Wavelets and economics

Abstract

The use of wavelet analysis is very common in a large variety of disciplines, such as signal and image processing, quantum mechanics, geophysics, medicine, biology, etc. In economics, however, wavelets are still a mysterious, but colorful, tool for time-series analysis. The pioneering work of Ramsey and Lampart [26] is unknown to the majority of economists. Among the exceptions to this rule, one can point to [4], [14], and [12]. See [6], for a recent survey of wavelet applications to economic data. Probably, wavelets are not more popular among economists, because wavelet multivariate analysis is still incipient. Recently, however, Gallegati [11] — using the maximum overlap discrete wavelet transform — and Crowley and Mayes [5] and Aguiar-Conraria and Soares [1] — using the continuous wavelet transform — showed how the cross-wavelet analysis could be fruitfully used to uncover time-frequency interactions between two economic timeseries. Still, most surely, wavelets will not become very fashionable in economics until a concept analogous to the spectral partial-coherence is developed. On this regard, the proficient reader may be interested in our most recent working-paper [2]. We present a brief and self-contained introduction to the wavelet tools used, namely the continuous wavelet transform, the wavelet coherency and the wavelet phasedifference. Then we apply these tools to a real world economic problem — the study of the synchronization of the Portuguese and Spanish economic cycles, in the last 5 decades. Decades that include the democratic transition in both countries (mid-1970s), the European Union membership of both countries (1986), and the adoption of a single currency, the Euro (1999).