Skip to main content

Dynamic Structural Equations in Discrete and Continuous Time

  • Chapter
Economic Evolution and Demographic Change

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 395))

  • 105 Accesses

Abstract

Static structural equations models such as LISREL (Jöreskog/Sörbom, 1981) or EQS (Bentler, 1989) are now very popular in the social sciences in order to model causal relations between components of a system. The LISREL model represents a synthesis of path and factor analysis models. Originally it was designed to analyze cross sectional data but there are attempts to use it for longitudinal (time series and panel) data (see, e.g. Arminger/Müller, 1990, Oud/van den Bercken/Essers, 1990).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arminger, G., Müller, F. (1990), Lineare Modelle zur Analyse von Paneldaten, Westdeutscher Verlag.

    Google Scholar 

  • Arnold, L. (1974), Stochastic Differential Equations, Wiley, New York

    Google Scholar 

  • Aström, K. (1970), Introduction to Stochastic Control Theory, Academic Press, New York

    Google Scholar 

  • Bartlett, M.S. (1946), On the theoretical specification and sampling properties of autocorrelated time-series, Journal of the Royal Statistical Society (Supplement), 7, 27–41

    Article  Google Scholar 

  • Basawa, I.V., Prakasa Rao, B.L.S. (1980), Statistical Inference for Stochastic Processes, Academic Press, London

    Google Scholar 

  • Bellach, B. (1983), Parameter Estimators in Linear Stochastic Differential Equations and their Asymptotic Properties, Math. Operationsforsch. Statist., Ser. Statistics, 14, 1, 141–191

    Article  Google Scholar 

  • Bentler, P. (1989),EQS structural equations program manual, BMDP Statistical Software, Los Angeles Bergstrom, A.R. (1966), Non Recursive Models as Discrete Approximations to Systems of Stochastic Differential Equations, in: Bergstrom (1976)

    Google Scholar 

  • Bergstrom, A.R. (ed.; 1976 ), Statistical Inference in Continuous Time Models, North Holland, Amsterdam

    Google Scholar 

  • Box, G.E.P., Tiao, G.C. (1973), Bayesian Inference in Statistical Analysis, Addison Wesley, Reading, MA Caines, P.E. ( 1988 ), Linear Stochastic Systems, Wiley, New York

    Google Scholar 

  • Campillo, F., Le Gland, F. (1989), MLE for partially observed diffusions: direct maximization vs. the EM algorithm, Stochastic Processes and their Applications, 33, 245–274

    Article  Google Scholar 

  • Dembo, A., Zeitouni, 0. (1986), Parameter Estimation of Partially Observed Continuous Time Stochastic Processes Via the EM Algorithm, Stochastic Processes and their Applications, 23, 91–113

    Google Scholar 

  • Dennis, J.E. Jr, Schnabel, R.B. (1983), Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Florens-Zmirou, D. (1989), Approximate Discrete-Time Schemes for Statistics of Diffusion Processes, Statistics, 20, 4, 547–557

    Article  Google Scholar 

  • Hamerle, A., Nagl, W., Singer, H. (1991), Problems with the estimation of stochastic differential equations using structural equations models, Journal of Mathematical Sociology, 16, 3, 201–220

    Article  Google Scholar 

  • Hannan, E.J., Deistler (1988), The Statistical Theory of Linear Systems, Wiley, New York Harvey, A.C., Stock, J. (1985), The estimation of higher order continuous time autoregressive models, Econometric Theory, 1, 97–112

    Google Scholar 

  • Jöreskog, K., Sörbom, D. (1981), LISREL V, National Educational Resources, Chicago

    Google Scholar 

  • Jones, R.H. (1984), Fitting Multivariate Models to Unequally Spaced Data, in: Parzen, E. (ed.; 1984), Time Series Analysis of Irregularly Observed Data, Springer, New York, 158–188

    Google Scholar 

  • Kalman, R.E., Bucy, R.S. (1961), New Results in Linear Filtering and Prediction Theory, Trans. ASME, Ser. D: J. Basic Eng., 83, 95–108

    Google Scholar 

  • Kappler, E. (1931), Versuche zur Messung der Avogadro-Loschmidtschen Zahl aus der Brownschen Bewegung einer Drehwaage, Annalen der Physik, 11, 233–256

    Article  Google Scholar 

  • Le Breton, A. (1976), On continuous and discrete sampling for parameter estimation in diffusion type processes, Mathematical Programming Study, 5, 124–144

