An Application of the Estimation of a Varma Model with a Latent Variable as a State Space Model

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


This study is an extension of previous studies, Hagnell (1991) and Hagnell(1996), where the data used are annual time series for the whole of Sweden during the period 1751-1850 for the crude birth rate, the death rate for ages 20-50 years, the crude marriage rate and an index of the real wages. The aim of the study of Hagnell (1991) was to investigate the relationships between ferility, adult mortality, nuptiality, and real wages, using VARMA and VAR models. In Hagnell(1996) we use instead of the observed variable real wages, a latent variable called real income. There are three observed stationary variables available which measure the real income. These are a real wages index ( used by Hagnell (1991) ), a harvest assessment, and the first difference of the logged rye price. Thus real income can be interpreted as a latent variable with three indicators, the real wages index, the harvest assessment, and the first difference of the logged rye price. The idea of real income as a latent variable was used previously in a study of the dependence of adult mortality on real income, Hagnell (1992). We start out from the VARMA(1,1) model, identified in Hagnell (1991), and then estimate the same model with the observed variable real wages replaced by the latent variable real income. In Hagnell(1996), in order to estmate such a model we construct LISREL models, Jöreskog and Sörbom (1989), following the approach of Molenaar (1985). The first simple LISREL model ignores that our data are time series which are auto- and crosscorrelatated while the more complex models consider autocorrelation of the first order. A more theoretical justification of this approach is given in Variyam(1994) and in Hershberger et al (1996). Here, we use for the same model as above instead a state model approach, Durbin and Koopman (2001). Comparisons are made with the earlier approach with Lisrel models.


  • Mats Hagnell
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics


  • tate Space model, Varma model, Lisrel model
Original languageEnglish
Title of host publicationProceedings of the Conference Compstat 2002, Short Communications and Posters
EditorsS. Klinke, P. Ahrend, L. Richter
PublisherPhysica Verlag
ISBN (Print)3-00-009819-4
Publication statusPublished - 2002
Publication categoryResearch
EventCompstat 2002, Symposium in Computational Statistics - Berlin, Germany
Duration: 2002 Aug 242002 Aug 28


ConferenceCompstat 2002, Symposium in Computational Statistics