An approximate innovation method for the estimation of diffusion processes from discrete data

Journal of Time Series Analysis

Volumn 27, Issue 1, 2006, Pages 77-97

  Jimenez, J C ^a   Ozaki, T ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645150618     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2005.00454.x     Document Type: Article

References (43)

1. ASTROM, K. J. (1969) On the choice of sampling rates in parametric identification of time series. Information Sciences 1, 273-78.
2. BASAWA, I. V. and PRAKASA RAO, B. L. S. (1980) Statistical Inference for Stochastic Processes. New York: London Academic Press.
3. BIBBY, B. M. and SORENSEN, M. (1995) Martingale estimation function for discrete observed diffusion processes. Bertnoulli 1, 17-39.
4. BRIGO, D. and HANZON, B. (1998) On some filtering problems arising in mathematical finance. Insurance: Mathematics and Economics 22, 53-64.
5. CHIARELLA, C., HUNG, H. and To, T. D. (2005) The volatility structure of the fixed income market under the HJM framework: a nonlinear filtering approach. Working Paper 151, Quantitative Finance Research Center, Sydney.
6. Cox, J. C., INGERSOLL, J. E. and Ross, S. A. (1985) A theory of the term structure of interest rates. Econometrica 53, 285-408.
7. GEYER, A. L. J. and PICHLER, S. (1996) A state-space approach to estimate and test multi-factor Cox-Ingersoll-Ross models of term structure. Journal of Financial Research 22, 107-30.
8. GHYSELS, E., HARVEY, A. C. and RENAULT, E. (1996) Stochastic volatility. In Handbook of Statistics, Vol. 14 (eds G. S. MADDALA and C. R. RAO). Amsterdam, pp. 119-91.
9. Hu, Y. (2000) Optimal times to observe in Kalman-Bucy models. Stochastics Stochastic Reports 69, 123-40.
10. JAZWINSKI, A. H. (1970) Stochastic Processes and Filtering Theory. Academic Press.
11. JENSEN, J. L. and PETERSEN, N. V. (1999) Asymptotic normality of the maximin likelihood estimator in state-space models. Annals Statistics 27, 514-35.
12. JIMENEZ, J. C. (1996) Local linearization method for the numerical solution of stochastic differential equations and nonlinear Kalman filters. In Proceeding of the Symposium: Studies on Data Analysis by Statistical Software. Fuji Kenshu-Jyo, Japan, Nov. 1995, 291-92.
13. JIMENEZ, J. C. and OZAKI, T. (2002) Linear estimation of continuous-discrete linear state space models with multiplicative noise. Systems and Control Letters 47, 91-101. Erratum appears in V49, page 161, 2003.
14. JIMENEZ, J. C. and OZAKI, T. (2003) Local linearization filters for nonlinear continuous-discrete state space models with multiplicative noise. International Journal of Control 76. 1159-70.
15. KAILATH, T. (1971) Some extensions of the innovations theorem. Bell System Technical Journal 50, 1487-94.
16. KAILATH, T. (1974) A view of three decades of linear filtering theory. IEEE Transactions Information Theory 20, 146-81.
17. KAILATH, T. (1981) Lectures on Wiener and Kalman Filtering. New York: Springer-Verlag.
18. KAILATH, T. (1991) From Kalman filtering to innovations, martingales, scattering and other nice things. In Mathematical System Theory: The Influence of R.E. Kalman (ed. A.C. ANTOULAS). Berlin: Springer-Verlag, pp. 55-88.
19. KALLIANPUR, G. (1980) Stochastic Filtering Theory. New York: Springer-Verlag.
20. KALMAN, R. E. (1960) A New approach to linear filtering and prediction problems. Transactions of the ASME, Series D: Journal of Basic Engineering 82, 35-45.
21. KALMAN, R. E. and BUCY, R. S. (1961) A new result in linear filtering and prediction problems. Journal of Basic Engineering 83, 95-108.
22. KLOEDEN, P. E. and PLATEN, E. (1995) Numerical Solution of Stochastic Differential Equations (2nd edn). Berlin: Springer-Verlag.
23. LIUNG, L. (1999) System Identification, Theory for the User (2nd edn). Englewood Cliffs: Prentice Hall.
