Concurrent processing of heteroskedastic vector-valued mixture density models

References

• Bauwens , L. , Hafner , C. M. and Rombouts , J. V.K. 2007 . Multivariate mixed normal conditional heteroskedasticity . Comput. Stat. Data Anal. , 51 ( 7 ) : 3551 – 3566 .
   Web of Science ®Google Scholar
• Bera , A. K. , Higgins , M. L. and Lee , S. 1992 . Interaction between autocorrelation and conditional heteroskedasticity: A random coefficient approach . J. Bus. Econ. Stat. , 10 : 133 – 142 .
   Web of Science ®Google Scholar
• Bishop , C. M. 1995 . Neural Networks for Pattern Recognition , New York : Oxford University Press, Inc .
   Google Scholar
• Black , F. Studies of Stock Price Volatility Changes . Proceedings of the 1976 Meetings of the Business and Economic Statistics, American Statistical Society . pp. 177 – 181 .
   Google Scholar
• Bollerslev , T. 1986 . Generalized autoregressive conditional heteroskedasticity . J. Econometrics , 31 : 307 – 327 .
   Web of Science ®Google Scholar
• Bose , A. and Mukherjee , K. 2003 . Estimating the ARCH parameters by solving linear equations . J. Time Ser. Anal. , 24 : 127 – 136 .
   Web of Science ®Google Scholar
• Dempster , A. P. , Laird , N. M. and Rubin , D. B. 1977 . Maximum likelihood from incomplete data via the EM algorithm . J. R. Statist. Soc. B ,
   Google Scholar
• Dennis , J. E. and Schnabel , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Non-linear Equations , Englewood Cliffs , NJ : Prentice-Hall Inc .
   Google Scholar
• Dickey , D. and Fuller , W. 1979 . Distribution of the estimators for autoregressive time series with a unit root . J. Am. Statist. Assoc. , 74 : 427 – 431 .
   Web of Science ®Google Scholar
• Doornik , J. A. and Hendry , D. F. 1997 . Modelling Dynamic Systems Using PcFiml 9.0 for Windows , London : Rhomson Business Press .
   Google Scholar
• Efron , B. and Tibshirani , R. 1985 . The bootstrap method for assessing statistical accuracy . Behaviormetrika , 17 : 1 – 35 .
   Google Scholar
• Engle , R. 1982 . Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation . Econometrica , 50 ( 4 ) : 987 – 1007 .
   Web of Science ®Google Scholar
• Engle , R. and Granger , C. 1987 . Co-integration and error correction: representation, estimation, and testing . Econometrics , 55 ( 2 ) : 251 – 276 .
   Web of Science ®Google Scholar
• Ferreira da Silva , A. R. 2009 . Bayesian mixture models of variable dimension for image processing . Comput. Methods Programs Biomed , 94 : 1 – 14 .
   PubMed Web of Science ®Google Scholar
• Frühwirth-Schnatter , S. 2006 . Finite Mixture and Markov Switching Models , New York : Springer .
   Google Scholar
• Gill , P. E. , Murray , W. and Saunders , M. A. 2007 . User's Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming University of California, San Diego, La Jolla and Stanford University, CA
   Google Scholar
• Gujarati , D. N. 2003 . Basic Econometrics , 856 – 862 . New York : McGraw-Hill .
   Google Scholar
• Hansen , L. 1982 . Large sample properties of generalized method of moments estimators . Econometrica , 50 : 1029 – 1054 .
   Web of Science ®Google Scholar
• Hastie , T. and Tibshirani , R. 1996 . Discriminant analysis by Gaussian mixtures . J.R. Statist. Soc. B , 58 : 155 – 176 .
   Google Scholar
• Höglund , R. and Östermark , R. 1991 . Automatic ARIMA modelling by the Cartesian search algorithm . J. Forecasting , 10 : 465 – 476 .
