Fibonacci Sequence Wave Principle & Wave Ratio
In addition to the Golden Ratio, the Fibonacci Sequence (or Summation Series, as Elliott called it) became an integral part of the Wave Principle, and is used in both wave ratio analysis, and in analyzing relationships between waves with respect to price and time. The Sequence is derived from the following observations Fibonacci made: The sum of any two adjacent numbers forms the next higher number in the sequence;
Example: 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, |
and on into infinity. In this sequence, he also observed the following relationship between the sequence numbers: The ratio of any number to the next higher number is approximately .618 to 1, and to the next lower number 1.618 to 1. Between alternate numbers in the sequence, the ratio is approximately .382, whose inverse is 2.618. These might be considered "primary" Fibonacci ratios. There are secondary and even tertiary ratios that are useful in trading, which I discuss below in more depth. Before we continue, though, I should say a few words about sentiment, which, in effect, is what produces wave patterns, and is the engine behind what we might call the "Fibonacci Effect."
Sentiment
Elliott contended there was an order in the market, and that it reflected natural cycles in human nature. Some academicians and others dispute that there is any "order" to the market, much less something so seemingly esoteric as "natural human cycles." However, an experienced application of Elliott Wave directly challenges their view. The advent of Fractal Analysis as popularized by Benoit B. Mandelbrot also has a Fibonacci basis and corroborates Elliott's principle, as does the work of Gann and Sklarew.
People, like the changes of the seasons, go through their cycles. We know this based on bio-rhythm research conducted over thirty years ago, which showed human beings do, in fact, go through emotional peaks and troughs, sexual peaks and troughs, physical peaks and troughs, and intellectual peaks and troughs that recur cyclically as the human organism renews itself. This apparently happens individually and en masse. When applied to the market, the effects of "news" are more likely to be determined by the sentiment then prevailing, than the particular event itself. Indeed, the record shows that trends in progress continue to their completion despite periodic reversals, and regardless of news events (whether good or bad) that occur in between. This is perhaps less obvious when viewed day-to-day, but very obvious when viewed in historical context. We've frequently seen cases where stocks have sold-off despite a report of good earnings, as well as the opposite case, where stocks experienced ridiculously high valuations when the fundamentals didn't justify them. These contradictory actions show the emotionally charged nature of the market, and how important, therefore, an understanding of sentiment is to trading. Wave analysis, combined with Fibonacci analysis, provide a mathematical roadmap to marking these sentiment swings.