24. LIUNG, L. and CAINES, P. E. (1979) Asymptotic normality of prediction error estimators for approximate system models. Stochastics 3, 29-46.
25. NIELSEN, J. N., MADSEN, H., MELGAARD, H. and BAADSGAARD, M. (1998) Estimation of embedded parameters in stochastic differential equations using discrete-time measurements. Technical Reports 1998, Informatics and Mathematical Modelling, Technical University of Denmark.
26. NIELSEN J. N., MADSEN, H. and MELOAARD, H. (2000a) Estimating parameters in discretely, partially observed stochastic differential equations. Technical Reports 2000, No. 7, Informatics and Mathematical Modelling, Technical University of Denmark.
27. NIELSEN, J.N., MADSEN, H. and YOUNG, P. C. (2000b) Parameter estimation in stochastic differential equations: an overview. Annual Review of Control 24, 83-94.
28. NIELSEN, J. N., VESTERGAARD, M. and MADSEN, H. (2000c) Estimation in continuous-time stochastic volatility models using nonlinear filters. International Journal of Theoretical and Applied Finance 3, 1-30.
29. NOLSOE, K., NIELSEN, J. N. and MADSEN, H. (2000) Prediction-based estimating function for diffusion processes with measurement noise. Technical Reports 2000, No. 10, Informatics and Mathematical Modelling, Technical University of Denmark.
30. OZAKI, T. (1993) A local linearization approach to nonlinear filtering. International Journal of Control 57, 75-96.
31. OZAKI, T. (1994) The local linearization filter with application to nonlinear system identification. In Proceedings of the first US/Japan Conference on the Frontiers of Statistical modelling: An Informational Approach (ed. H. BOZDOGAN). Netherlands: Kluwer Academic Publishers, pp. 217-240.
32. OZAKI, T. and JIMENEZ, J. C. (2002) An innovation approach for the estimation, selection and prediction of discretely observed continuous-time stochastic volatility models. Research Memo. No. 855, The Institute of Statistical Mathematics, Tokyo.
33. OZAKI, T., JIMENEZ, J. C. and HAOGAN-OZAKI, V. (2000) Role of the likelihood function in the estimation of chaos models. Journal of Time Series Analysis 21, 363-87.
34. OZAKI, T., JIMENEZ, J. C., ILNO, M., SHI, Z. and SUGAWARA, S. (2001) Use of stochastic differential equation models in financial time series analysis: monitoring and control of currencies in exchange market. In Proc. Japan-US Joint Seminar on Statistical Time Series Analysis. Kyoto, Japan, June 2001, 17-24.
35. PEDROSO, L., MARRERO, A., DE ARAZOZA, H. (2003) Nonlinear parametric model identification using genetic algorithms. In Lecture Notes in Computer Science 2687: Artificial Neural Nets Problem Solving Methods, 473-80. Berlin: Springer-Verlag.
36. PRAKASA RAO, B. L. S. (1999) Statistical inference for diffusion type processes, Oxford University Press, Oxford.
37. RIERA J. J., WAN, X., JIMENEZ, J. C. and KAWASHIMA, R. (2005) Nonlinear local electro-vascular coupling: from neuronal masses to data. Technical Report 2005-345, Instituto de Cibernetica, Matematica y Fisica, La Habana.
38. RIERA, J. J., WATANABE, J., IWATA, K., MIURA, N., AUBERT, E., OZAKI, T. and KAWASHIMA, R. (2004) A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals. Neuroimage 21, 547-67.
39. SCHWEPPE, F. (1965) Evaluation of likelihood function for Gaussian signals. IEEE Transactions on Information Theory 11, 61-70.
40. SHOJI, I. (1998) A comparative study of maximum likelihood estimators for nonlinear dynamical systems. International Journal of Control 71, 391-404.
41. SINGER, H. (1993) Continuous-time dynamical systems with sampled data, error of measurement and unobserved components. Journal of Time Series Analysis 14, 527-45.
42. SOERENSEN, M. (2000) Prediction-based estimating functions. Econometrics Journal 3, 123-47.
43. VALDES, P. A., JIMENEZ, J. C., RIERA, J., BISCAY, R. and OZAKI, T. (1999) Nonlinear EEG analysis based on a neural mass model. Biological Cybernetics 81, 415-24.