   Web of Science ®Google Scholar
• IMSL MATH/Library Users Manual, Vol. 1–3 (QA76.73 in NIST Gaithersburg Research Information Center, Admin E-120), IMSL Inc., Houston, TX, 1987
   Google Scholar
• Jenkins , G. M. and Priestley , M. B. 1957 . Spectral analysis of time series . J.R. Statist. Soc. B , 19 : 1 – 12 .
   Google Scholar
• Jeong , J.-W. , Kim , T.-S. , Kim , S.-H. and Singh , M. 2004 . “ Application of Independent Component Analysis with Mixture Density Model to Localize Brain Alpha Activity in fMRI and EEG ” . Vol. 14 , 170 – 180 . Wiley Periodicals Inc .
   Google Scholar
• Johnston , J. and DiNardo , J. 1997 . Econometric Methods, , 4 , New York : McGraw Hill .
   Google Scholar
• Kittler , J. 1998 . Combining classifiers: a theoretical framework . Pattern Analysis and Applic. , 1 : 18 – 27 .
   Web of Science ®Google Scholar
• Künsch , H. 1989 . The jackknife and the bootstrap for general stationary observations . Ann. Stat. , 17 ( 3 ) : 1217 – 1241 .
   Web of Science ®Google Scholar
• Laurent , S. , Bauwens , L. and Rombouts , J. V.K. 2006 . Multivariate GARCH models: A survey . J. Appl. Econometrics , 21 ( 1 ) : 79 – 109 .
   Web of Science ®Google Scholar
• Lawrence , C. , Zhou , J. L. and Tits , A. 1998 . CFSQP Version 2.5d , College Park , MD : Institute for Systems Research and Electrical Engineering Department, University of Maryland . February
   Google Scholar
• Liesenfeld , R. 2001 . A generalized bivariate mixture model for stock price volatility and trading volume . J. Econometrics , 104 ( 1 ) : 141 – 178 .
   Web of Science ®Google Scholar
• Lim , D. , Ong , Y.-S. , Jin , Y. , Sendhoff , B. and Lee , B.-S. 2007 . Efficient hierarchical parallel genetic algorithms using grid computing . Future Generat. Comput. Syst. , 23 ( 4 ) : 658 – 670 .
   Web of Science ®Google Scholar
• Ljung , L. 1987 . System Identification, Theory for the User , Englewood Cliffs , NJ : Prentice Hall, Inc .
   Google Scholar
• Long , J. S. and Ervin , L. 2000 . Using heteroskedasticity-consistent standard errors in the linear regression model . Am. Statist. , 54 : 217 – 224 .
   Web of Science ®Google Scholar
• MacKinnon , J. G. and White , H. 1985 . Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties . J. Econometrics , 29 : 53 – 57 .
   Web of Science ®Google Scholar
• Mandelbrot , B. 1963 . The variation of certain speculative prices . J. Bus. , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• Maros , I. 2003 . A generalized dual phase-2 simplex algorithm . Eur. J. Oper. Res. , 149 ( 1 ) : 1 – 16 .
   Web of Science ®Google Scholar
• McLahlan , G. J. and Basford , K. E. 1988 . Mixture Models: Inference and Applications to Clustering , New York : Marcel Dekker .
   Google Scholar
• McLahlan , G. J. and Peel , D. 2000 . Finite Mixture Models , Wiley .
   Google Scholar
• Mooney , C. Z. and Duval , R. D. 1993 . Bootstrapping: A Nonparametric Approach to Statistical Inference , Newbury Park , CA : Sage Publications, Inc .
   Google Scholar
• Ormoneit , D. and Tresp , V. 1998 . Averaging, maximum penalized likelihood and Bayesian estimation for improving Gaussian mixture probability density estimates . IEEE Trans. Neural Netw. , 9 ( 4 ) : 639 – 650 .
   PubMed Web of Science ®Google Scholar
• Östermark , R. 1996 . A flexible multicomputer algorithm for artificial neural networks . Neural Netw. , 9 ( 1 ) : 169 – 178 .
