Earlier we introduced the history of the birth of wave theory and the three cores respectively. On the surface, wave theory seems to be quite simple and easy to use. In fact, because each complete process of rising/falling contains an eight-wave cycle, there are small cycles in the big cycle, and smaller cycles in the small cycle, that is, there are small waves in the big waves, and fine waves in the small waves. Therefore, counting waves becomes quite complicated and difficult to grasp. In addition, its impulsive waves and corrective waves often have extended waves and other changing and complex patterns (every wave is not equal, it can be compressed, extended, simple, or complex. In short, everything depends on the pattern. Accurate; Among them, compression refers to failure waves, and extension refers to extension waves and variation waves), making it more difficult to define the exact division of waves.
In order to better divide the hierarchical relationship of each wave, there are three corresponding principles in the wave theory. Which three principles? They are the golden section principle, the correction wave depth principle and the alternation principle , among which the former is very important and we will describe it in detail.
The Magical Fibonacci Sequence
We have explained earlier that the wave theory consists of three core components- wave shape, amplitude ratio, and duration . Moreover, when introducing the two cores, it is pointed out that the application of the Fibonacci sequence in these two fields is inseparable. Here, an important term is introduced: the Fibonacci sequence. Usually, everyone calls it the "magic Fibonacci sequence". How amazing is it? This has to be learned from the Leaning Tower in Italy.
Most people who have been to Pisa, Italy, have seen the famous Leaning Tower. For its architect, Bonanna, the tower, though tilted a bit, was a good monument. Do Bonanna, the Leaning Tower of Pisa, and the stock market and Elliott theory stand up? This seems to be a bit of a misnomer.
However, many people don't know that not far from the tower, there is a small statue. He is the famous mathematician in the 13th century-Leonardo Fibonacci. So what does Fibonacci have to do with the Elliott Wave Theory, which studies stock market behavior? The answer is inextricably linked!
Eliot explained in his "Laws of Nature" that the mathematical basis of the wave theory is a series of numbers discovered (more precisely, rediscovered) by Fibonacci in the 13th century. The sequence was later named after its discoverer and is generally known as the Fibonacci sequence (or Fibonacci numbers).
During Fibonacci's lifetime three major works were published, the most famous of which is "Liber Abaci" (known as "The Book of Calculations"). This book introduced Arabic numerals to Europe, gradually replacing the ancient Roman numerals. His works also contributed to the later development of mathematics, physics, astronomy, and engineering. In The Book of Counting, the Fibonacci sequence appears for the first time, written as a solution to the mathematical problem of rabbit breeding. This set of numbers is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc., and so on, to infinity.
Figure 1: Fibonacci's Rabbit Breeding Sequence
This sequence has many interesting properties, not least the fact that there is a continuity relationship between its numbers:
1. The sum of any two adjacent numbers is equal to the number after the two. For example, the sum of 3 and 5 is 8, the sum of 5 and 8 is 13, and so on.
2. Except for the first four numbers, the ratio of any number to the next adjacent number tends to be 0.618. For example: 1/1=1.00, 1/2=0.50, 2/3=0.67, 3/5=0.60, 5/8=0.625, 8/12=0.615, 13/1=0.619, and so on. Note that the above ratio fluctuates around 0.618, and the further you go, the smaller the fluctuation. In addition, please also pay attention to the values of 1.00, 0.50, and 0.67, which we will often use in proportional analysis and percentage retracement.
3. The ratio of any number to the previous adjacent number is approximately equal to 1.618, or the reciprocal of 0.618. For example, 13/18=0.72, 21113=1.615, such as 21=1.619. The larger the number, the closer the corresponding two ratios are to 0.618 and 1.618 respectively.
4. The ratio of two numbers next to each other tends to be 2.618, or its reciprocal, 0.382. For example, 13/34=0.382, 34/13=2.615.
There are many other interesting relationships, the above-mentioned ones being the most famous and the most important. As we said earlier, Fibonacci just rediscovered this sequence. This is because the mathematicians of ancient Greece and Egypt have long been familiar with the two ratios of 1.618 and 0.618. They are the famous golden ratio, or the golden ratio.
famous golden ratio
What is the golden ratio? Divide a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. Its ratio is an irrational number whose approximate value to the first three digits is 0.618. Because the shape designed according to this ratio is very beautiful, it is called the golden section, also known as the ratio of China and foreign countries. The point that divides the line segment is called the golden section point.
Figure 2: Golden ratio diagram
The golden section was discovered by the ancient Greek philosopher Pythagoras. After repeated comparisons, he finally determined that the ratio of 1:0.618 was the most perfect. Later, the German esthetician Zessing called this ratio the golden ratio.
