In general it must be noted that these indicators show very clearly the prevailing trend. The weak side of these indicators is the fact that they delay a little, and work bad during flats. In the framework of this class we will review "Moving average" (MA) indicator and "Moving average convergence/divergence" (MACD).

"Moving average" - is one of the simplest indicators. From the mathematic point of view it is average price of analyzed financial instrument for the last n-time intervals. The difference of "Moving average" from the simple average resides in the fact that while forming a new price bar, the first bar is taken into account unlike the last one. Thus the average "moves" to the right with the formation of new prices. Let us see the illustration.

*Picture 13. MA construction*

The last (current) MA value in x-point, denoted by red sphere is a simple arithmetical average (sum of the value divided into its quantity) of n of last prices of the given financial instrument. B-area, noted by yellow colour - is a period of averaging, i.e. that bars quantity that takes for the MA value calculation. The larger averaging period the less "flexible" will MA be, and later it will react on the new trend. However it will filter better small and insignificant changes in price. The smaller MA period, the more sensible it will be, but it will lead to the situation when it will react on the price changes that do not compose a trend.

The arrow on the illustration shows the direction of the movement of this period (i.e. with the appearance of a new price the interval will move one bar right). On the illustration we can see, that in the beginning of the given period there is area that is equal to n (denoted as A), for which the value of moving average with n averaging period is impossible to define, because of lack of information.

As we can see on the illustration MA shows very good the general direction of the development of the trend, well smoothing small price fluctuations, which are not significant for the trading. We must note that MA indicator itself might be considered as the simplest numerical filter (NF). The delay is connected with the nature of MA. The size of delay is the half of averaging period.

In the conclusion of description of this indicator, it is noted, that there are lots of variants of calculation of moving averages. Firstly, not only n closing prices (close) may be the original source of data for MA calculation. Instead of it "Typical price" (Typical price = (High + Low + Close) or " Median price" (Median price = (High + Low) or other price features might be used. Also in the role of enter (enter features) another MA indicator may be used (in general, it may be any other indicator). In this case the phrase "double price smoothing" is used. On the analogy the price might be smoothen three, four and etc times, it has to be remembered that the smoothing like this increases the delay.

Secondly, there are different types of MA (simple, exponential, measured, smoothen etc). Apart from this there is the whole underclass of dynamic moving averaging that aims to adjust to the market. If the flat formation happens (where classic MA works badly), the averaging period of dynamic MA increases to decrease the quantity of false signals. As soon as the indicator fixes the beginning of the movement, MA period decreases sharply to reflect more flexibly a new trend.

Moving average convergence/divergence. This indicator is based on two exponential moving average convergence and is calculated as the difference between them. One of them is called "fast" and the other - "slow" (respectively to their periods). It is clear, that "fast" moving average convergence may be both higher and lower than "slow" one. And this leads to the situation when the size of difference between them can appear both in the area of positive numbers and negative ones. In the chart this data is denoted (as a rule) in the form of histogram, but they also may be depicted with a simple curve. Also the indicator has "signal" line that looks like simple Moving average convergence of histogram value.

*Picture 14. MACD construction*

MACD has a number of features.

Firstly, crossing:

- to buy in time of crossing of histogram signal line bottom-up;
- to sell in time of crossing of histogram signal line top-down.

Secondly, it is overbought/oversold, that may be judged by the analytics depending on the distance of histogram from zero value.

Thirdly, it is divergence. Bullish divergence appears when histogram MACD forms new maximums and the price cannot form them. Bearish divergence is the situation when histogram form new minimums, and the price cannot do the same. Divergences overbought and oversold areas are considered to be the strongest and the most significant signals.

*Picture 15. MACD bullish divergence*

As we can see on the illustration, at a-point the price has formed a local maximum that is correspond to MACD maximum at a-point. MACD indicator at b-point has formed a new maximum, that is larger than previous one. At the same time, at b-point the price cannot reach a-level.

It has to be noted that MACD is plotted in separate area of a chart (in contrast to MA that is depicted directly at the price chart).