Spectral analysis of business and consumer survey data

Abstract

The main objective of this study is two-fold. First, we aim to detect the underlying existing periodicities in business and consumer survey data. With this objective, we conduct a spectral analysis of all survey indicators. Second, we aim to provide researchers with a filter especially designed for business and consumer survey data that circumvents the a priori assumptions of other filtering methods. To this end, we design a low-pass filter that allows extracting the components with periodicities similar to those that can be found in the dynamics of economic activity. The European Commission (EC) conducts monthly business and consumer tendency surveys in which respondents are asked whether they expect a set of variables to rise, fall or remain unchanged. We apply the Welch method for the detection of periodic components in each of the response options of all monthly survey indicators. This approach allows us to extract the harmonic components that correspond to the cyclic and seasonal patterns of the series. Unlike other methods for spectral density estimation, the Welch algorithm provides smoother estimates of the periodicities. We find remarkable differences between the periodicities detected in the industry survey and the consumer survey. While business survey indicators show a common cyclical component of low frequency that corresponds to about four years, for most consumer survey indicators we do not detect any relevant cyclic components, and the obtained lower frequency periodicities show a very irregular pattern across questions and reply options. Most methods for seasonal adjustment are based on a priori assumptions about the structure of the components and do not depend on the features of the specific series. In order to overcome this limitation, we design a low-pass filter for survey indicators. We opt for a Butterworth filter and apply a zero-phase filtering process to preserve the time alignment of the time series. This procedure allows us to reject the frequency components of the survey indicators that do not have a counterpart in the dynamics of economic activity. We use the filtered series to compute diffusion indexes known as balances, and compare them to the seasonally-adjusted balances published by the EC. Although both series are highly correlated, filtered balances tend to be smoother for the consumer survey indicators.