Fibonacci in the Stock Market: Fibonacci Analysis Can Enhance Your Elliott Wave Performance. Here's an Example of How to Apply Fibonacci Ratios to Forecasting. (Trading: Techniques)
Prechter, Robert R., Jr., Modern Trader
A completed Elliott wave usually displays Fibonacci price and time relationships among its components. I have long maintained that Wave V in the stock market, which began at the lows of 1974 or 1982, would end when it reached a Fibonacci relationship to the preceding wave structure dating from the Depression lows of 1932.
The Dow Jones Industrial Average (DJIA), enjoying the greatest stock mania of all time, surged past several of these relationships along the way. At its final high, though, it reached one of the projected targets and satisfied two standard Fibonacci relationships simultaneously.
TWO RELIABLE RELATIONSHIPS
That the advance from 1974/1982 is a fifth wave is important because there are several guidelines of wave development that indicate what the extent of a fifth wave is likely to be.
In his 1946 book, Nature's Law (republished in R.N. Elliott's Masterworks), R.N. Elliott observed that there are two ways that fifth waves are typically related to preceding price action. With subsequent research, I was able to add some nuances to his formulas. To summarize these observations, we can say that in most cases, wave 5 should have a Fibonacci relationship to wave 1, or the net travel of waves 1 through 3, or both.
"An ideal wave" (below) shows an idealized wave in which wave (5) satisfies both guidelines in being related by Fibonacci to wave (1) and to waves (1)(3). As we will see, the DJIA met this idealization at the January 2000 top.
MEASURING FROM 1982
In the five-wave advance dating from 1932, waves IIII took place from 1932 to 1966. The rise in terms of daily closing price extremes created a multiple of just more than 24 times. Wave V from 1982 to 2000 created a multiple of a bit more than 15 times. Note that this relationship is eight to five. In other words, wave V produced 5/8 of the multiple of waves I-Ill (see "Wave V from 1982," above, right).
This relationship is exact. If we take the multiple of waves I through III out to four (or more) decimal places at 24.1424, and multiply it by 5/8, or 0.625, and project an upside target from its starting point at 776.92, we get 11722.95. The DJIA's all-time closing high on Jan. 14, 2000, was 11722.98.
We can further appreciate how close these numbers are by understanding that the smallest possible incremental DJIA change that a single stock within the average could produce at the time was 0. …