Higher-Order Markov Chains

Data sequences or time series occur frequently in many real world applications. One of the most important steps in analyzing a data sequence (or time series) is the selection of an appropriate mathematical model for the data. This is because it helps in predictions, hypothesis testing and rule discovery.

[1]  Xin Guo,et al.  Information and option pricings , 2001 .

[2]  D. Duffie,et al.  An Overview of Value at Risk , 1997 .

[3]  Philippe Jorion.  Value at risk: the new benchmark for controlling market risk , 1996 .

[4]  P. Best.  Implementing Value at Risk , 1999 .

[5]  Ingrid Zukerman,et al.  Pre-sending Documents on the WWW: A Comparative Study , 1999, IJCAI.

[6]  A. Raftery.  A model for high-order Markov chains , 1985 .

[7]  Robert J. Elliott,et al.  On filtering and estimation of a threshold stochastic volatility model , 2011, Appl. Math. Comput..

[8]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[9]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[10]  Michael K. Ng,et al.  A Data Cube Model for Prediction-Based Web Prefetching , 2004, Journal of Intelligent Information Systems.

[11]  R. Elliott,et al.  A stochastic differential game for optimal investment of an insurer with regime switching , 2011 .

[12]  Wai-Ki Ching,et al.  A NOTE ON THE STATIONARY PROPERTY OF HIGH-DIMENSIONAL MARKOV CHAIN MODELS , 2011 .

[13]  W.-K. Ching,et al.  A higher-order Markov model for the Newsboy's problem , 2003, J. Oper. Res. Soc..

[14]  Michael K. Ng,et al.  Building higher-order Markov chain models with EXCEL , 2004 .

[15]  Tak Kuen Siu,et al.  A game theoretic approach to option valuation under Markovian regime-switching models , 2008 .

[16]  M. Padberg.  Linear Optimization and Extensions , 1995 .

[17]  Robert J. Elliott,et al.  Option pricing and Esscher transform under regime switching , 2005 .

[18]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[19]  J. Logan,et al.  A structural model of the higher‐order Markov process incorporating reversion effects , 1981 .

[20]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[21]  Tak Kuen Siu,et al.  Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows , 2010, Appl. Math. Comput..

[22]  Farnoush Banaei Kashani,et al.  INSITE: A Tool for Real-Time Knowledge Discovery from Users Web Navigation * , 2000 .

[23]  Robert J. Elliott,et al.  Filtering a nonlinear stochastic volatility model , 2012 .

[24]  Henry Lieberman,et al.  Letizia: An Agent That Assists Web Browsing , 1995, IJCAI.

[25]  S. Pliska.  Introduction to Mathematical Finance: Discrete Time Models , 1997 .

[26]  Edwin Diday,et al.  Symbolic clustering using a new dissimilarity measure , 1991, Pattern Recognit..

[27]  Robert J. Elliott,et al.  An application of hidden Markov models to asset allocation problems , 1997, Finance Stochastics.

[28]  Rogemar S. Mamon,et al.  Hidden Markov Models In Finance , 2007 .

[29]  Vasant Naik,et al.  Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns , 1993 .

[30]  Robert J. Elliott,et al.  On Markov‐modulated Exponential‐affine Bond Price Formulae , 2009 .

[31]  T. Siu.  A Markov Regime-Switching Marked Point Process for Short-Rate Analysis with Credit Risk , 2010 .

[32]  Robert J. Elliott,et al.  American options with regime switching , 2002 .

[33]  R. Quandt.  The Estimation of the Parameters of a Linear Regression System Obeying Two Separate Regimes , 1958 .

[34]  Philip Best.  Implementing Value at Risk: Best/Implementing Value , 2005 .

[35]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[36]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[37]  Gang George Yin,et al.  Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model , 2003, SIAM J. Control. Optim..

[38]  John B. Moore,et al.  Hidden Markov Models: Estimation and Control , 1994 .

[39]  WK Ching,et al.  Advances in Data Mining and Modeling , 2003 .

[40]  R. Elliott,et al.  Stochastic Volatility Model with Filtering , 2006 .

[41]  Robert J. Elliott,et al.  Robust parameter estimation for asset price models with Markov modulated volatilities , 2003 .

[42]  Robert J. Elliott,et al.  An interest rate model with a Markovian mean reverting level , 2002 .

[43]  Robert J. Elliott,et al.  Drift and volatility estimation in discrete time , 1998 .

[44]  Robert J. Elliott,et al.  New finite-dimensional filters and smoothers for noisily observed Markov chains , 1993, IEEE Trans. Inf. Theory.

[45]  A. Beja.  Probability Bounds in Replacement Policies for Markov Systems , 1969 .

[46]  Robert J. Elliott,et al.  VaR and expected shortfall: a non-normal regime switching framework , 2009 .

[47]  Michael K. Ng,et al.  Higher‐order Markov chain models for categorical data sequences * , 2004 .

[48]  Jan P. A. M. Jacobs,et al.  The composite leading indicator of the Slovak Republic Business cycle: construction and forecast , 1999 .

[49]  S. Adke,et al.  Limit Distribution of a High Order Markov Chain , 1988 .

[50]  S. Goldfeld,et al.  A Markov model for switching regressions , 1973 .

[51]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[52]  Robert J. Elliott,et al.  Pricing and hedging contingent claims with regime switching risk , 2011 .

[53]  Robert J. Elliott,et al.  On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy , 2010, Ann. Oper. Res..

[54]  Wk Ching,et al.  A Cube Model for Web Access Sessions and Cluster Analysis , 2001 .

[55]  Y. H. Wang.  Approximating kth-order two-state Markov chains , 1992 .

[56]  A. Raftery,et al.  Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model , 1994 .

[57]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[58]  Robert J. Elliott,et al.  Regime Switching and European Options , 2002 .

[59]  Shangzhen Luo,et al.  Filtering of Hidden Weak Markov Chain -Discrete Range Observations , 2007 .

[60]  Michael K. Ng,et al.  A high-order Markov-switching model for risk measurement , 2009, Comput. Math. Appl..

[61]  W. Li,et al.  Some Results on the Estimation of a Higher Order Markov Chain , 1990 .

[62]  Gang George Yin,et al.  Markowitz's mean-variance portfolio selection with regime switching: from discrete-time models to their continuous-time limits , 2004, IEEE Transactions on Automatic Control.

[63]  H. Tong.  On a threshold model , 1978 .