Frequency domain analysis and filtering of business and consumer survey expectations

The main objective of this study is two-fold. First, we aim to detect the underlying existing periodicities in business and consumer survey expectations through spectral analysis. We use the Welch method to extract the harmonic components that correspond to the cyclic and seasonal patterns in all response options of monthly survey indicators. We find that business survey indicators show a common cyclical component of low frequency that corresponds to about four years, while 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. Second, we aim to provide researchers with a filter specially designed for business and consumer survey expectations that circumvents other filtering methods’ assumptions. Most seasonal adjustment methods are based on a priori assumptions about the structure of the components and do not depend on the features of the specific series. To overcome this limitation, 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. We opt for a Butterworth filter and apply a zero-phase filtering process to preserve the time series’ time alignment. We find that the balances computed with the filtered series are highly correlated with the seasonally-adjusted balances published by the European Commission, albeit the former tend to be smoother for the consumer survey indicators.