.000
observations. The key result is that, compared to a HMM, the slowly
decaying autocorrelation function is significantly better described
by a HSMM with negative binomial sojourn time and Normal
conditional distributions. | de |
dc.contributor.coReferee | Hering, Heinrich Prof. Dr. | de |
dc.contributor.thirdReferee | Benner, Wolfgang Prof. Dr. | de |
dc.subject.topic | Economics and Management Science | de |
dc.subject.ger | Hidden Markov Modell | de |
dc.subject.ger | Hidden Semi-Markov Modell | de |
dc.subject.ger | Finanzzeitreihen | de |
dc.subject.ger | Parameterschätzung | de |
dc.subject.eng | Hidden Markov Model | de |
dc.subject.eng | Hidden Semi-Markov Model | de |
dc.subject.eng | Financial Time Series | de |
dc.subject.eng | Computational Issues | de |
dc.subject.eng | Parameter Estimation | de |
dc.subject.bk | 31.73 | de |
dc.subject.bk | 31.70 | de |
dc.identifier.urn | urn:nbn:de:gbv:7-webdoc-784-9 | de |
dc.identifier.purl | webdoc-784 | de |
dc.identifier.ppn | 565552961 | de |