    Article  Google Scholar 

  • Liptser, R.S., Shiryayev, A.N. ( 1977, 1978), Statistics of Random Processes, Band I und I I, Springer, New York, Heidelberg, Berlin

    Google Scholar 

  • Louis, T.A. (1982), Finding the Observed Information Matrix when Using the EM Algorithm, Journal of the Royal Statistical Association B, 44, 2, 226–233

    Google Scholar 

  • Lorenz, E. (1963), Deterministic Nonperiodic Flow, J. Atmos. Sci., 20, 130 Merton, R.C. (1990), Continuous-time finance, Basil Blackwell, Cambridge, Mass. Nagl, W. ( 1991 ), Statistische Datenanalyse mit SAS, Campus, Frankfurt

    Google Scholar 

  • Otter, P.W. (1986), Dynamic structural systems under indirect observation: Identifiability and estimation aspects from a system theoretic perspective, Psychometrika, 51, 415–428

    Google Scholar 

  • Oud, J.H, van den Bercken, J.H., Essers, R.J. (1990), Longitudinal Factor Score Estimation Using the Kalman Filter, Applied Psychological Measurement, 14, 4, 395–418

    Article  Google Scholar 

  • Phillips, P.C.B. (1972), The Structural Estimation of a Stochastic Differential Equation System, in: Bergstrom (1976)

    Google Scholar 

  • Phillips, P.C.B. (1976), The estimation of linear stochastic differential equations with exogenous variables, in: Bergstrom (1976)

    Google Scholar 

  • Priestley, M.B. (1988), Non-linear and Non-stationary Time Series Analysis, Academic Press, London

    Google Scholar 

  • Rauch, H.E., Tung, F., Striebel, C.T. (1965), Maximum Likelihood Estimates of Linear Dynamic Systems, AIAA Journal, 3, 8, 1445–1450

    Article  Google Scholar 

  • Robinson, P.M. (1977), Estimation of a time series model from unequally spaced data, Stochastic Processes and their Applications, 6, 9–24

    Article  Google Scholar 

  • Rümelin, W. (1982), Numerical Treatment of Stochastic Differential Equations, SIAM J. Numer. Anal., 19, 3, 604–613

    Article  Google Scholar 

  • Sargan, J.D. (1976), Some Discrete Approximations to Continuous Time Stochastic Models, in: Bergstrom (1976)

    Google Scholar 

  • SAS Institute Inc. (1989), SAS/IML Software: Usage and Reference, Version 6, Cary, NC

    Google Scholar 

  • Schuss, Z. (1980), Theory and Applications of Stochastic Differential Equations, Wiley, New York

    Google Scholar 

  • Schuster, H.G. (1984), Deterministic Chaos, Physik-Verlag, Weinheim

    Google Scholar 

  • Schweppe, F. (1965), Evaluation of Likelihood Functions for Gaussian Signals, IEEE Transactions on Information Theory, 11, 61–70

    Article  Google Scholar 

  • Singer, H. (1990), Parameterschätzung in zeitkontinuierlichen dynamischen Systemen, Hartung-Gorre-Verlag, Konstanz

    Google Scholar 

  • Singer, H. (1991a), LSDE - A program package for the simulation, graphical display, optimal filtering and maximum likelihood estimation of Linear Stochastic Differential Equations, User’s guide, Meersburg

    Google Scholar 

  • Singer, H. (1991b), Continuous Time Dynamical Systems with Sampled Data, Errors of Measurement and Unobserved Components, Journal of Time Series Analysis, (in press)

    Google Scholar 

  • Singer, H. (1992a), Zeitkontinuierliche Dynamische Systeme, Campus, Frankfurt

    Google Scholar 

  • Singer, H. (1992b), The Aliasing Phenomenon in Visual Terms, Journal of Mathematical Sociology, 17, (in press)

    Google Scholar 

  • Yule, G.U. (1927), On a method for investigating periodicities in disturbed series with special reference to Wolfer`s sunspot numbers, Philos. Trans. Roy. Soc. London, Ser. A, 226, 267–298

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Singer, H. (1992). Dynamic Structural Equations in Discrete and Continuous Time. In: Haag, G., Mueller, U., Troitzsch, K.G. (eds) Economic Evolution and Demographic Change. Lecture Notes in Economics and Mathematical Systems, vol 395. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48808-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-48808-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56172-9

  • Online ISBN: 978-3-642-48808-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics