references.bib

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@Article{baum1970maximization,
  author    = {Leonard E. Baum and Ted Petrie and George Soules and Norman Weiss},
  title     = {A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains},
  journal   = {The Annals of Mathematical Statistics},
  year      = {1970},
  volume    = {41},
  number    = {1},
  month     = {feb},
  pages     = {164--171},
  doi       = {10.1214/aoms/1177697196},
  publisher = {Institute of Mathematical Statistics},
}

@Article{dempster1977maximum,
  author = {Dempster, A. P. and Laird, N. M. and Rubin, D. B.},
  title  = {Maximum likelihood from incomplete data via the EM algorithm},
  year   = {1977},
  journal = "Journal of the Royal Statistical Society: Series B (Methodological)",
  volume = 39,
  number = 1,
  pages = {1--38}
}

@Misc{mackay1997ensemble,
  author   = {MacKay, David J. C.},
  title    = {Ensemble Learning for Hidden Markov Models},
  year     = {1997},
  abstract = {The standard method for training Hidden Markov Models optimizes a point estimate of the model parameters. This estimate, which can be viewed as the maximum of a posterior probability density over the model parameters, may be susceptible to overfitting, and contains no indication of parameter uncertainty. Also, this maximummay be unrepresentative of the posterior probability distribution. In this paper we study a method in which we optimize an ensemble which approximates the entire posterior probability distribution. The ensemble learning algorithm requires the same resources as the traditional Baum--Welch algorithm. The traditional training algorithm for hidden Markov models is an expectation-- maximization (EM) algorithm (Dempster et al. 1977) known as the Baum--Welch algorithm. It is a maximum likelihood method, or, with a simple modification, a penalized maximum likelihood method, which can be viewed as maximizing a posterior probability density over the model parameters. Recently, ...},
}

@Misc{beal2003variational,
  author   = {Beal, Matthew J.},
  title    = {Variational algorithms for approximate Bayesian inference},
  year     = {2003},
  abstract = {The Bayesian framework for machine learning allows for the incorporation of prior knowledge in a coherent way, avoids overfitting problems, and provides a principled basis for selecting between alternative models. Unfortunately the computations required are usually intractable. This thesis presents a unified variational Bayesian (VB) framework which approximates these computations in models with latent variables using a lower bound on the marginal likelihood. Chapter 1 presents background material on Bayesian inference, graphical models, and propaga-tion algorithms. Chapter 2 forms the theoretical core of the thesis, generalising the expectation-maximisation (EM) algorithm for learning maximum likelihood parameters to the VB EM al-gorithm which integrates over model parameters. The algorithm is then specialised to the large family of conjugate-exponential (CE) graphical models, and several theorems are presented to pave the road for automated VB derivation procedures in both directed and undirected graphs (Bayesian and Markov networks, respectively). Chapters 3-5 derive and apply the VB EM algorithm to three commonly-used and important models: mixtures of factor analysers, linear dynamical systems, and hidden Markov models.},
}

@Article{hand2007finite,
  author    = {David J. Hand},
  title     = {Finite Mixture and Markov Switching Models by Sylvia Frühwirth-Schnatter},
  journal   = {International Statistical Review},
  year      = {2007},
  volume    = {75},
  number    = {2},
  month     = {jul},
  pages     = {255--255},
  doi       = {10.1111/j.1751-5823.2007.00015_8.x},
  publisher = {Wiley-Blackwell},
}

@Book{fruehwirth-schnatter2006finite,
  author    = {Sylvia Frühwirth-Schnatter},
  title     = {Finite Mixture and Markov Switching Models},
  year      = {2006},
  publisher = {Springer New York},
  doi       = {10.1007/978-0-387-35768-3},
}

@Misc{jordan2003introduction,
  author    = {Jordan, Michael I},
  title     = {An introduction to probabilistic graphical models},
  year      = {2003},
  publisher = {In Preparation},
}

@Article{viterbi1967error,
  author    = {A. Viterbi},
  title     = {Error bounds for convolutional codes and an asymptotically optimum decoding algorithm},
  journal   = {{IEEE} Transactions on Information Theory},
  year      = {1967},
  volume    = {13},
  number    = {2},
  month     = {apr},
  pages     = {260--269},
  doi       = {10.1109/tit.1967.1054010},
  publisher = {Institute of Electrical and Electronics Engineers ({IEEE})},
}

