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Abstract
In an earlier paper we developed a stochastic model incorporating a double-Markov modulated mean-reversion model. The model is based on an explicit discretisation of the corresponding continuous time dynamics. Here we discuss parameter estimation via the technique of M-ary detection.
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References
- AGGOUN, L. and ELLIOTT, R.J. 2004 Measure Theory and Filtering: Introduction with Applications. Cambridge Series in Statistical and Probabilistic Mathematics.
- BAUM, L.E. and PETRIE, T. 1966 Statistical Inference for Probabilistic Functions of Finite State Markov Chains. Annals of the Institute of Statistical Mathematics, 37: 1554-1563.
- DEMP, A.P., LAIRD, N.M. and RUBIN, D.B. 1977 Maximum Likelihood from Incomplete Data via the EM algorithm. Jour. of the Royal Statistical Society B (39) 1-38.
- ELLIOTT, C., ELLIOTT, R.J. and MALCOLM, W.P. 2005 Commodity prices and regime switching bases, Conference on Stochastic Modelling of Complex Systems, Daydream Island, Queensland Australia 10-16 July.
- ELLIOTT, R.J., AGGOUN, L. and MOORE, J.B. 1995 Hidden Markov Models: Estimation and Control. Springer-Verlag, New-York. Applications of Mathematics No. 29.
- ELLIOTT, R.J. 1982 Stochastic Calculus and Applications. Springer-Verlag, New-York. Applications of Mathematics No. 18.
- ELLIOTT, R.J., FISCHER, P. and PLATEN, E. 1999 Filtering and parameter estimation for a mean-reverting interest rate model, Canadian Applied Mathematics Quarterly, 7: 381-400.
- ELLIOTT, R.J. and KOPP, P.E. 2005 Mathematics of Financial Markets, 2nd Edition, Springer-Verlag.
- KLOEDEN, P.E. and PLATEN, E. 1992. Numerical Solution of Stochastic Differential Equations Springer-Verlag, New-York. Applications of Mathematics No. 23.
- MALCOLM, W.P., AGGOUN, L., and Al-LAWATI MOHAMED. 2008. On A Markov Modulated Mean Reverting Finance Model. Journal of Science and Technology, Sultan Qaboos University. 13: 55-62 .
- POOR, H. 1988. An Introduction to Signal Detection and Estimation, Springer-Verlag, New York.
References
AGGOUN, L. and ELLIOTT, R.J. 2004 Measure Theory and Filtering: Introduction with Applications. Cambridge Series in Statistical and Probabilistic Mathematics.
BAUM, L.E. and PETRIE, T. 1966 Statistical Inference for Probabilistic Functions of Finite State Markov Chains. Annals of the Institute of Statistical Mathematics, 37: 1554-1563.
DEMP, A.P., LAIRD, N.M. and RUBIN, D.B. 1977 Maximum Likelihood from Incomplete Data via the EM algorithm. Jour. of the Royal Statistical Society B (39) 1-38.
ELLIOTT, C., ELLIOTT, R.J. and MALCOLM, W.P. 2005 Commodity prices and regime switching bases, Conference on Stochastic Modelling of Complex Systems, Daydream Island, Queensland Australia 10-16 July.
ELLIOTT, R.J., AGGOUN, L. and MOORE, J.B. 1995 Hidden Markov Models: Estimation and Control. Springer-Verlag, New-York. Applications of Mathematics No. 29.
ELLIOTT, R.J. 1982 Stochastic Calculus and Applications. Springer-Verlag, New-York. Applications of Mathematics No. 18.
ELLIOTT, R.J., FISCHER, P. and PLATEN, E. 1999 Filtering and parameter estimation for a mean-reverting interest rate model, Canadian Applied Mathematics Quarterly, 7: 381-400.
ELLIOTT, R.J. and KOPP, P.E. 2005 Mathematics of Financial Markets, 2nd Edition, Springer-Verlag.
KLOEDEN, P.E. and PLATEN, E. 1992. Numerical Solution of Stochastic Differential Equations Springer-Verlag, New-York. Applications of Mathematics No. 23.
MALCOLM, W.P., AGGOUN, L., and Al-LAWATI MOHAMED. 2008. On A Markov Modulated Mean Reverting Finance Model. Journal of Science and Technology, Sultan Qaboos University. 13: 55-62 .
POOR, H. 1988. An Introduction to Signal Detection and Estimation, Springer-Verlag, New York.