   Web of Science ®Google Scholar
• Östermark , R. 1999 . Solving irregular econometric and mathematical optimization problems with a genetic hybrid algorithm . Comput. Econ. , 13 ( 2 ) : 103 – 115 .
   Google Scholar
• Östermark , R. 2002 . Automatic detection of parsimony in heteroskedastic time series processes. Empirical tests on global asset returns with parallel geno-mathematical programming . Soft Comput. , 6/1 : 45 – 63 .
   Google Scholar
• Östermark , R. 2005 . Portfolio management under competing representations . Kybernetes Int. J. Syst. Cybern. , 34 ( 9/10 ) : 1517 – 1550 .
   Web of Science ®Google Scholar
• Östermark , R. 2007 . A flexible platform for mixed-integer non-linear programming problems . Kybernetes Int. J. Syst. Cybern. , 36 ( 5/6 ) : 652 – 670 .
   Web of Science ®Google Scholar
• Östermark , R. 2009 . Geno-mathematical identification of the multi-layer perceptron . Neural Comput. Appl. , 18 : 331 – 334 .
   Web of Science ®Google Scholar
• Östermark , R. 2008b . Scalability of the genetic hybrid algorithm on a parallel supercomputer . Kybernetes Int. J. Syst. Cybern. , forthcoming
   Web of Science ®Google Scholar
• Östermark , R. and Höglund , R. 1997 . Multivariate EGARCHX-modelling of the international asset return signal response mechanism . Int. J. Finance Econ. , 2 ( 3 ) : 249 – 262 .
   Web of Science ®Google Scholar
• Östermark , R. and Saarinen , M. 1994 . Parallel implementation of a VARMAX – algorithm. Practical aspects and experiences . Parallel Comput. , 20 : 1711 – 1720 .
   Google Scholar
• Pantula , S. G. 1988 . Estimation of autoregressive models with ARCH errors . Sankhya , 50 : 119 – 138 .
   Google Scholar
• Park , S. K. and Miller , K. W. 1988 . Random number generators: Good ones are hard to find . Commun. ACM , 31 ( 10 ) : 1192
   Web of Science ®Google Scholar
• Press , W. H. , Teukolsky , S. A. , Vetterling , W. T. and Flannery , B. P. 2007 . Numerical Recipes: The Art of Scientific Computing , 3 , New York : Cambridge University Press .
   Google Scholar
• Richardson , S. and Green , P. J. 1997 . On Bayesian analysis of mixtures with an unknown number of components (with discussion) . J. R. Statist. Soc. Ser B , 59 : 731 – 792 .
   Google Scholar
• Schittkowski , K. 2007 . “ NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed and Non-monotone Line Search ” . Germany : University of Bayreuth . User's Guide, Version 2.24
   Google Scholar
• Schittenkopf , C. and Dorffner , G. 2001 . Risk-neutral density extraction from option prices: Improved pricing with mixture density networks . IEEE Trans. Neural Netw. , 12 : 716 – 725 .
   PubMed Web of Science ®Google Scholar
• Schittenkopf , C. , Dorffner , G. and Dockner , E. J. 2000 . Forecasting time-dependent conditional densities: A semi-nonparametric neural network approach . J. Forecasting , 19 ( 4 ) : 355 – 374 .
   Web of Science ®Google Scholar
• Searle , S. R. 1982 . Matrix Algebra Useful for Statistics , New York : John Wiley & Sons .
   Google Scholar
• Wong , C. S. and Li , W. K. 2000 . “ On a mixture autoregressive model ” . Vol. 62 , 95 – 115 . J. R. Statist. Soc. Ser. B .
   Google Scholar
• Wong , C. S. and Li , W. K. 2001 . On a mixture autoregressive conditional heteroskedastic model . J. Am. Statist. Assoc. , 96 : 982 – 995 .
   Web of Science ®Google Scholar