@InCollection{rabiner1990tutorial,
  author    = {Lawrence R. Rabiner},
  title     = {A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition},
  booktitle = {Readings in Speech Recognition},
  year      = {1990},
  publisher = {Elsevier},
  pages     = {267--296},
  doi       = {10.1016/b978-0-08-051584-7.50027-9},
}

@Article{baum1967inequality,
  author    = {Leonard E. Baum and J. A. Eagon},
  title     = {An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology},
  journal   = {Bulletin of the American Mathematical Society},
  year      = {1967},
  volume    = {73},
  number    = {3},
  month     = {may},
  pages     = {360--364},
  doi       = {10.1090/s0002-9904-1967-11751-8},
  publisher = {American Mathematical Society ({AMS})},
}

@Article{baum1972inequality,
  author  = {Baum, Leonard E.},
  title   = {An inequality and associated maximaization technique in stattistical estimation for probablistic functions of Markov process},
  journal = {Inequalities},
  year    = {1972},
  volume  = {3},
  pages   = {1--8},
}

@INPROCEEDINGS{bengio1994input,
AUTHOR={Bengio, Yoshua and Frasconi, Paolo},
TITLE={An Input Output HMM Architecture},
YEAR={1994},
PAGES={427-434},
BOOKTITLE="Proceedings of the 7th International Conference on Neural Information Processing Systems ({NIPS} 1994)",
VENUE={Denver, Colorado}
}

@Book{doob1953stochastic,
  author    = {Doob, Joseph L},
  title     = {Stochastic processes},
  year      = {1953},
  volume    = {7},
  number    = {2},
  publisher = {Wiley New York},
}

@Book{bishop2006pattern,
  author    = {Bishop, Christopher M.},
  title     = {Pattern Recognition and Machine Learning (Information Science and Statistics)},
  year      = {2006},
  publisher = {Springer-Verlag New York, Inc.},
  isbn      = {0387310738},
  address   = {Secaucus, NJ, USA},
}

@Book{murphy2012machine,
  author    = {Murphy, Kevin P.},
  title     = {Machine Learning},
  year      = {2012},
  date      = {2012-09-18},
  publisher = {MIT Press Ltd},
  isbn      = {0262018020},
  pagetotal = {1104},
  ean       = {9780262018029},
}

@InProceedings{hassan2005stock,
  author       = {Hassan, Md Rafiul and Nath, Baikunth},
  title        = {Stock market forecasting using hidden Markov model: a new approach},
  booktitle    = {Intelligent Systems Design and Applications, 2005. ISDA'05. Proceedings. 5th International Conference on},
  year         = {2005},
  organization = {IEEE},
  pages        = {192--196},
}

@Article{carpenter2017stan,
  author  = {Carpenter, Bob and Gelman, Andrew and Hoffman, Matt and Lee, Daniel and Goodrich, Ben and Betancourt, Michael and Brubaker, Michael A and Guo, Jiqiang and Li, Peter and Riddell, Allen},
  title   = {Stan: A Probabilistic Programming Language},
  journal = {Journal of Statistical Software},
  year    = {2017},
  date    = {2017-01-11},
  volume  = {76},
  issue   = {1},
  doi     = {10.18637/jss.v076.i01},
}

@Article{betancourt2017identifying,
  author  = {Michael Betancourt},
  title   = {Identifying Bayesian Mixture Models},
  journal = {Stan Case Studies},
  year    = {2017},
  volume   = {4},
  url     = {http://mc-stan.org/users/documentation/case-studies/identifying_mixture_models.html},
}

@Manual{team2017stan,
  author   = {{Stan Development Team}},
  title    = {Stan Modeling Language: User’s Guide and Reference Manual},
  year     = {2017},
  date     = {2017-04-14},
  subtitle = {Version 2.17.0.},
}

@Article{gelman1992inference,
  author    = {Gelman, Andrew and Rubin, Donald B},
  title     = {Inference from iterative simulation using multiple sequences},
  journal   = {Statistical Science},
  year      = {1992},
  pages     = {457--472},
  volume = 7,
  number = 4,
  doi = "10.1214/ss/1177011136"
}

@incollection{gelman2011inference,
  author  = {Gelman, Andrew and Shirley, Kenneth and others},
  title   = {Inference from simulations and monitoring convergence},
  booktitle = {Handbook of Markov Chain Monte Carlo},
  year    = {2011},
  pages   = {163--174},
  chapter = 6,
  editor  = {Steve Brooks and Andrew Gelman and Galin L. Jones and Xiao-Li Meng},
  publisher = "CRC Press",
  series = "Chapman \& Hall/CRC Handbooks of Modern Statistical Methods"
}

