Applied Econometric Time Series

We introduce a variant of the FFF into the trend function of US real GDP in order to allow for gradual effects of unknown numbers of structural breaks occurring at unknown dates. We find that the hypothesis of no breaks can be rejected, and the Fourier components are significant. Our new cycle matches the NBER chronology very well, especially for the Great Recession of 2009.

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We utilize two verydifferent methodologies to examine the underlying reasons for shifts in grain prices. A simple VAR indicates the important effects of mean shifts in real energy prices,exchange rates, and interest rates on grain prices. We go on to develop a parametric model of structural change that allows for smoothly shifting means.

Appendix    VAR Code   Data      Fourier Tests  MYLAGSELECT.SRC 

We identify structural changes in commodity prices using the Bai-Perron procedure, low frequency Fourier functions, and a procedure that specifies shifts to be smooth logistic functions of time. We find that the pattern in the timing of shifts is suggestive of the causal factors underlying the recent boom.

Appendix    Code    Data  MYBAIPERRON.SRC  MYLAGSELECT.SRC 

graphstyles_03_09_11_1.txt

The paper illustrates the use of a Fourier approximation to model nonlinear series when the form of the linearity is unknown. 

DATA   CODE

An early application allowing the intercept and the AR(1) term to vary over time. The paper investigates terrorist incidents using a linear model with pre-specified interventions that represent significant policy impacts. Next, a threshold autoregressive (TAR) model is applied to the data. TAR estimates indicate that increases above the mean are not sustainable during high-activity eras, but are sustainable during low-activity eras. By applying a Fourier approximation to the nonlinear estimates, we get improved results. 

DATA    CODE