Coherence Coefficient for Official Statistics

Abstract

One of the quality requirements in official statistics is coherence of statistical information across domains, in time, in national accounts, and internally. However, no measure of its strength is used. The concept of coherence is also met in signal processing, wave physics, and time series. In the current article, the definition of the coherence coefficient for a weakly stationary time series is recalled and discussed. The coherence coefficient is a correlation coefficient between two indicators in time indexed by the same frequency components of their Fourier transforms and shows a degree of synchronicity between the time series for each frequency. The usage of this coefficient is illustrated through the coherence and Granger causality analysis of a collection of numerical economic and social statistical indicators. The coherence coefficient matrix-based non-metric multidimensional scaling for visualization of the time series in the frequency domain is a newly suggested method. The aim of this article is to propose the use of this coherence coefficient and its applications in official statistics.

Keywords

• weakly stationary time series
• Fourier transform
• periodogram
• Granger causality
• multidimensional scaling