The Application of the Spectral Envelope in the Business Cycle

Progress in the theory of multivariate time series analysis has taken place in two contexts: the time and frequency domains. Several methods have been proposed but, depending on the data, it is sometimes necessary to apply appropriate transformations to reduce the variance of the trends or the estimates. In the case of multivariate series, it has been shown that the use of a spectral envelope facilitates the generation of a good estimate by using principal components in frequency space. To illustrate the usefulness of the spectral envelope, we use the relationship we find between business cycles and frequency space which lies in the way in which economic fluctuations can be analysed and understood by decomposing the data into components of different frequencies. This approach, based on spectral analysis, makes it possible to identify variations in the time series of economic variables (such as employment, inflation, etc.) that follow cyclical or periodic patterns, typical characteristics of business cycles.