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Working Paper

Maximum Likelihood in the Frequency Domain: A Time to Build Example

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A well known result is that the Gaussian log-likelihood can be expressed as the sum overdifferent frequency components. This implies that the likelihood ratio statistic has a similarlinear decomposition. We exploit these observations to devise diagnostic methods that areuseful for interpreting maximum likelihood parameter estimates and likelihood ratio tests.We apply the methods to the estimation and testing of two real business cycle models. Thestandard real business cycle model is rejected in favor of an alternative in which capitalinvestment requires a planning period.
03.01.1999ISSN 2573-7953 WP 99-01DOI 10.26509/frbc-wp-199901
JEL Classification Codes E2, E22, E1, C52, C32, C12

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Christiano, Lawrence, and Robert Vigfusson. 1999. “Maximum Likelihood in the Frequency Domain: A Time to Build Example.” Federal Reserve Bank of Cleveland, Working Paper No. 99-01. https://doi.org/10.26509/frbc-wp-199901