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Working Paper

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

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.

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