Advertisement

Issues in Aggregating Time Series: Illustration Through an AR(1) Model

  • Zhenqiu (Laura) LuEmail author
  • Zhiyong Zhang
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)

Abstract

Intra-individual variation is time dependent variation within a single participant’s time series. When data are collected from more than one subject, methods developed for single subject intra-individual relationship may not fully work and laws governing inter-individual relationship may not apply to intra-individual relationship. There are relative few methods in dealing with the analysis of pooling multiple time series. This article aims to investigate empirically the comparability of methods for pooling time series data and to address related issues through an AR(1) model. In this article, multiple time series are formulated, pooling estimation methods are derived and compared, simulation studies results are summarized, and related practical issues are addressed.

Keywords

Time series analysis First-order autoregressive model Pooling multiple subjects Longitudinal analysis Maximum likelihood estimation 

References

  1. Cattell, R. B. (1952). The three basic factor-analytic research designs—Their interrelations and derivatives. Psychological Bulletin, 49, 499–520.CrossRefGoogle Scholar
  2. Cattell, R. B., Cattell, A. K. S., & Rhymer, R. M. (1947). P-technique demonstrated in determining psychophysical source traits in a normal individual. Psychometrika, 12, 267–288.CrossRefGoogle Scholar
  3. Cattell, R. B., & Scheier, I. H. (1961). The meaning and measurement of neuroticism and anxiety. New York: Ronald.Google Scholar
  4. Daly, D. L., Bath, K. E., & Nesselroade, J. R. (1974). On the confounding of inter—And intraindividual variability in examining change patterns. Journal of Clinical Psychology, 30, 33–36.CrossRefGoogle Scholar
  5. Molenaar, P. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181–202.CrossRefzbMATHGoogle Scholar
  6. Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology—this time forever. Measurement: Interdisciplinary Research and Perspectives, 2, 201–218.Google Scholar
  7. Molenaar, P. C. M., Huizenga, H. M., & Nesselroade, J. R. (2003). The relationship between the structure of interindividual and intraindividual variability: A theoretical and empirical vindication of developmental systems theory. In U. M. Staudinger & U. Lindenberger (Eds.), Understanding human development: Dialogues with lifespan psychology (pp. 339–360). Norwell: Kluwer Academic Publishers.Google Scholar
  8. Nesselroade, J. R., & Molenaar, P. (2003). Quantitative models for developmental processes. In J. Valsiner & K. Connolly (Eds.), Handbook of developmental psychology (pp. 622–639). London: Sage.Google Scholar
  9. Nesselroade, J. R., & Molenaar, P. C. M. (1999). Pooling lagged covariance structures based on short, multivariate time-series for dynamic factor analysis. In R. H. Hoyle (Ed.), Statistical strategies for small sample research (pp. 224–250). Newbury Park, CA: Sage.Google Scholar
  10. Nesselroade, J. R., & Ram, N. (2004). Studying intraindividual variability: What we have learned that will help us understand lives in context. Research in Human Development, 1, 9–29.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of GeorgiaAthensUSA
  2. 2.University of Notre DameNotre DameUSA

Personalised recommendations