Ralf Becker

A Stationarity Test in the Presence of an Unknown Number of Smooth Breaks

Macroeconomic variables have been shown to display a wide variety of structural breaks of unknown number, duration and form. This poses a challenge since improperly modelled breaks can result in a seriously misspecified model. In this paper, we develop a new test for stationarity that approximates the unknown form of structural breaks using a selected frequency component from a Fourier approximation. Our proposed test performs quite well when breaks are gradual, and shows reasonable power. The appropriate use of the test is illustrated by examining real exchange rates in the post-Bretton Woods period. Copyright 2006 The Authors Journal compilation 2006 Blackwell Publishing Ltd.

Modeling Inflation and Money Demand Using a Fourier-Series Approximation

Abstract The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The method uses a Fourier approximation to capture any variation in the intercept term. As such, the issue becomes one of deciding which frequencies to include in the approximation. The test has good power to detect multiple structural breaks. Perhaps the most important point is that successive applications of the test can be used to ‘back-out’ the form of the time-varying intercept. A number of diagnostic tests indicate that a linear autoregressive model of the U.S. inflation rate (as measured by the CPI) is inappropriate. It is shown that our methodology is capable of ‘backing-out’ the form of the nonlinearity. We also explored the nature of the approximation using an extended example concerning the demand for M3. Using quarterly U.S. data over the 1959:1–2004:2 period, we confirmed the standard result that the demand for money is not a stable linear function of real income, the price level and a short-term interest rate. The incorporation of the time-varying intercept resulting from the Fourier approximation appears to result in a stable money demand function. The form of the intercept term suggests a fairly steady growth rate in the demand for M3 until late-1987. At that point, there was a sharp and sustained drop in demand. Money demand continued to decline until mid-1995 and then resumed its upward trend. The implied error-correction model appears to be reasonable in that money and the price level (but neither income nor the interest rate) adjust to eliminate any discrepancy in money demand.

Using discrete-time techniques to test continuous-time models for nonlinearity in drift

This paper examines whether or not a discrete-time econometric test for nonlinearity in mean may be used in cases where the data are believed to be generated in continuous time. It is demonstrated that appropriate bootstrapping techniques are required to yield a test statistic with sensible statistical properties. The technique is demonstrated by using it to examine 7-day Eurodollar rates for nonlinearity in mean.