@Article{cook2006validation,
  author    = {Cook, Samantha R and Gelman, Andrew and Rubin, Donald B},
  title     = {Validation of software for Bayesian models using posterior quantiles},
  journal   = {Journal of Computational and Graphical Statistics},
  year      = {2006},
  volume    = {15},
  number    = {3},
  pages     = {675--692},
  publisher = {Taylor \& Francis},
  doi = "10.1198/106186006X136976"
}

@Misc{sdt2017shinystan,
  author = {{Stan Development Team}},
  title  = {shinystan: Interactive Visual and Numerical Diagnostics and Posterior Analysis for Bayesian Models.},
  year   = {2017},
  note   = {R package version 2.3.0},
  url    = {http://mc-stan.org/},
}

@Misc{sdt2017rstan,
  author = {{Stan Development Team}},
  title  = {{RStan}: the {R} interface to {Stan}},
  year   = {2017},
  note   = {R package version 2.15.1},
  url    = {http://mc-stan.org/},
}

@MastersThesis{wisebourt2011hierarchical,
  author = {Wisebourt, Shaul Sergey},
  title  = {Hierarchical Hidden Markov Model of High-Frequency Market Regimes Using Trade Price and Limit Order Book Information},
  year   = {2011},
  school = {University of Waterloo},
}

@Article{ord2008secret,
  author    = {Ord, Tim},
  title     = {The secret science of price and volume},
  journal   = {Master Traders: Strategies for Superior Returns from Today's Top Traders},
  year      = {2008},
  pages     = {87--105},
  publisher = {Wiley Online Library},
}

@Article{sandoval2015computational,
  author    = {Sandoval, Javier and Hern{\'a}ndez, Germ{\'a}n},
  title     = {Computational visual analysis of the order book dynamics for creating high-frequency foreign exchange trading strategies},
  journal   = {Procedia Computer Science},
  year      = {2015},
  volume    = {51},
  pages     = {1593--1602},
  publisher = {Elsevier},
}

@Misc{fine1998hierarchical,
  author   = {Fine, Shai and Singer, Yoram},
  title    = {The Hierarchical Hidden Markov Model: Analysis and Applications},
  year     = {1998},
  abstract = {. We introduce, analyze and demonstrate a recursive hierarchical generalization of the widely used hidden Markov models, which we name Hierarchical Hidden Markov Models (HHMM). Our model is motivated by the complex multi-scale structure which appears in many natural sequences, particularly in language, handwriting and speech. We seek a systematic unsupervised approach to the modeling of such structures. By extendingthe standard forward-backward(BaumWelch) algorithm, we derive an efficient procedure for estimating the model parameters from unlabeled data. We then use the trained model for automatic hierarchical parsing of observation sequences. We describe two applications of our model and its parameter estimation procedure. In the first application we show how to construct hierarchical models of natural English text. In these models different levels of the hierarchy correspond to structures on different length scales in the text. In the second application we demonstrate how HHMMs can b...},
}

@MastersThesis{tayal2009regime,
  author = {Tayal, Aditya},
  title  = {Regime switching and technical trading with dynamic Bayesian networks in high-frequency stock markets},
  year   = {2009},
  school = {University of Waterloo},
}

@Article{domingos2012few,
  author     = {Domingos, Pedro},
  title      = {A Few Useful Things to Know About Machine Learning},
  journal    = {Commun. ACM},
  year       = {2012},
  volume     = {55},
  number     = {10},
  month      = oct,
  pages      = {78--87},
  issn       = {0001-0782},
  doi        = {10.1145/2347736.2347755},
  url        = {http://doi.acm.org/10.1145/2347736.2347755},
  acmid      = {2347755},
  address    = {New York, NY, USA},
  issue_date = {October 2012},
  numpages   = {10},
  publisher  = {ACM},
}

@Misc{murphy2001linear,
  author   = {Murphy, Kevin P. and Paskin, Mark A.},
  title    = {Linear Time Inference in Hierarchical HMMs},
  year     = {2001},
  abstract = {The hierarchical hidden Markov model (HHMM) is a generalization of  the hidden Markov model (HMM) that models sequences with structure  at many length/time scales [FST98]. Unfortunately, the original inference  algorithm is rather complicated, and takes O(T    ) time, where T is  the length of the sequence, making it impractical for many domains. In  this paper, we show how HHMMs are a special kind of dynamic Bayesian  network (DBN), and thereby derive a much simpler inference algorithm,  which only takes O(T ) time. Furthermore, by drawing the connection  between HHMMs and DBNs, we enable the application of many standard  approximation techniques to further speed up inference.},
}

