Hostname: page-component-5f745c7db-szhh2 Total loading time: 0 Render date: 2025-01-06T06:50:24.636Z Has data issue: true hasContentIssue false

A Dynamic Factor Model for the Analysis of Multivariate Time Series

Published online by Cambridge University Press:  01 January 2025

Peter C. M. Molenaar*
Affiliation:
University of Amsterdam
*
Requests for reprints should be sent to Dr. P. C. M. Molenaar, Department of Psychology, University of Amsterdam, 8 Weesperplein, 1018 XA Amsterdam, THE NETHERLANDS.

Abstract

As a method to ascertain the structure of intra-individual variation, P-technique has met difficulties in the handling of a lagged covariance structure. A new statistical technique, coined dynamic factor analysis, is proposed, which accounts for the entire lagged covariance function of an arbitrary second order stationary time series. Moreover, dynamic factor analysis is shown to be applicable to a relatively short stretch of observations and therefore is considered worthwhile for psychological research. At several places the argumentation is clarified through the use of examples.

Type
Original Paper
Copyright
Copyright © 1985 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I would like to thank WM. van der Molen, G. J. Mellenbergh and L. H. M. Oppenheimer, who provided valuable ideas that led to this formulation.

References

Anderson, T. W. (1963). The use of factor analysis in the statistical analysis of multiple time series. Psychometrika, 28, 125.CrossRefGoogle Scholar
Bentler, P. M., & Bonett, D. G. (1980). Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88, 588606.CrossRefGoogle Scholar
Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control, San Francisco: Holden-Day.Google Scholar
Box, G. E. P., & Tiao, G. C. (1977). A canonical analysis of multiple time series. Biometrika, 64, 355365.CrossRefGoogle Scholar
Brillinger, D. R. (1975). Time series: Data analysis and theory, New York: Holt, Rinehart & Winston.Google Scholar
Cattell, R. B. (1952). Factor analysis, New York: Harper.Google Scholar
Cattell, R. B. (1957). Personality and motivation: Structure and measurement, Yonkers-on-Hudson: World Book.Google Scholar
Cattell, R. B. (1963). The structuring of change byP-technique and incrementalR-technique. In Harris, C. W. (Eds.), Problems in measuring change, Madison: The University of Wisconsin Press.Google Scholar
Duffy, E. (1962). Activation and behavior, New York: Wiley.Google Scholar
Eiting, M. H., & Mellenbergh, G. J. (1980). Testing covariance matrix hypotheses: An example from the measurement of musical abilities. Multivariate Behavioral Research, 15, 203223.CrossRefGoogle Scholar
Grossberg, S. (1982). Studies of mind and brain: Neural principles of learning, perception, development, cognition, and motor control, Dordrecht: Reidel.CrossRefGoogle Scholar
Hannan, E. J. (1970). Multiple time series, New York: Wiley.CrossRefGoogle Scholar
Haykin, S. (1979). Nonlinear methods of spectral analysis, New York: Springer-Verlag.Google Scholar
Holtzman, W. H. (1962). Methodological issues inP-technique. Psychological Bulletin, 59, 243256.CrossRefGoogle Scholar
Holtzman, W. H. (1963). Statistical methods for the study of change in the single case. In Harris, C. W. (Eds.), Problems in measuring change, Madison: The University of Wisconsin Press.Google Scholar
Hutt, S. J., Lenard, H. G., & Prechtl, H. F. R. (1969). Psychophysiological studies in newborn infants. In Lipsitt, L. P., Reese, H. W. (Eds.), Advances in child development and behavior, New York: Academic Press.Google Scholar
Jazwinsky, A. H. (1970). Stochastic processes and filtering theory, New York: Academic Press.Google Scholar
Jenkins, G. M., & Watts, D. G. (1968). Spectrum analysis and its applications, San Francisco: Holden-Day.Google Scholar
Jöreskog, K. G. (1976). Structural equation models in the social sciences: Specification, estimation, and testing, Uppsala: University of Uppsala.Google Scholar
Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices. Psychometrika, 43, 443477.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1978). LISREL IV: Analysis of linear structural relationships by the method of maximum likelihood, Chicago: International Educational Services.Google Scholar
Kashyap, R. L., & Rao, R. A. (1976). Dynamic stochastic models from empirical data, New York: Academic Press.Google Scholar
Molenaar, P. C. M. (1981). Dynamical factor models, Utrecht: State University of Utrecht.Google Scholar
Molenaar, P. C. M. (1982a, September). A dynamic factor model for short sample paths of a time series. Paper presented at the meeting of the European Mathematical Psychology, Bielefeld, West-Germany.Google Scholar
Molenaar, P. C. M. (1982b). On the validity of basic ERP waveforms obtained by principal component analysis and by confirmatory component analysis. Unpublished manuscript.Google Scholar
Molenaar, P. C. M. (1984, August). Dynamic factor analysis of a multivariate non-stationary time series. Paper presented at the meeting of the European Mathematical Psychology, Zeist, Holland.Google Scholar
Porges, S. W., Bohrer, R. E., Keren, G., Cheung, M. N., Franks, G. J., & Drasgow, F. (1981). The influence of methylphenidate on spontaneous autonomic activity and behavior in children diagnosed as hyperactive. Psychophysiology, 18, 4248.CrossRefGoogle ScholarPubMed
Priestley, M. B., Subba Rao, T., & Tong, H. (1973). Identification of the structure of multivariable stochastic systems. In Krishnaiah, P. R. (Eds.), Multivariate analysis III, New York: Academic Press.Google Scholar
Stone, R. (1947). On the interdependence of blocks of transactions. Journal of the Royal Statistical Society B, 9, 132.CrossRefGoogle Scholar
Subba Rao, T. (1975). An innovation approach to the reduction of the dimensions in a multivariate stochastic system. International Journal of Control, 21, 673680.CrossRefGoogle Scholar
Subba Rao, T., & Tong, H. (1974). Identification of the covariance structure of state space models. Bulletin of the Institute of Mathematics and its Applications, 10, 201203.Google Scholar
Tukey, J. W. (1978). Can we predict where “time series” should go next?. In Brillinger, D. R., & Tiao, G. C. (Eds.), Directions in time series, Ames: Iowa State University.Google Scholar