×

SEM modeling with singular moment matrices. I: ML-estimation of time series. (English) Zbl 1202.62124

Summary: A structural equation model (SEM) with deterministic intercepts is introduced. The Gaussian likelihood function does not contain determinants of sample moment matrices and is thus well-defined for only one statistical unit. The SEM is applied to a dynamic state space model and compared with the Kalman filter (KF) approach. The likelihood of both methods are shown to be equivalent, but for long time series numerical problems occur in the SEM approach, which are traced to the inversion of the latent state covariance matrix. Both approaches are compared on several aspects. The SEM approach is now open for idiographic \((N = 1)\) analysis and estimation of panel data with correlated units.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
62P20 Applications of statistics to economics
65C60 Computational problems in statistics (MSC2010)

Software:

LSDE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1007/BF02479833 · Zbl 0335.62058
[2] Arminger G., Lineare Modelle zur Analyse von Paneldaten [Linear Models of the Analysis of Panel Data] (1990)
[3] Bollerslev T., Handbook of Econometrics 4 pp 2959– (1994)
[4] Caines P., Linear Stochastic Systems (1988) · Zbl 0658.93003
[5] Dennis J., Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983) · Zbl 0579.65058
[6] Golub G., Matrix Computations, 3. ed. (1996) · Zbl 0865.65009
[7] Jazwinski A., Stochastic Processes and Filtering Theory (1970) · Zbl 0203.50101
[8] Liptser R., Statistics of Random Processes 1, 2. ed. (2001)
[9] Magnus J. R., Matrix Differential Calculus, 2. ed. (1999) · Zbl 0912.15003
[10] Mardia K., Multivariate Analysis (1979)
[11] Möbus C., Hypothesenprüfung, Band 5 der Serie Forschungsmethoden der Psychologie der Enzyklopädie der Psychologie pp 239– (1983)
[12] DOI: 10.1016/S1041-6080(00)80001-1
[13] Oud J., Advances in Longitudinal and Multivariate Analysis in the Behavioral Sciences pp 3– (1993)
[14] DOI: 10.1109/TIT.1965.1053737 · Zbl 0127.10805
[15] Singer H., Parameterschätzung in zeitkontinuierlichen dynamischen sy-stemen [Parameter estimation in continuous time dynamical systems] (1990)
[16] Singer H., LSDE–A Program Package for the Simulation, Graphical Display, Optimal Filtering and Maximum Likelihood Estimation of Linear Stochastic Differential Equations, User’s guide (1991)
[17] DOI: 10.1111/j.1467-9892.1993.tb00162.x · Zbl 0780.62064
[18] DOI: 10.1017/S0266466600009701 · Zbl 04527980
[19] Singer H., The European Association of Methodology (EAM) Methodology and Statistics Series: Vol. 2. Longitudinal Models in the Behavioral and Related Sciences pp 73– (2007)
[20] Singer H., Statistica Neerlandica 62 pp 29– (2008)
[21] Singer , H. ( 2009 ).SEM modeling with singular moment matrices. Part II: ML-estimation of sampled stochastic differential equations(Diskussions-beiträge Fakultät Wirtschaftswissenschaft Nr. 442). Hagen, Germany: FernUniversität. Retrieved August 25, 2010, fromhttp://www.fernuni-hagen.de/FBWIWI/forschung/beitraege/pdf/db442.pdf
[22] Söderström T., System Identification (1989)
[23] DOI: 10.1016/0304-4076(83)90066-0 · Zbl 0534.62083
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.