What is the relationship between the Fibonacci sequence and the golden section? It is found through research that the ratio of two adjacent Fibonacci numbers gradually tends to the golden ratio as the serial number increases. That is, f(n-1)/f(n)-→0.618…. Since Fibonacci numbers are all integers, the quotient of dividing two integers is a rational number, so it is only gradually approaching the irrational number of the golden ratio. But when we continue to calculate the larger Fibonacci numbers later, we will find that the ratio of two adjacent numbers is indeed very close to the golden ratio.
The golden ratio is found throughout society, in music, art, architecture, and biology. The Greeks used the golden ratio to build the Parthenon, and the Egyptians built the Great Pyramid with the golden ratio. Pythagoras, Plato, and Leonardo da Vinci all knew its properties. There are too many examples to enumerate, so it can be seen that the Fibonacci ratio (that is, the golden ratio) is indeed everywhere in nature, and it is also permeated with human activities in essence.
equiangular spiral
When it comes to the golden section ratio, we have to talk about the equiangular spiral that is intricately related to it.
An equiangular spiral refers to a spiral in which the distance of the arms increases geometrically. Let L be any straight line passing through the origin, then the angle A of the intersection of L and the equiangular spiral is always equal. It was discovered by Descartes in 1638, and Jacob. Bernoulli later revisited it. He discovered many properties of equiangular spirals, such as equiangular spirals are still equiangular spirals after various appropriate transformations.
It is generally believed that the logarithmic spiral is a kind of "growth shape" throughout the entire space window, and it is just constructed on the basis of the golden ratio. Furthermore, from the most subtle structure of nature to the most macroscopic cosmic phenomenon, the shape of the logarithmic spiral is always consistent.
Here are two typical examples. The outline of a snail shell and the appearance of the Milky Way both have the same logarithmic spiral shape (as is the case with the human ear). This last point is more on topic. Because the stock market not only belongs to the category of large-scale human group activities, but also a manifestation of the "growth phenomenon" of nature (all human activities are characterized by this without exception), it is generally believed that the stock market Markets necessarily obey the same law of logarithmic spirals.
Well, if I continue to talk about it, I will digress! Let us return to the wave theory again. Some people may ask, since the Fibonacci sequence is so magical, besides being a data basis in the wave theory, it should be more useful, right?
Yes! In addition to being the data basis of the wave theory, the Fibonacci sequence also plays an important role in the wave theory, that is, to measure the price target and the length of time.
How to use the Fibonacci sequence in the Wave Principle?
wave-to-wave relationship
We know that the wave theory consists of three aspects- wave shape, amplitude ratio, and duration . If the shape of the wave determines the choice of the general trend, then the volatility ratio and duration provide us with reliable buying and selling points and time. As for the calculation of points and time, it is inseparable from the application of the Fibonacci sequence!
Figure 3: The complete wave structure organized by the Fibonacci sequence
First, let's look at Figure 3, which shows a complete wave pattern; in fact, the basic wave structure shown in this picture is organized according to the Fibonacci sequence. A complete cycle consists of 8 waves, 5 of which are up and 3 down - all of which are Fibonacci numbers. Subdividing it into the following two levels, we get 34 waves and 144 waves respectively-they are also Fibonacci numbers. However, the application of the Fibonacci sequence in the wave theory is not limited to counting waves. There is also a proportional relationship between the waves. Some of the most commonly used Fibonacci ratios are listed below:
1. Only one of the three main waves is extended, and the other two are equal in duration and magnitude. If wave 5 is extended, then wave 1 and wave 3 are roughly equal. If wave 3 is extended, then wave 1 and wave 5 converge.
2. Multiply the first wave by 1.618, and then add it to the bottom point of the second wave, you can get the minimum target of the third wave.
3. Multiply wave 1 by 3.236 (=2*1.618), and then add it to the apex and bottom of wave 1 respectively, which are roughly the maximum and minimum targets of wave 5.
4. If waves 1 and 3 are approximately equal, we expect wave 5 to be extended. The method of estimating the price target is to first measure the distance from the bottom of wave 1 to the top of wave 3, multiply by 1.618, and finally add the result to the bottom of wave 4.
5. In a correction, if it is the usual 5-3-5 zigzag, then the c wave is often equal in length to the a wave.
6. Another way to estimate the length of wave c is to multiply the length of wave a by 0.618 and then subtract the resulting product from the bottom of wave a.
