Forex trading for beginners Part 10: MATHEMATICAL ANALYSIS, Indicators

MATHEMATICAL ANALYSIS

Mathematical analysis, as a branch of technical analysis, began to be widely used with the advent of the computer. The ability to analyze a large number of charts for various markets, the quick calculation of multiple indicators, and the possibility of modifying them for different market situations determined the popularity of mathematical analysis among analysts of various financial markets.

Computer technical analysis is more objective than traditional chart analysis. If one can argue about the presence of the “head and shoulders” pattern on the chart, then one cannot say about the direction of the indicator. If it goes up, then definitely up; and if it goes down, then definitely down.

Indicators allow a deeper assessment of the balance of power between bulls and bears in the market, but they also have a drawback: they often contradict each other. Some are better at picking up trends; others are better at horizontal playing ranges. Some are great at signaling reversals, while others are better at tracing the direction of trends. The task of the analyst is to select appropriate indicators for the analysis of various market situations. Before working with an indicator, you need to have a clear idea of ​​what exactly it measures and how to apply it. Only then can you rely on his signals.

Types of indicators

Professionals divide indicators into two groups: trend-following indicators and oscillators. Trend indicators are great tools for analyzing a market that is moving up or down, but when it is stagnant, their signals are unreliable and often false. Signalers are great at picking up changes in inactive markets, but once a trend is established, they give premature and even false signs. The secret of successful trading lies in the ability to choose the indicators of different groups in such a way that their flaws cancel each other out and their advantages are preserved.

Trend indicators: Moving Averages, Bollinger Bands, Moving Average Divergence (MACD), Moving Average Divergence Histogram (OsMA), and others. The indicators of this group give synchronous or delayed signals, i.e., simultaneously or after a trend reversal.

Signalers (oscillators) help identify turning points. These include the stochastic index (Stochastic Oscillator), relative strength index (RSI), trading channel index (Commodity Channel Index), inertia (momentum), and others. Indicators of this group give leading or synchronous signals and often appear before price changes.

With any trend, prices increase, maintain or lose speed. A decrease in the speed of an uptrend or downtrend is an early warning signal that the trend may be changing. Therefore, if, for example, the upward trend loses speed, then this is a warning about a possible trend reversal.

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Trend indicators

Moving averages. (Moving Averages – MA)

Technical indicator Moving Average (MA) shows the average value of the instrument price for a certain period of time. When calculating the Moving Average, a mathematical averaging of the price of the instrument for a given period is performed. As the price changes, its average value either grows or falls.

The signal is calculated by the mutual arrangement of two moving averages, one of which should have a shorter period (fast MA) and the other, respectively, a larger (slow MA). Their parameters can be specified in variables.

A BUY signal is issued when the fast MA is higher than the slow one, and the

SELL signal when the slower one is faster than the fast one.

The “no signal” state is not used.

Moving averages (MA), being a simple tool for smoothing price series, make any trends more visible. There are three main types of MA: simple (simple), weighted (weighted) and exponential (exponential).

A simple moving average (MA) is defined as the average closing price of the last N candles, where N is called the period (order) of the average. It is calculated as the arithmetic mean using the formula:

MA \u003d (sums of closing prices for the period) / N

The level of MA depends on two factors: the final prices and the order of the average. If it is required to calculate a three-day simple MA, and on the first, second, and third in a row, the closing prices were 19, 21, and 20 points, then a simple three-day MA is 20 points ((19+21+20)/3=20). Suppose that on the fourth day, the final price was 22. Then the three-day MA will increase to 21, i.e. (21+20+22)=21. From the example, we can see that the set of averaged values ​​is continuously moving in time, with His name moving average.

The advantage of a simple MA is its simplicity. The disadvantage is the equivalence of all candles. Because the result of averaging is postponed near the last candle, it would be more correct to assume that the latest quotes are more important than for the previous period. In addition to everything, with the elimination of the old price from the calculations, the simple MA will change to events that have already passed and have, in fact, a decreasing value.

To eliminate this drawback, weighted moving averages (Weighted Moving Average-WMA) are used. Each candle from the period under consideration is assigned its weight, increasing from left to right.

WMA=(sum of products of prices and weights) / (sum of weights)

Giving more weight to later candles on the period under consideration improves information content and reduces WMA lag. However, there remains, albeit to a lesser extent, the disadvantage of resetting the last price and its influence on the final averaging position.