@Misc{maheu2000identifying,
  author   = {Maheu, John M. and McCurdy, Thomas H.},
  title    = {Identifying Bull and Bear Markets In Stock Returns},
  year     = {2000},
  abstract = {This article uses a Markov-switching model that incorporates duration dependence to capture non-linear structure in both the conditional mean and the conditional variance of stock returns. The  model sorts returns into a high-return stable state and a low-return volatile state. We label these  as bull and bear markets. respectively. The filter identifies all major stock-market downturns in  over 160 years of monthly data. Bull markets have a declining hazard functions although the best  market gains come at the start of a bull market. Volatility increases with duration in bear markets. ALlowing},
}

@Misc{lunde2004duration,
  author   = {Lunde, Asger and Timmermann, Allan G.},
  title    = {Duration dependence in stock prices: An analysis of bull and bear markets},
  year     = {2004},
  abstract = {First version. Comments are very welcome This paper investigates the presence of bull and bear market states in stock price dynamics. A new definition of bull and bear market states based on sequences of stopping times tracing local peaks and troughs in stock prices is proposed. Duration dependence in stock prices is investigated through posterior mode estimates of the hazard function in bull and bear markets. We find that the longer a bull market has lasted, the lower is the probability that it will come to a termination. In contrast, the longer a bear market has lasted, the higher is its termination probability. Interest rates are also found to have an important effect on cumulated changes in stock prices: increasing interest rates are associated with an increase in bull market hazard rates and a decrease in bear market hazard rates.},
}

@Article{gordon2000preference,
  author    = {Gordon, Stephen and St-Amour, Pascal},
  title     = {A preference regime model of bull and bear markets},
  journal   = {The American Economic Review},
  year      = {2000},
  volume    = {90},
  number    = {4},
  pages     = {1019--1033},
  publisher = {JSTOR},
}

@Article{chauvet2000coincident,
  author    = {Chauvet, Marcelle and Potter, Simon},
  title     = {Coincident and leading indicators of the stock market},
  journal   = {Journal of Empirical Finance},
  year      = {2000},
  volume    = {7},
  number    = {1},
  pages     = {87--111},
  publisher = {Elsevier},
}

@Article{lo2000foundations,
  author    = {Lo, Andrew W and Mamaysky, Harry and Wang, Jiang},
  title     = {Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation},
  journal   = {The journal of finance},
  year      = {2000},
  volume    = {55},
  number    = {4},
  pages     = {1705--1765},
  publisher = {Wiley Online Library},
}

@Article{karpoff1987relation,
  author    = {Karpoff, Jonathan M},
  title     = {The relation between price changes and trading volume: A survey},
  journal   = {Journal of Financial and quantitative Analysis},
  year      = {1987},
  volume    = {22},
  number    = {1},
  pages     = {109--126},
  publisher = {Cambridge University Press},
}

@Article{gallant1992stock,
  author    = {Gallant, A Ronald and Rossi, Peter E and Tauchen, George},
  title     = {Stock prices and volume},
  journal   = {The Review of Financial Studies},
  year      = {1992},
  volume    = {5},
  number    = {2},
  pages     = {199--242},
  publisher = {Oxford University Press},
}

@Article{brock1992simple,
  author    = {Brock, William and Lakonishok, Josef and LeBaron, Blake},
  title     = {Simple technical trading rules and the stochastic properties of stock returns},
  journal   = {The Journal of finance},
  year      = {1992},
  volume    = {47},
  number    = {5},
  pages     = {1731--1764},
  publisher = {Wiley Online Library},
}

@Article{park2007what,
  author    = {Park, Cheol-Ho and Irwin, Scott H},
  title     = {What do we know about the profitability of technical analysis?},
  journal   = {Journal of Economic Surveys},
  year      = {2007},
  volume    = {21},
  number    = {4},
  pages     = {786--826},
  publisher = {Wiley Online Library},
}

