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2014 | OriginalPaper | Buchkapitel

1. Robustification of an On-line EM Algorithm for Modelling Asset Prices Within an HMM

verfasst von : Christina Erlwein-Sayer, Peter Ruckdeschel

Erschienen in: Hidden Markov Models in Finance

Verlag: Springer US

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Abstract

In this paper, we establish a robustification of Elliott’s on-line EM algorithm for modelling asset prices within a hidden Markov model (HMM). In this HMM framework, parameters of the model are guided by a Markov chain in discrete time, parameters of the asset returns are therefore able to switch between different regimes. The parameters are estimated through an on-line algorithm, which utilizes incoming information from the market and leads to adaptive optimal estimates. We robustify this algorithm step by step against additive outliers appearing in the observed asset prices with the rationale to better handle possible peaks or missings in asset returns.

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Nächstes Kapitel Stochastic Volatility or Stochastic Central Tendency: Evidence from a Hidden Markov Model of the Short-Term Interest Rate

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In mathematical rigor, the IF, when it exists, is the Gâteaux derivative of T into the direction of the tangent δ _x − F. For details, also on stronger notions like Hadamard or Fréchet differentiability, see, e.g., Fernholz [8] or [25, Chap. 1].

Names OBRE and MBRE are used, e.g., in Hampel et al. [16] while OMSE is used in Ruckdeschel and Horbenko [30].

Usually Λ _θ is the logarithmic derivative of the density w.r.t. the parameter, i.e., \(\varLambda _{\theta }(x) = \partial /\partial \theta \log p_{\theta }(x)\).

Ang, A., Bekaert, G.: International asset allocation with regime shifts. Rev. Financ. Stud. 15, 1137–1187 (2002)CrossRef

Cai, J.: A Markov model of switching-regime ARCH. J. Bus. Econ. Stat. 12, 309–316 (1994)

Elliott, R.J.: Exact adaptive filters for Markov chains observed in Gaussian noise. Automatica 30, 1399–1408 (1994)CrossRef

Elliott, R.J., Hinz, J.: A method for portfolio choice. Appl. Stoch. Models Bus. Ind. 19, 1–11 (2003)CrossRef

Elliott, R.J., van der Hoek, J.: An application of hidden Markov models to asset allocation problems. Financ. Stoch. 1, 229–238 (1997)CrossRef

Elliott, R.J., Aggoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control. Applications of Mathematics, vol. 29. Springer, New York (1995)

Erlwein, C., Mamon, R., Davison, M.: An examination of HMM-based investment strategies for asset allocation. Appl. Stoch. Model. Bus. Ind. 27(3), 204–221 (2009)CrossRef

Fernholz, L.T.: Von Mises Calculus for Statistical Functionals. Lecture Notes in Statistics, vol. 19. Spinger, New York (1983)

Fox, A.J.: Outliers in time series. J. R. Stat. Soc. Ser. B 34, 350–363 (1972)

10.

Fraley, C., Raftery, A.E.: Model-based clustering, discriminant analysis and density estimation. J. Am. Stat. Assoc. 97, 611–631 (2002)CrossRef

11.

Fraley, C., Raftery, A.E., Murphy, T.B., Scrucca, L.: mclust version 4 for R: normal mixture modeling for model-based clustering, classification, and density estimation. Technical report No. 597, Department of Statistics, University of Washington (2012)

12.

Gray, S.F.: Modeling the conditional distribution of interest rates as a regime-switching process. J. Financ. Econ. 42, 27–62 (1996)CrossRef

13.

Guidolin, M., Timmermann, A.: Asset allocation under multivariate regime switching. J. Econ. Dyn. Control 31, 3503–3544 (2007)CrossRef

14.

Hamilton, J.D.: A new approach to the economic analysis of nonstationary time series and the business cycle. Econom. J. Econom. Soc. 57, 357–384 (1989)

15.

Hampel, F.R.: Contributions to the theory of robust estimation. Dissertation, University of California, Berkely (1968)

16.

Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. Wiley, New York (1986)

17.

Huber, P.J.: Robust Statistics. Wiley, New York (1981)CrossRef

18.

Kohl, M.: RobLox: optimally robust influence curves and estimators for location and scale. R package version 0.8.2. http://robast.r-forge.r-project.org/ (2012)

19.

Kohl, M., Deigner, H.P.: Preprocessing of gene expression data by optimally robust estimator. BMC Bioinform. 11, 583 (2010)CrossRef

20.

Kohl, M., Rieder, H., Ruckdeschel, P.: Infinitesimally robust estimation in general smoothly parametrized models. Stat. Methods Appl. 19, 333–354 (2010)CrossRef

21.

Knight, F.H.: Risk, Uncertainty, and Profit. Houghton Mifflin, Boston (1921)

22.

Mamon, R., Erlwein, C., Gopaluni, B.: Adaptive signal processing of asset price dynamics with predictability analysis. Inform. Sci. 178, 203–219 (2008)CrossRef

23.

Markowitz, H.: Portfolio selection. J. Financ. 7(1), 77–91 (1952)

24.

Maronna, R.A., Martin, R.D. Yohai, V.J.: Robust Statistics: Theory and Methods. Wiley, Chichester (2006)CrossRef

25.

Rieder, H.: Robust Asymptotic Statistics. Springer, New York (1994)CrossRef

26.

Rieder, H., Kohl, M., Ruckdeschel, P.: The cost of not knowing the radius. Stat. Methods Appl. 17(1), 13–40 (2008)CrossRef

27.

Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)CrossRef

28.

Rousseeuw, P.J., van Driessen, K.: A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212–223 (1999)CrossRef

29.

Ruckdeschel, P.: Ansätze zur Robustifizierung des Kalman Filters. Bayreuther Mathematische Schriften, vol. 64. Mathematisches Inst. der Univ. Bayreuth, Bayreuth (2001)

30.

Ruckdeschel, P., Horbenko, N.: Robustness properties of estimators in generalized pareto models. Technical report ITWM N^o182. http://www.itwm.fraunhofer.de/fileadmin/ITWM-Media/Zentral/Pdf/Berichte_ITWM/2010/bericht_182.pdf (2010)

31.

Sass, J., Haussmann, U.G.: Optimizing the terminal wealth under partial information: the drift process as a continuous time Markov chain. Financ. Stoch. 8, 553–577 (2004)CrossRef

32.

Zakai, M.: On the optimal filtering of diffusion processes. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 11, 230–243 (1969)CrossRef

Titel: Robustification of an On-line EM Algorithm for Modelling Asset Prices Within an HMM
verfasst von: Christina Erlwein-Sayer
Peter Ruckdeschel
Verlag: Springer US
Buch: Hidden Markov Models in Finance
Print ISBN: 978-1-4899-7441-9

Electronic ISBN: 978-1-4899-7442-6

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-1-4899-7442-6_1

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