by Arthur Merrill
The market certainly moves in waves. Is there regularity in these cyclical waves that can give us useful
clues to the future?
Any curve can be approximated by adding together a number of sine waves, each with a different period
and amplitude (Figure 1). The component curves can be calculated by Fourier analysis.
In one study made by Gertrude Shirk of the Foundation for the Study of Cycles, the most important
underlying cycles ranked by amplitude at the crest were:
All of these cycles, with the exception of the 46-year cycle, were found to have statistical significance. I
have found that cycles based on the calendar can be useful. In the week, Monday tends to be a declining
day and Friday a rising day. In the monthly cycle, the first three days of the month have a significantly
A calendar cycle that is currently interesting is the four-year presidential cycle. I've checked back through
24 presidential terms, all of the way back to 1886. There was considerable variation, but the average is
shown in Figure 2. In this chart, the four-year term is divided into 16 three-month periods. The percent
change in each period was calculated and averaged. The changes were then corrected for trend.
Note the election year. Prices tended downward, on the average, in the first six months but zoomed up in
the second half. After the election, prices averaged downward for a year and a half, reaching the trough in
the middle of the second year after the election.