Real and complex wavelets in asset classification: An application to the US stock market

- Our wavelet-based tests provide evidence of mean reversion in industry indexes.
- Financial and real business cycles show both amplitude comovement and phase locking.
- No one cycle in industry portfolios is totally disconnected from the business cycle.
- We point to the need to reclassify industry portfolios as defensive and cyclical.

In the paper we suggest the use of wavelets to classify equities and industries into defensive and cyclical categories. We demonstrate that real- and complex-valued wavelets better serve the purpose of equity classification than more traditional approaches, and that this takes place through a more reliable and detailed dependence measurement and risk assessment. In particular, we introduce a family of wavelet-based tests of the random walk hypothesis exploring local features of spectra, which enable examining mean reversion and cyclicality of prices. The suggested approach is illustrated with an analysis of daily and monthly US industry indexes.