There has been a lot of discussion recently about whether the cycles are “running short” relative to Hurst’s nominal model. The answer to that question depends on one’s definition of nominal model.
A little discussed fact is that Hurst created two nominal models, a nominal time domain model (54 months,18 months, etc.) and a nominal spectral domain model which he stated was of “considerably more character” than the time model. The difference between the two is best illustrated with an example.
The first two charts below are monthly charts of the DOW from 1900 to present. The price wave at the bottom of the chart is the 4 year wave extracted using Hurst’s bandpass filter design derived from his spectral model.
The chart below plots the period of each oscillation (solid black line) over the past 100+ years. As you can see the period of the wave is constantly changing. The yellow dotted line is a smooth five oscillation running moving average of the wave period. The dashed red line is 54 months and the solid red line is the historical average of about 44 months. During the time period of Hurst’s analysis, the average period of the price wave was approximately 53 months, hence the 54 month nominal period. However the chart shows that from 1900 to 1945 and from 1975 to today the average period is shorter.
In order to calculate the average period of the 4 year wave to create a top-down nominal model one must decide how many oscillations to average and what time span is to be used, hence the title “Dynamic Nominal Model.” Fortunately the modulations are very, very slow which probably only require adjusting every 15 years or so.
Therefore if one defines his or her nominal model based on the average period of the 4 year wave from 50 years ago, then the cycles are running short. If one defines his or her nominal model based on the average of the most recent five or six oscillations of the 4 year wave, then the cycles are running normal.