IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/7675.html
   My bibliography  Save this paper

Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series

Author

Listed:
  • Bulla, Jan

Abstract

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.

Suggested Citation

  • Bulla, Jan, 2006. "Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series," MPRA Paper 7675, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7675
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/7675/1/MPRA_paper_7675.pdf
    File Function: original version
    Download Restriction: no

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    2. Bulla, Jan & Bulla, Ingo & Nenadic, Oleg, 2010. "hsmm -- An R package for analyzing hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 611-619, March.
    3. repec:eee:pacfin:v:44:y:2017:i:c:p:127-149 is not listed on IDEAS

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:7675. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.