The Phase Method: 1998 by Christopher L. Cagan, Ph.D.
Here's a unique technique to understand the cycles prevalent in the markets.
The broad movement of the stock market, as measured by the Dow Jones Industrial Average (DJIA), tends to rise and fall on a roughly cyclic basis super-imposed on a long-term trend of growth. Here is a new method of analyzing these motions, called the phase method.
First, take the monthly Dow index and divide by a deflator (for our purposes here, the average of the Consumer Price Index [CPI] and Producer Price Index [PPI], with 1982-84 = 1.00 as the base period) to compute the real DJIA in constant dollars and remove the effect of paper inflation. Take the natural logarithm as the result, to be called LNRLDOW. This series works on a logarithmic or percentage basis, so a motion from 1,000 to 2,000 has the same magnitude as a motion from 2,000 to 4,000 (Figure 1).