Conclusion

The possible existence of cycles or waves in financial time series data is a controversial subject that remains unresolved. The results of standard spectral methods have been unsuccessful, so far, in isolating reliable waveforms in this data. This has led many skeptics to argue that the pursuit of cycles in financial data is futile. On the other hand, cycle analysts argue that the reason cycles have not been definitively isolated is that they change their characteristics too frequently and that standard mathematics cannot adjust quickly enough. However, a simple observation of price data shows that prices oscillate. If prices oscillate in a regular manner, the preceding analysis should be sufficient to identify this regularity and to make it useful for the projection of price action in the future. The concepts of Hurst, Ehlers, Tillman, and others—mostly professional engineers—are intriguing, and even if the ideas are difficult to apply, they provide interesting insights into the workings of the financial markets.