Stylized Facts: Method

Abstract

In Chapter 1 I have argued that a thorough determination of stylized facts is the first step in a project to explain economic fluctuations. This chapter will provide a set of tools to establish stylized facts that are interesting in their own right and relevant for the assessment of business cycle theories. When dealing with economic fluctuations, it is natural to analyze time series in the frequency domain by means of spectral analysis. Given that this method seems an ideal tool for studying cyclical phenomena, one might wonder why it has not been used more in economics. In my opinion, the answer lies in two problems that spectral analysis faces when confronted with economic data. First, it can be applied only to stationary time series. Because most economic variables contain a trend component, this must be effectively removed. The failure to do this leads to the “typical spectral shape” of Granger (1966), where most of the mass of the spectrum is in the low frequency range. However, it was recognized in the recent literature that trend removal might distort the cyclical characteristics of a time series. This has already been discussed in Section 2.3. The second problem is that many economic series are so short that classical (nonparametric) methods of spectral analysis cannot be successfully used. Maximum-entropy spectral analysis, developed by Burg (1967, 1975) and flrst applied in economics by Sebold-Bender (1990), yields a solution. This new method is briefly described in Section 3.2, and, for the multivariate case, in Section 3.3. Section 3.1 surveys some basic ideas of spectral analysis, which are essential for understanding the empirical results of the next chapter.