Department of Economics and Finance

University of Alabama

Tuscaloosa, AL 35487

wenders

**Grain Prices, Oil Prices, and Multiple Smooth Breaks in a VAR.** (with Paul Jones). *Studies in Nonlinear Dynamics and Econometrics*. 20(4). 2015.

(https://www.degruyter.com/view/journals/snde/20/4/article-p399.xml)

Ignored structural breaks in a VAR result in a misspecified model such that Grangercausality tests are improperly sized. Instead of modeling structural breaks as being sharp, changes in the relationship between the maize and petroleummarkets are likely to have occurred gradually. We show the Flexible Fourier Form has good size and power properties in testing for smooth structural change in a VAR. When applied to a VAR including maize and oil prices, we uncover important linkages between the two markets.

**A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks** (with Junsoo Lee). *Oxford Bulletin of Economics and Statistics* 74 (4), 2012. pp. 574-599.

We develop a unit-root test based on a simple variant of Gallant’s (1981) flexible Fourier form. The test relies on the fact that a series with several smooth structural breaks can often be approximated using the low frequency components of a Fourier expansion. Hence, it is possible to test for a unit root without having to model the precise form of the break. Our unit root test employing Fourier approximation has good size and power for the types of breaks often used in economic analysis. The appropriate use of the test is illustrated using several interest rate spreads.

Code to generate Table 1 Critical Values

**On the Use of the Flexible Fourier Form in Unit Roots Tests, Endogenous Breaks, and Parameter Instability**. (With Paul Jones) in Ma and Wohar "Recent Advances in Estimating Nonlinear Time Series." Springer. (2014)

The paper summarizes a number of papers that use a variant of Gallant’s (1981) Flexible Fourier Form to control for the unknown number and form of the breaks. The paper details and illustrates several unit root tests, stationarity tests, and tests for parameter instability that are based on a Fourier approximation.

**The Flexible Fourier Form and the Dickey-Fuller Type Unit Root Tests** (with Junsoo Lee). *Economic Letters*. (2012). 117 (1), 196-199

The paper develops a Dickey-Fuller type unit-root test with a Fourier function in the deterministic term. The test can complement the Fourier LM test and has good size and power properties.

**A Stationarity test in the Presence of an Unknown Number of Smooth Breaks. **(with Ralf Becker and Junsoo Lee) *Journal of Time Series Analysis* (2006). 27 (3), 381-409

The paper develops a test with the null of stationarity that allows for the possibility of anunknown number of structural breaks, or other nonlinearities, in the data-generating process.The test is based on the fact that the behavior of a breaking process can often be captured using a single frequency component of a Fourier approximation.

A General Test for Time Dependence in Parameters (with R. Becker and S. Hurn). *Journal of Applied Econometrics*.19: (2004). 899–906.

A new test for time-dependent parameters is proposed. The Trig-test is based on a trigonometric expansion to approximate the unknown functional form of the variation in the parameters concerned.

Copyright 2014 Applied Econometric Time Series. All rights reserved.

Department of Economics and Finance

University of Alabama

Tuscaloosa, AL 35487

wenders