Essays on Identifiability and Estimation in Multivariate Time Series Analysis

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This thesis is concerned with identifiability analysis and estimation of multivariate linear dynamic models. A particular emphasis is given firstly to models with strictly fewer inputs than outputs, secondly to the case of mixed frequency data, and lastly to linear multivariate rational expectations model. Chapter 2 deals with spectral factorization, i.e. obtaining a transfer function from the spectral density, of singular rational spectral densities. Chapter 3 deals with the identifiability problem for singular AR models, shows that the identifiability problem in this case is very similar to the one for usual multivariate ARMA models, and introduces a new canonical form. Chapter 4 deals with identifiability from mixed frequency data in the sense that we want to obtain the underlying high frequency AR model from (mixed frequency) population second moments which can be observed in principle. The case of singular and as well as the case of non-singular innovation covariance matrix is treated. The main result is that “typically” identifiability can be ensured using second moments. Chapter 5 is concerned with stochastic singularity in multivariate linear rational expectations models. It provides important preliminary work for treating identifiability analysis and estimation of structural singular ARMA models. The main result is the derivation of the number of free parameters in the reduced form of a rational expectations model in the stochastically singular case. It holds under very general restrictions on the parameter space such that state-of-the-art macroeconomic models can be analyzed. Chapter 6 extends the analysis of indeterminate equilibria of rational expectations models in (Lubik and Schorfheide, Journal of Economic Dynamics and Control, 2003). It is shown that there are certain parameter constellations that lead to models which
are deemed to have an indeterminate solution according to the analysis given by Lubik and Schorfheide even though the solution is actually unique.
StatusPublicerad - maj 2015
Externt publiceradJa
MoE-publikationstypG5 Doktorsavhandling (artikel)


  • 511 Nationalekonomi
  • 112 Statistik
  • 111 Matematik

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