University of Illinois Urbana-Champaign

Exact Maximum Likelihood Estimation of the Kalman Filter Model

Bos, Theodore

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Description

Title
Exact Maximum Likelihood Estimation of the Kalman Filter Model
Author(s)
Bos, Theodore
Issue Date
1982
Department of Study
Economics
Discipline
Economics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Abstract
  • The interpretation of the Kalman filter model (KFM) used in this thesis is one where the transition equation allows the coefficients of a regression equation to follow an autoregressive-moving average process. Thus the KFM is a generalization of the random coefficients model.
  • The purpose of this thesis is to present the existing literature on the exact maximum likelihood estimation of the KFM and to extend this literature by making the calculation of the estimates of the parameters of the KFM more efficient. This is done by deriving closed-form solutions for some of these parameters and explaining why the derivation of closed-form solutions for the other parameters is impossible, and by proving that the information matrix for all these parameters is block diagonal. This is carried out for the most general KFM.
  • Also, an alternate derivation of the likelihood of a KFM is developed. This alternate derivation leads to the estimates of the first two moments of the varying coefficients, given all the data.
  • To provide information on the usefulness of the applicability of the KFM, it is employed in the estimation of the market model for each asset of a large sample of stocks on the New York Stock Exchange. It is discovered here that Watson's test for a simple KFM has some undesirable properties. These properties are then identified while carrying out a Monte Carlo study on Watson's test.
  • The estimation of KFMs is also employed in the testing of the dual hypothesis of whether the market for short-term Treasury Bills is efficient and whether the equilibrium real interest rate is invariant over time.
Graduation Semester
1982
Type of Resource
text
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