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Using Fibonacci Numbers & Relationships -
Topic Progress:

The Fibonacci Sequence and the ratios derived from it are used in a variety of ways in technical analysis. We’ll outline a few of these just below:

Elliott Wave Analysis

You’ll find Fibonacci numbers and ratios everywhere in Elliott Wave Theory. For example, corrective wave patterns are made up of “sets” of three waves. Impulsive patterns are constituted of five waves. These, of course, sum to eight – all three being numbers in the Fibonacci Sequence.

Further, Fibonacci Ratios are used by analysts to project how far a given wave is likely to carry, and although Elliott himself did not write anything relating to timing, additional work since his death has postulated that important highs and lows may well be “spaced” in accordance with Fibonacci numbers.


Fibonacci numbers and ratios are often used in Cycle Theory. Again, an in-depth study of Cycle Theory requires highly specialized software, so we won’t go into any detail here, other than to make a brief mention of it.

Moving Averages

Often, analysts reference numbers in the Fibonacci Sequence to determine the number of periods over which a moving average is calculated. Fibonacci numbers are also used in selecting a relationship between the lines in a double (or triple) moving average system. This usage, however, is beyond the scope of this introductory course.

Retracements and Expansions

Dow Theory reveals that prevailing trends are interrupted by counter trends which retrace a portion of the previous trend. The extend of such a retracement is usually found to be a Fibonacci Ratio of the extent of the previous move (i.e., 23.6%, 38.2%, 50%, or 61.8%).

In a similar vein, once the prevailing trend has completed, the next major trend move is in the opposite direction, and generally expands in a Fibonacci relationship in the direction opposite to the previous major trend (i.e., 23.6%, 38.2%, 50%, 61.8%, 100%, 123.6%, 150%, 161.8%, and so on).

Time Zones

This is similar to Cycle Theory in that the approximate time intervals between important highs and lows is thought to be spaced using Fibonacci numbers. As with Cycle Theory, this is beyond the scope of our introductory course.


Fibonacci arcs are drawn from the end point of a trend, with the radius at Fibonacci ratios of the range of the trend. Historic data indicates that highs and lows generally fall on the arcs. Note that the positioning of the arcs is dependent on the scaling used in the charts. This too, lies beyond the scope of our introductory course.


Fibonacci fans are drawn from the starting point of a trend, below its trend line, dividing the range of the trend in Fibonacci ratios. Historic data indicates that generally, important highs and lows fall on the fan lines.

Note that some technical analysts combine Fibonacci arcs and fans, with the expectation that significant support or resistance will appear at the junctions of the fans and arcs. Also note that some forecasting software displays Fibonacci retracements, expansions, time zones, arcs, and fans on their price charts. Again, this falls outside the scope of our introductory course, but we wanted to be sure to give it a mention so you’re aware of it, as a means of guiding additional study.