Parameter optimization for differential equations in asset price forecasting

References

• Akaike , H. 1974 . A new look at the statistical model identification . IEEE Trans. Automat. Con. , 19 ( 6 ) : 716 – 723 .
   Web of Science ®Google Scholar
• Anderson , S. C. and Born , J. A. 2002 . Closed-end Fund Pricing: Theories and Evidence , Boston : Kluwer Academic Publishers .
   Google Scholar
• Ascher , U. M. and Petzold , L. R. 1998 . Computer Methods for Ordinary Differential Equations and Differential-algebraic Equations , PA : SIAM, Philadelphia .
   Google Scholar
• Bartholomew-Biggs , M. 2005 . Nonlinear Optimization with Financial Applications , Boston : Kluwer Academic Publishers .
   Google Scholar
• Biegler , L. T. and Tjoa , I. B. 1991 . Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic equation systems . Ind. Eng. Chem. Res. , 30 : 376 – 385 .
   Google Scholar
• Bodie , Z. , Kane , A. and Marcus , A. J. 2005 . Investments , 6 , Boston, MA : Irwin McGraw-Hill .
   Google Scholar
• Bremermann , H. 1970 . A method of unconstrained global optimization . Math. Biosci. , 9 : 1 – 15 .
   Google Scholar
• Broyden , C. G. 1970 . The convergence of a class of double rank minimization algorithms . part 1, J. Inst. Math. Appl. , 6 : 76 – 90 .
   Google Scholar
• Broyden , C. G. 1970 . The convergence of a class of double rank minimization algorithms . part 2, J. Inst. Maths. Appl. , 6 : 222 – 231 .
   Google Scholar
• Caginalp , G. and Balenovich , D. 1999 . Asset flow and momentum: Deterministic and stochastic equations . Phil. Trans. Rov. Soc. , 357 ( 1758 ) : 2119 – 2133 .
   Google Scholar
• Caginalp , G. and Balenovich , D. 2003 . A theoretical foundation for technical analysis . J. Tech. Anal. , 59 : 5 – 22 .
   Google Scholar
• Caginalp , G. and Ilieva , V. Hybrid methods for testing support and resistant . (preprint)
   Google Scholar
• Caginalp , G. and Laurent , H. 1998 . The predictive power of price patterns . Appl. Math. Finan. , 5 : 181 – 206 .
   Google Scholar
• Dennis , J. E. , Gay , D. M. and Welsch , R. E. 1981 . An adaptive nonlinear least-squares algorithm . ACM Trans. Math. Soft. , 7 : 348 – 368 .
   Web of Science ®Google Scholar
• Dunker , A. M. 1984 . The decoupled direct method of calculating sensitivity coefficients in chemical kinetics . J. Chem. Phys. , 81 : 2385 – 2393 .
   Web of Science ®Google Scholar
• Duran , A. 2006 . Overreaction behavior and optimization techniques in mathematical finance , Pittsburgh, PA : University of Pittsburgh . Ph.D. thesis
   Google Scholar
• Duran , A. and Caginalp , G. 2007 . Overreaction diamonds: Precursors and aftershocks for significant price changes . Quant. Finance, , 7 ( 3 ) : 321 – 342 .
   Web of Science ®Google Scholar
• Guay , M. and McLean , D. D. 1995 . Optimization and sensitivity analysis for multi-response parameter estimation in systems of ordinary differential equations . Comp. Chem. Eng. , 19 ( 12 ) : 1271 – 1285 .
   Google Scholar
• Higham , N. J. 1996 . Accuracy and Stability of Numerical Algorithms , SIAM, Philadelphia .
   Google Scholar
• Hutchinson , J. M. 1994 . A radical basis approach to financial time series analysis , Boston, MA : MIT . Ph.D. thesis
   Google Scholar
• Kiehl , M. 1999 . Sensitivity analysis of ODEs and DAEs – Theory and implementation guide . Optim. Meth. Soft. , 10 ( 6 ) : 803 – 821 .
   Web of Science ®Google Scholar
• Kramer , M. A. and Leis , J. R. 1988 . Simultaneous solution and sensitivity analysis of ODE systems . ACM Trans. Math. Soft. , 14 : 45 – 60 .
   Google Scholar
• Lee , S. L. and Hovland , P. D. Derivative techniques for forward sensitivity analysis in time-dependent problems . ANL/MCS-P1153-0404 (preprint)
   Google Scholar
• Mak , D. K. 2003 . The Science of Financial Market Trading , New Jersey : World Scientific .
   Google Scholar
• Maly , T. and Petzold , L. R. 1996 . Numerical methods and software for sensitivity analysis of differential-algebraic systems . Appl. Numer. Math. , 20 : 57 – 79 .
   Web of Science ®Google Scholar
• Mendenhall , W. , Beaver , R. J. and Beaver , B. M. 2003 . Introduction to Probability and Statistics , 11 , Pacific Grove : Brooks/Cole .
   Google Scholar
• Milstein , J. The inverse problem: Estimation of kinetic parameters . Proceedings of an Internation Workshop on, Modelling of Chemical Reactions Systems . Vol. 18 , pp. 92 – 101 . Heidelberg Series: Springer Series in Chemical Physics .
   Google Scholar
• Milstein , J. 1985 . Spline and weighted random directions method for nonlinear optimization . Math. Biosci. , 74 : 247 – 256 .
   Google Scholar
• Nocedal , J. and Wright , S. J. 2006 . Numerical Optimization , 2 , New York : Springer Series in Operations Research, Springer-Verlag .
   Google Scholar
• Poterba , J. M. and Summers , L. H. 1988 . Mean reversion in stock prices: Evidence and implications . J. Finan. Econ. , 22 : 27 – 59 .
   Web of Science ®Google Scholar
• Rapach , D. E. , Wohar , M. E. and Rangvid , J. 2005 . Macro variables and international stock return predictability . Int. J. Forecast. , 21 ( 1 ) : 137 – 166 .
   Web of Science ®Google Scholar
• Serban , R. and Hindmarsh , A. C. CVODES: The sensitivity-enabled ODE solver in SUNDIALS . Proceedings of the ASME International Design Engineering Technical Conferences . September 24–28 . Long Beach, CA
   Google Scholar