Abstract
Hidden Markov models (HMMs) have been applied to many real-world applications. Usually HMMs only deal with the first-order transition probability distribution among the hidden states, see for instance Sect.1.4. Moreover, the observable states are affected by the hidden states but not vice versa. In this chapter, we study both higher-order hidden Markov models and interactive HMMs in which the hidden states are directly affected by the observed states. We will also develop estimation methods for the model parameters in both cases.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Baum L (1972) An inequality and associated maximization techniques in statistical estimation for probabilistic function of Markov processes. Inequality 3:1–8
Bunke H, Caelli T (2001) In: Bunke H, Caelli T (eds) Hidden Markov models: applications in computer vision. World Scientific, Singapore
Ching W (1998) Iterative methods for manufacturing systems of two stations in Tandem. Appl Math Lett 11:7–12
Ching W, Ng M (2006) Markov chains: models, algorithms and applications. International series on operations research and management science. Springer, New York, 224 Pages
Ching W, Ng M, Fung E (2003) In: Liu J, Cheung Y, Yin H (eds) Higher-order Hidden Markov models with applications to DNA sequences. IDEAL2003, Lecture notes in computer science, vol 2690. Springer, Berlin, pp 535–539
Ching W, Siu T, Fung E, Ng M, Li W (2007) Interactive hidden Markov models and their applications. IMA J Manag Math 18:85–97
Ching W, Siu T, Li L, Li T, Li W (2009) Modeling default data via an interactive hidden Markov model. Comput Econ 34:1–19
Giampieri G, Davis M, Crowder M (2005) Analysis of default data using hidden Markov models. Quant Finance 5:27–34
MacDonald I, Zucchini W (1997) Hidden Markov and other models for discrete-valued time series. Chapman & Hall, London
Rabiner L (1989) A tutorial on hidden Markov models and selected applications in speech recognition. Proc IEEE 77:257–286
Siu T, Ching W, Fung E, Ng M (2005) Extracting information from spot interest rates and credit ratings using double higher-order hidden Markov models. Comput Econ 26:251–284
Viterbi A (1967) Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans Inform Theory 13:260–269
Woo W, Siu T (2004) A dynamic binomial expansion technique for credit risk measurement: a bayesian filtering approach. Appl Math Finance 11:165–186
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ching, WK., Huang, X., Ng, M.K., Siu, TK. (2013). Hidden Markov Chains. In: Markov Chains. International Series in Operations Research & Management Science, vol 189. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6312-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6312-2_8
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-6311-5
Online ISBN: 978-1-4614-6312-2
eBook Packages: Business and EconomicsBusiness and Management (R0)