@Misc{gsoc2017bayesian,
  author       = {Damiano, Luis and Peterson, Brian G and Weylandt, Michael},
  title        = {Bayesian Hierarchical Hidden Markov Models applied to financial time series},
  year         = {2017},
  howpublished = {\url{https://github.com/luisdamiano/gsoc17-hhmm}},
  journal      = {GitHub repository},
  publisher    = {Google Summer of Code 2017},
}

@Article{gelman2017prior,
  author  = {Gelman, Andrew and Simpson, Daniel and Betancourt, Michael},
  title   = {The prior can generally only be understood in the context of the likelihood},
  journal = {arXiv preprint arXiv:1708.07487},
  year    = {2017},
}

@Article{baum1966statistical,
  author    = {Baum, Leonard E and Petrie, Ted},
  title     = {Statistical inference for probabilistic functions of finite state Markov chains},
  journal   = {The Annals of Mathematical Statistics},
  year      = {1966},
  volume    = {37},
  number    = {6},
  pages     = {1554--1563}
}

@Article{baum1968growth,
  author    = {Baum, Leonard E and Sell, George},
  title     = {Growth transformations for functions on manifolds},
  journal   = {Pacific Journal of Mathematics},
  year      = {1968},
  volume    = {27},
  number    = {2},
  pages     = {211--227},
  publisher = {Mathematical Sciences Publishers},
}

@Book{casella2002statistical,
  author    = {Casella, George and Berger, Roger L},
  title     = {Statistical Inference},
  year      = {2002},
  edition    = {2},
  publisher = {Duxbury Pacific Grove, CA},
}

@Article{bakis1976continuous,
  author        = {Bakis, Raimo},
  title         = {Continuous speech recognition via centisecond acoustic states},
  journal       = {The Journal of the Acoustical Society of America},
  year          = {1976},
  volume        = {59},
  number        = {S1},
  pages         = {S97--S97},
  __markedentry = {[Bebop:]},
  publisher     = {ASA},
}

@Article{jelinek1976continuous,
  author        = {Jelinek, Frederick},
  title         = {Continuous speech recognition by statistical methods},
  journal       = {Proceedings of the {IEEE}},
  year          = {1976},
  volume        = {64},
  number        = {4},
  pages         = {532--556},
  __markedentry = {[Bebop:6]},
  doi           = "10.1109/PROC.1976.10159",
  publisher     = {IEEE},
}

@ARTICLE{Bollerslev:1986,
AUTHOR="Tim Bollerslev",
TITLE="Generalized autoregressive conditional heteroskedasticity",
JOURNAL="Journal of Econometrics",
VOLUME="31",
NUMBER="3",
PAGES={307-327},
YEAR="1986",
DOI="10.1016/0304-4076(86)90063-1",
URL="http://www.sciencedirect.com/science/article/pii/0304407686900631"
}

@INCOLLECTION{Bollerslev:2010,
AUTHOR="Tim Bollerslev",
TITLE="Glossary to ARCH",
BOOKTITLE="Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle",
YEAR=2010,
CHAPTER=8,
DOI="10.1093/acprof:oso/9780199549498.003.0008",
SERIES="Advanced Texts in Econometrics",
PUBLISHER="Oxford University Press",
EDITOR="Tim Bollerslev and Jeffrey Russell and Mark Watson"
}

@ARTICLE{Haas:2004a,
AUTHOR="Markus Haas and Stefan Mittnik and Marc S. Paolella",
TITLE="Mixed Normal Conditional Heteroskedasticity",
VOLUME=2,
NUMBER=1,
JOURNAL="Journal of Financial Econometrics",
YEAR=2004,
PAGES={211-250},
DOI="10.1093/jjfinec/nbh009"
}

@ARTICLE{Haas:2004b,
AUTHOR="Markus Haas and Stefan Mittnik and Marc S. Paolella",
TITLE="A New Approach to Markov-Switching {GARCH} Models",
VOLUME=2,
NUMBER=1,
JOURNAL="Journal of Financial Econometrics",
YEAR=2004,
PAGES={493-530},
DOI="10.1093/jjfinec/nbh020"
}

@MISC{Ardia:2017,
AUTHOR="David Ardia and Keven Bluteau and Kris Boudt and Leopoldo Catania",
TITLE="Forecast Risk with Markov-Switching {GARCH} Models: A Large-Scale Performance Study",
YEAR=2017,
JOURNAL="SSRN Pre-Print",
VOLUME=2918413,
DOI="10.2139/ssrn.2918413"
}

@Comment{jabref-meta: databaseType:biblatex;}