# Fibonacci numbers – the basics

The theory, named after the Italian mathematician Fibonacci, who lived in XII – XIII century, makes it possible to use the coefficients (Fibonacci numbers), who play an important role in the prognosis of the market movement. Fibonacci develops a digital row (Fibonacci row), which consists of sequence of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, etc.), amongst which there have been established permanent proportions, in particular a relation of all of these numbers to the next member of the row, which asymptotically strives for 0.618 and a relation of every member to the previous member, which asymptotically strives for 1.618 (Fibonacci coefficients or the Golden section). The Golden section is commonly seen in the structure of many natural objects and phenomena – from the structure of a sea-shell to the shape of the hurricane whirlwinds and the galaxy.
At the financial markets, the Fibonacci coefficients are used in different ways, but in particular they appear as an instrument for a prognosis of the price aim and measuring of the closing level of the losing position (“stop-loss”). Usually, during the determination of this level, it is estimated 61.8% from the previous price alteration, which enables the investor to move the “stop-loss” a bit lower than this level. Thanks to this, if the correction level exceeds the expected one, the investor will avoid the redundant wastes. On the other side, if the correction reaches approximately the aim level, the result will increase the probability the investor’s chosen direction of the price movement to be right.

## Elliott Waves – Bases of the Wave Theory

Elliott Wave Theory is a system of empirically derived rules for an interpretation of the market movements. According to Elliott, they follow alternations of five waves in the direction of the basic trend and of three waves in the opposite direction. At rising trend these alternations of five waves with three waves form a complete cycle of eight waves at the Bull market. The whole sequence of the first five waves is called impulsive, and the second one of three waves – corrective. In the frames of the Bull movement, every wave from the waves 1, 3, 5 is an impulsive wave that consists of five waves of lower ratio, while the waves 2 and 4 are corrective as they both fall apart into three smaller waves. The under waves of the impulsive sequence are numerated with ciphers, whereas the corrective under waves – with letters.
It is clear that after the second five-waved impulse, there comes second three-waved correction, after which a five-waved impulse starts again. This sequence of the movement creates a five-waved impulsive figure, developing the basic trend, after which a three-waved correction is supposed to follow.
The waves of every ratio can subdivide into waves of lower ratio or they can unite into a wave of higher ratio.
For the interpolation of the Elliott Waves there are several rules.

• The development of the second wave is never equal to 100% of the upsurge of the first wave, for example at Bull’s market the second wave is never going to reach a lower level than the beginning of the first.
• The third wave in the impulsive sequence never appears shortest, very often she is the longest.
• The fourth wave never ends in the price interval of the first wave and the market movement stays the same irrespective of its size or movement duration.

Besides that, the combination of small-scale movements creates similar large-scale movement. Respectively, the large-scale movements consist of small-scale components, geometrically similar to them. These movements come together in compound market movements of five or three waves with repetitive sequence, where the analysts can be used (along with the upper indicated rules) for identification of the running graphic figures. As the market hesitations have the inclination to correspond to the basic trend rather than to be against it, the corrective waves are often hardly recognizable until the completion of their formation. Therefore, the suspension of the development of the corrective waves becomes harder predictable than the suspension of the development of the impulsive and traders are due to show significantly greater cautiousness at the stagnative, corrective market, rather than at clear impulsive trend. Moreover, at that time when the impulsive waves exist in three basic forms, the varieties of the corrective graphic figures are significantly more, so they can unite, forming long correction with great complexity. Regarding the correction, it is important to remember that the impulsive waves can be only five. In this sense, the initial five-waved movement against the basic trend could never be a complete correction; it could be only its part.

## Impulsive waves and their variations

### Extensions

In every given five-waved sequence exists a tendency one of the three impulsive under waves (i.e. wave 1, wave 2, wave 3) to become extension of the continuing movement, like a rule with inner subdivision. Sometimes these subdivisions have, for example, the same amplitude and duration, like the waves of high ratio of a basic impulsive sequence, leading the total number of the waves with the same size in the basic sequence to nine, instead of the normal five. At nine-waved sequence, it is sometimes difficult to define which of the waves has become an extension. This, actually, is not that significant, as the number of the waves – five and nine, are equally important for the technical analysis. Examples for the extension in different wave configurations make it clear, that the general significance of the figure stays in all cases the same. Extensions can also be formed in the other extensions. Although the extension of all the five waves is not that unusual, extension of the extension takes places most of the times on the third wave.
The extensions can be used as an useful guidance for everything that refers to the lengths of the waves to be. The majority of the impulsive sequences contains extensions only in one of the three impulsive under waves. That way, if the first and the third wave have the same size, the fifth wave will be extended, especially if the trade volume on the time of the fifth wave is bigger than that one during the third wave.

### Diagonal Triangles

There are some figures, known from the Technical Analysis Theory, in particular two types of triangles, which are about to take into consideration in the Elliott Theory.
The diagonal triangles from the first type are common only at the waves C and according to Elliott they are a proof of the fact that the previous movement has passed too quickly and has gone too far. All types of the wave figures, including wave 1, 3, 5 consists of three-waved movements and their fourth waves in the interval of the first waves’ prices. The rising diagonal triangle from the first type appears as “Bear” as usually, after it comes a sharp decrease, eventually to the level of the beginning of the figure development. Opposite to it, the falling diagonal triangle from the first type appears as “Bull”, as after it follows a rise in the price.
The diagonal triangles from the second type are significantly more seldom seen than the triangles from the first type. This figure, which can be rarely found on the first wave or on the wave A, reminds of a triangle from the first type on account of a similarity with the line of resistance and support and partly mutually recovers with the first and fourth wave. Meanwhile, it considerably distinguish from the triangles from the first type, as its five-waved impulsive waves usually appear like five-waved impulsive waves in contrast to the three-waved under waves from the first type.

