An Application of the Estimation of a Varma Model with a Latent Variable as a State Space Model
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Abstract
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 17511850 for the crude birth rate, the death rate for ages 2050 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.
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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Title of host publication  Proceedings of the Conference Compstat 2002, Short Communications and Posters 
Editors  S. Klinke, P. Ahrend, L. Richter 
Publisher  Physica Verlag 
ISBN (Print)  3000098194 
Publication status  Published  2002 
Publication category  Research 
Peerreviewed  No 
Event  Compstat 2002, Symposium in Computational Statistics  Berlin, Germany Duration: 2002 Aug 24 → 2002 Aug 28 
Conference
Conference  Compstat 2002, Symposium in Computational Statistics 

Country  Germany 
City  Berlin 
Period  2002/08/24 → 2002/08/28 