Real and Complex Wavelets in Asset Classification. Some Methodological Remarks with Example

Abstract

In the paper we suggest a wavelet methodology of asset classification into defensive and cyclical groups. We demonstrate that such tools of bivariate wavelet analysis like wavelet gain, coherency, phase-locking value, and amplitude correlation together with term structures of risk defined via univariate wavelet spectra serve better the purpose of asset and industry classification than the traditional approach based on beta coefficients, correlations, and variance comparison. Not only are the wavelet quantities better suited to nonparametrically examine time-varying dependencies in the frequency bands of interest, i.e., the frequencies associated with business cycles, but they also correct the information provided by the coefficients computed according to the classical approach for possible phase shifts, time-variable amplitudes, and changing phase differences. Because of this they offer both a more reliable risk assessment and a more detailed dependence measurement that can potentially be of use in building investment strategies.The approach is illustrated with an analysis of industry portfolios on the US stock market, showing that the wavelet methodology can lead to a partial reclassification of market sectors and documenting dependence between the US business cycle and cycles in the US asset price series, taking the form of both phase locking and amplitude comovement. Furthermore, our wavelet-based tests of the random walk hypothesis, which explore local features of spectra, point to somewhat more frequent violations of this hypothesis in daily and monthly US industry indexes than the ordinary variance ratio tests.