### Failure (Crossed fifth waves)

Elliott calls failure the impulsive figure, whose highest point of the fifth wave does not exceed the highest point of the third wave. It is visible that the crossed fifth wave contains the necessary impulsive (i.e. five-waved) structure for a completion of the movement of high ratio. All in all, its failure in the attempt to outrun the previous extremum of the impulsive wave is a sign of weakness of the running trend and probable setting of a sharp development.
Indicators
The indicator is a sequence of values which are obtained after applying the mathematical formula to the data about the course (the price of a given financial instrument). The data can include all kinds of combinations from the listing of opening, the listing of closing, the lowest point, the highest point for a definite historical period.
The indicator suggests different possibilities for analyzing the pricing conduct. In order to estimating some of the indicators, for example the moving average ones are used simple formulas and the technology is relatively easy to understand. Others, such as “Stochastics” use complicated formulas and require better preparation, so that they are correctly understood. Regardless to the ratio of complexity of their estimation, the indicators offer unique perspective for measuring the power of the market and the direction of the markets’ listings.
The indicators have three basic functions: they warn, confirm and predict.

• The indicator can be used as a warning for the more detailed exploration of the pricing conduct. If the inertia moment reduces, this could be a signal for a break into a definite level of support. Or if there is a big positive divergence, it can give indication for an eventual break at the support level.
• The indicators can be used as an additional confirmation of the signals, generated from the usage of other instruments for technical analysis.
• Some investors and traders use the indicators for a prediction of the future course movements.

### Advices for using the indicators

The indicators indicate, show. That may sound direct, but sometimes the traders ignore the course movements and concentrate only on the indicator. The indicators filter the pricing conduct using formulas. That’s why there are derivatives, not direct reflection of the courses (prices).
That should be taken into consideration when analyzing and every analysis with the help of an indicator should be accompanied with the clear thought of the course levels. Even when generating obvious signals, they should be contextualizing along with other instruments of the technical analysis.
The indicator can give signal of a purchase, if the graphic image shows a descending triangle with sequent lower peaks; the signal can turn out wrong.
There are two basic types of indicators – leading and falling behind.
The leading indicators give preliminary indications for the courses movements. Most of the leading indicators take the shape of transitory oscillators. The concept “momentum” measures the tempo with which the course changes during the given period of time. The indicator expresses the level of change as a coefficient.
With the increasing of the course, its momentum also increases.
The faster the course increases, the greater the course momentum becomes.

The usage of leading indicators has many advantages. The main one is the generation of early signals for positioning of the market. They generate more signals and make it possible to trade more often. The early signals can warn for future movements and are most appropriate when there are course hesitations without definite trend. When the market is at a rising trend, the most optimal usage is to identify underestimated levels for purchase. And vice versa, at a falling trend, the leading indicators can be used for identification of overestimated levels for sale.
The basic disadvantages are that the early and more frequent signals involve a mistake of a higher level, which makes the possibility of a potential loss greater.

### Falling behind indicators

The falling behind indicators follow the course movements and it is generally accepted for them to be classified as trend indicators, i.e. following the trend. The trend indicators work best when there exists a market trend.
One of the main advantages of the falling behind indicators is the possibility to catch a movement and the open position to be kept until the direction of the movement stays the same. The longer the trend exists, the less signals are generated and the less trade is done.
The disadvantages are that these indicators are not meant for the cases when the course movements are limited in definite range and also they give short signals, which leads to missing of a significant part of the movement.

### MA (Moving Average)

The MA is known as one of the most common and easy to use indicators.
It shows the averaging value of a given currency course for a definite period of time. When calculating a MA, a mathematical analysis of the average value is done for a preliminary terminational time period. The hesitations of the currency courses for a definite period of time lead to increasing or decreasing the average course value.
Three main types of MAs are used: simple (also called arithmetic), exponential and weighted.
MA can be estimated over every series of data, including the course of opening, closing, highest, lowest course, trading volumes or any other indicators. It is often the case when double moving averages are used.
The only thing where moving averages of different types diverge from each other is when weight coefficients, which are assigned to the latest data, are different. In case we are talking of simple moving average, all prices of the time period in question are equal in value. Exponential and Weighted moving averages attach more value to the latest prices.
The most common way to interpreting the price moving average is to compare its dynamics to the price action. When the instrument price rises above its moving average, a buy signal appears, if the price falls below its moving average, what we have is a sell signal.

### Time periods, used for construction of a moving average

The moving averages, built for shorter periods are more sensitive and they identify the new trends earlier, but they also give some wrong signals.
The longer moving averages are more reliable, but at the same time they catch the big trends. The critical element of the MA is the choice of a number of periods for the construction. The number of periods should be conformable to the marker cycle, which we are analyzing. For a period of a MA it is best to use the half length of the cycle, which we are analyzing.
If the length of the cycle to from peak to peak is approximately 30 days, it is advisable to use a MA for a fifteen-day period. If it is 20 days, we use a ten-day MA. Some traders use 14 and 9 days for a period of a MA, as they think that they are going to generate signals shortly before the other market participants.

• 200 days (40weeks) – this period is used when analyzing the longer cycles;
• 20 to 65 days (4 to 13 weeks) – appropriate for interstitial cycles;
• 5 to 20 days – for the short cycles

As time passes by, the length of the cycles varies and that’s why we always check if we are using the appropriate MA.

Perfect number of periods = duration of the cycle in periods/2 + 1