Abstract
Recently, a number of new techniques to analyze complex, non-linear and non-stationary economic and financial data have been introduced. One of the techniques that may substitute conventional approaches based on a Fourier transform (FT) is wavelet transform (WT). On the other hand, despite the fact that wavelets have a huge potential enabling accurate representation of relationships between economic variables in the time-scale space, their use in economics is still rather limited with apparent reasons. In this paper, we will examine the use of the wavelets for the analysis of complex economic events and introduce the so-called truncated wavelets and an additional metric that may be valuable for processing of real economic and financial data. The presented approach may also contribute to the enhancement of our understanding of economic phenomena. The results are illustrated on a real example.
Highlights
Economists have usually been attempted to explain and forecast variations of financial and economic data using macroeconomic fundamentals
As it was mentioned in the paper, the use of wavelet transform in economics and finance is much smaller compared to other fields of science and technology
One of the reasons for this is a common practice to use conventional methods based on a Fourier or Gabor transform, though it is evident that they cannot be applied to real data due to their highly non-stationary characteristics
Summary
Economists have usually been attempted to explain and forecast variations of financial and economic data using macroeconomic fundamentals. One can see that according to the Heisenberg principle, we need a continuous representation of the signal in the frequency domain to achieve a high resolution in the time domain Since, this is not the case in real situation, a Gabor transform assumes an empirically chosen window (not small and not large) and reduces to the Fourier transforms of a signal in time stripes in which the signal’s mean (expected value) does not change much within the chosen window. This is not the case in real situation, a Gabor transform assumes an empirically chosen window (not small and not large) and reduces to the Fourier transforms of a signal in time stripes in which the signal’s mean (expected value) does not change much within the chosen window This corresponds to the situation when we fix. In the case of wavelet transform WT, the time resolution is adjusted to the frequency with the window width narrowing when focusing on high frequencies
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