Document Zbl 0780.62064

Continuous-time dynamical systems with sampled data, errors of measurement and unobserved components. (English) Zbl 0780.62064

J. Time Ser. Anal. 14, No. 5, 527-545 (1993).

Summary: Maximum likelihood estimation of sampled continuous-time stochastic processes is considered. The likelihood is directly maximized with respect to the original structural parameters using a scoring algorithm with exact analytical derivatives. Furthermore, the case of unobserved states and errors of measurement is treated via EM and quasi-Newton algorithms. The proposed methods are illustrated with simulation studies and analysis of sunspot activity.

Cited in 15 Documents

MSC:

62M09	Non-Markovian processes: estimation
65C99	Probabilistic methods, stochastic differential equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
93E10	Estimation and detection in stochastic control theory

Keywords:

continuous/discrete state space model; discrete measurements; maximum likelihood estimation; EM algorithm; sampled continuous-time stochastic processes; scoring algorithm; exact analytical derivatives; unobserved states; errors of measurement; quasi- Newton algorithms; simulation studies; sunspot activity

Cite Review PDF

Full Text: DOI

References:

[1]	Arato M., Linear Stochastic Systems with Constant Coefficients. (1982) · doi:10.1007/BFb0043631
[2]	Arnold L., Stochastic Differential Equations. (1974) · Zbl 0278.60039
[3]	Azencott R., Series of Irregular Observations. (1986) · Zbl 0593.62088 · doi:10.1007/978-1-4612-4912-2
[4]	Bartlett M. S., J. R. Statist. Soc. 7 pp 27– (1946)
[5]	Bartlett M. S., In Introduction to Stochastic Processes. (1978) · Zbl 0365.60002
[6]	Bergstrom A. R., Statistical Inference in Continuous Time Models (1976) · Zbl 0348.00027
[7]	Bergstrom A. R., Economet. Theory 4 pp 365– (1988) · doi:10.1017/S0266466600013359
[8]	Caines P., Linear Stochastic Systems. (1988) · Zbl 0658.93003
[9]	DOI: 10.1016/0304-4149(86)90018-9 · Zbl 0608.62095 · doi:10.1016/0304-4149(86)90018-9
[10]	Dempster A. P., J. R. Statist. Soc. B 39 pp 1– (1977)
[11]	Dennis J. E., Numerical Methods for Unconstrained Optimization and Nonlinear Equations. (1983) · Zbl 0579.65058
[12]	DOI: 10.1080/00018738000101406 · doi:10.1080/00018738000101406
[13]	Doreian P., Modelling Social Processes. (1976)
[14]	Gelb A., Applied Optimal Estimation (1974)
[15]	Golub G. H., Matrix Computations. (1983) · Zbl 0559.65011
[16]	R. L. Goodrich(1978 ) Stochastic models of human growth . Ph.D. Thesis , Division of Applied Sciences, Harvard University, Cambridge, MA.
[17]	Hamerle A., Parameter Estimation in Continuous Time Dynamic Systems using Panel Data. (1988)
[18]	DOI: 10.2307/1911996 · Zbl 0516.93063 · doi:10.2307/1911996
[19]	Harvey A. C., Economet. Theory 1 pp 97– (1985) · doi:10.1017/S0266466600011026
[20]	DOI: 10.2307/2287656 · Zbl 0444.62104 · doi:10.2307/2287656
[21]	Jagger G., J. R. Statist. Soc. A 140 (4) pp 454– (1977)
[22]	Jazwinski A. H., Stochastic Processes and Filtering Theory. (1970) · Zbl 0203.50101
[23]	DOI: 10.2307/1268653 · Zbl 0342.62066 · doi:10.2307/1268653
[24]	Jones R. H., Time Series Analysis of Irregularly Observed Data pp 158– (1984) · doi:10.1007/978-1-4684-9403-7_8
[25]	DOI: 10.1137/0908007 · Zbl 0607.62113 · doi:10.1137/0908007
[26]	DOI: 10.2307/2347338 · doi:10.2307/2347338
[27]	Le Breton A., Math. Program. 5 pp 124– (1976)
[28]	Lewis F. L., Optimal Estimation. (1986)
[29]	Liptser R. S., Statistics of Random Processes (1977) · Zbl 0364.60004 · doi:10.1007/978-1-4757-1665-8
[30]	Louis T. A., J. R. Statist. Soc. B 44 (2) pp 226– (1982)
[31]	Mardia K. V., Multivariate Analysis. (1979) · Zbl 0432.62029
[32]	Mcdonald R. P., Gen. Syst. 18 pp 37– (1973)
[33]	DOI: 10.2307/2285651 · Zbl 0289.62058 · doi:10.2307/2285651
[34]	Phillips P. C. B., Statistical Inference in Continuous Time Models (1972)
[35]	Phillips P. C. B., Statistical Inference in Continuous Time Models (1973)
[36]	Priestley M. B., Non-linear and Non-stationary Time Series Analysis. (1988) · Zbl 0687.62072
[37]	Rao C. R., Linear Statistical Inference and its Applications, 2. ed. (1973) · Zbl 0256.62002 · doi:10.1002/9780470316436
[38]	Rauch H. E., AIAA J. 3 (8) pp 1445– (1965)
[39]	Sargan J. D., Statistical Inference in Continuous Time Models (1976) · Zbl 0357.62067
[40]	DOI: 10.1109/TIT.1965.1053737 · Zbl 0127.10805 · doi:10.1109/TIT.1965.1053737
[41]	Singer H., Parameterschatzung in zeitkontinuierlichen dynamischen Systemen. (1990)
[42]	DOI: 10.1080/00207178208922605 · Zbl 0473.93071 · doi:10.1080/00207178208922605
[43]	Van Kampen N. G., Stochastic Processes in Physics and Chemistry. (1981) · Zbl 0511.60038
[44]	Waldmeier M., The Sunspot Activity in the Years 1610-1960. (1961)
[45]	DOI: 10.1016/0304-4076(83)90066-0 · Zbl 0534.62083 · doi:10.1016/0304-4076(83)90066-0
[46]	DOI: 10.1063/1.1705306 · Zbl 0173.29604 · doi:10.1063/1.1705306
[47]	DOI: 10.1098/rsta.1927.0007 · JFM 53.0509.02 · doi:10.1098/rsta.1927.0007

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.