7. In the case of 3-3-5 flat adjustment, wave b may reach or even exceed the apex of wave a, so the length of wave c is approximately equal to 1.618 times the length of wave a.
8. In a symmetrical triangle, each subsequent wave is approximately 0.618 times the previous wave.
In addition to the ratios listed above, there are actually many more, but the above are the most commonly used. These ratios help determine price targets for major and corrective waves.
Through the above ratios, can we quickly have a clearer grasp of the point and time of the future market?
For example, in a certain market, if the rise of wave 1 is 100 points and the bottom of wave 2 is around 50 points, then, based on the multiplication of wave 1 by 1.618 and the bottom point of wave 2, the target price of wave 3 is 212 Doesn't the point jump off the paper? In terms of the time period, the same logic can be used to calculate.
Percentage retracement in wave theory
After talking about the ratio, let's talk about the percentage retracement of Fibonacci. Because with the percentage retracement, we can also estimate the price target. In retracement analysis, the most commonly used percentages are 61.8% (usually approximately 62%), 38% and 50%, and these three are often used golden ratio values; among them, in a strong trend, The minimum drawdown is usually around 38%. In fragile trends, the maximum return percentage is usually 62%.
We said earlier that in the Fibonacci sequence, except for the first four numbers, the Fibonacci ratio tends to be 0.618. The first three odds are 1/1 (100%), 1/2 (50%), and 2/3 (67%). Many people don't know that when they are learning Elliott's theory, the 50% retracement they are familiar with is actually a Fibonacci ratio. The same goes for a two-thirds retracement (a one-third retracement as an interval Fibonacci ratio, also part of Elliott's theory). A full retracement (100%) of a previous bull or bear market also marks an important support or resistance zone.
Figure 4: Fibonacci's Golden Section
Well, after talking about the price calculation of volatility ratio, it's time to talk about Fibonacci's time target. Although we haven't talked much about the duration of the wave theory, there is no doubt that the Fibonacci time relationship exists, but it is more difficult to predict this relationship, and some wave theory analysts feel that it is in the three core which is the least important.
Fibonacci time targets are calculated from the positions of significant tops and bottoms counting into the future. On the daily chart, analysts start from important turning points and count backwards to the 13th, 21st, 34th, 55th, or 89th trading day, expecting that the future top or bottom will appear at these "Fiji" Bonacci Day". We can apply this technique on weekly charts, monthly charts, and even annual charts. For example, if it is on a weekly chart, then the analyst can follow the Fibonacci sequence to look for time targets week by week.
It is important to point out that there are too many to count about the significance of the time factor in market forecasting. What we are trying to say here is that Fibonacci numbers are everywhere, and even in cycle analysis, we encounter them unexpectedly. for example. The 54-year Compo cycle is a well-known long-term economic cycle that has a strong influence on most commodity markets, and 54 is a clear approximation to the Fibonacci number 55. Finally, by the way, this wonderful set of numbers is also useful in other fields of analysis. For example, in moving average analysis, we often use Fibonacci numbers. This is not surprising, since most successful moving averages have roots in prevailing cycles in various markets.
summary
We know that the wave theory consists of three aspects: wave shape, ratio and time; therefore, in terms of forecasting, the ideal situation is that the three aspects of wave shape, ratio analysis, and time target coincide. For example, wave analysis shows that wave 5 has been completed; and wave 5 has covered 1.618 times the distance from the bottom point of wave 1 to the top of wave 3; at the same time, it has been exactly 13 weeks since the starting point of this trend (the previous trough) , exactly 34 weeks from the previous peak to now. Further, if the fifth wave has lasted for 21 weeks. Then, we are pretty sure that an important top in the market is about to occur.
Figure 5: Wave structure diagram with waves within waves
Studies of stock and futures market charts have shown that there are many kinds of Fibonacci timing relationships. However, the problem is that we have too many choices. For example, we can measure Fibonacci's time targets in various ways such as top-to-top, top-to-bottom, bottom-to-bottom, and bottom-to-top. Unfortunately, we can only confirm these relationships after the fact. Many times it is not clear which relationship is right for the situation at hand. This is where the short board of the wave theory lies. After all, no theory is perfect.
Here, what we need to understand is that Fibonacci numbers play an extremely important role in the quantitative analysis of wave theory; among them, 0.382 and 0.618 are two commonly used ratios of golden magic numbers, and their frequency of use is higher than that of other ratios. Much higher. When using the magic number ratio above, if investors cooperate with the wave pattern and the assistance of dynamic system indicators, they can better predict the signal of the peak and bottom of the stock price. That's it.
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