This disadvantage is finally eliminated by the exponential moving average (Exponentially moving average, EMA) because. It includes all the prices of the previous period, not just the segment specified when setting the moving average period. Resetting the latest data, in this case, does not occur; they disappear from the calculations gradually and imperceptibly. Calculated according to the formula:

EMA=EMA (t-1)+(К*(Price(t)-EMA(t-1))

where EMA (t-1) – ESS value for the previous time

Price(t) – current price value

K=2/(N+1)

N – period of average

To analyze the market using moving averages, the correct choice of the averaging period is important. A relatively short MA is more sensitive to price fluctuations and reveals new trends faster. But it changes direction more often, and its zigzags give more false signals. A relatively long MA writes out zigzags less frequently but also reacts to the turning points of the stock exchange more slowly. The trader’s task is to choose the order of MA such that it meets the requirements of the current trading strategy.

Usually, the MA order is chosen from the Fibonacci series: 8,13,21,34,55,89,144. Moreover, the shorter the time interval of the analyzed chart, the longer the MA period is determined. Also, in different markets and different time intervals, different types of MA are the most suitable. For long periods, simple MAs are the most effective; for short intraday intervals of up to 1 hour, it is better to use exponential MAs.

If it is possible to reveal the cyclicity of the market, then it is reasonable to link it with the MA order in such a way that the length of the MA order would be equal to half of the dominant cycle. The disadvantage of this method is the fragility and variability of the detected cycles.

General rules for moving average analysis:

1. Follow the direction of movement of the MA. The direction of transactions must be consistent with the direction of the MA. In an uptrend, the MA line serves as a good support line from which to buy. In a downtrend, the MA line will be a good resistance line for selling from the MA line. An almost horizontal MA with small zigzags indicates a sluggish market without a target and benchmarks, where it is not worth catching trends.
2. Find the points of greatest discrepancy between the price chart and the average. A significant price correction or trend reversal usually follows large divergences.
3. 3. Find the points of intersection of the price chart and the MA. Crossing can be a signal for a reversal of the dominant trend.

Recommended orders of average

Price chart	Orders of average
5 days	8, 13, 21
1 day	8, 13, 21, 55, 89
3 hour	8, 34, 55, 89, 144
1 hour	5,13, ​​34, 55, 89, 144
less than 15 min.	34, 55, 144

Bollinger band. (Bollinger Band – BB)

Bollinger bands (Bollinger Bands, BB) are similar to Envelopes . The difference between them is that the boundaries of the Trading Lanes (Envelopes) are located above and below the moving average curve at a fixed distance expressed in percent, while the Bollinger Bands boundaries are constructed at distances equal to a certain number of standard deviations. Since the magnitude of the standard deviation depends on volatility, the bands themselves adjust their width: it increases when the market is unstable, and decreases in more stable periods.

There are three types of signals:

BUY – the closing price of the previous candle below the lower line,

SELL – the closing price of the last candle above the upper line,

“no signal” – the price of closing the candle between the lines.

The Bollinger band is built as a band around the average. Still, the width of the band is proportional to the standard deviation from the moving average for the analyzed period.

BB in the FOREX market can be considered as an independent indicator and used only to confirm the readings of other indicators. Its meaning is to determine unusually sharp deviations in the exchange rate from the current trend. The construction algorithm is such that more than 95% of prices should be within this band.

In a well-chosen BB, the moving average is a good support level in a bullish trend and a good resistance level in a bearish trend. Channel boundaries can be indicators of market volatility (variability) and serve as minimum price benchmarks when opening positions.

Bollinger Bands are usually plotted on a price chart but can also be plotted on an indicator chart. The following applies to bands plotted on price charts. As in the case of moving average envelopes, the interpretation of Bollinger bands is based on the fact that prices tend to stay within the upper and lower boundaries of the band.

The features of VV are:

-A sharp price change usually occurs after a narrowing of the band, corresponding to a decrease in volatility.

-If prices break out of the band, we should expect the continuation of the current trend.

-If peaks and troughs inside the band follow peaks and troughs outside the band, a trend reversal is possible.

-Price movement, which starts from one of the borders of the band, usually reaches the opposite border. The latter observation is useful for predicting price targets.

BB convergence is observed when the market calms down and does not show significant fluctuations. There is a consolidation to the continuation of the current or the emergence of a new trend. The divergence of BB is observed when the current trend strengthens, or a new one begins. Divergence with increased volumes is a good confirmation of the trend.

Moving average divergences. (Moving Average Convergence/Divergence – MACD)

Technical Indicator Moving Average Convergence / Divergence (MACD) is the next dynamic trend indicator. It shows the relationship between the two moving average prices.

The Technical Indicator MACD is constructed as the difference between two exponential moving averages (EMA)

MACD is most effective in conditions where the market fluctuates with a large amplitude in the trading corridor. The most commonly used MACD signals are intersections, overbought / oversold conditions and discrepancies.

Operates with four variables. Signals are also simple:

BUY – the main line above the signal line,

SELL – the main line below the signal line.

“No signal” is not used.

Moving averages filter daily price spikes to identify trends. Well-known New York stock trader Gerald Appel has developed a more advanced indicator: moving average convergence-divergence (MACD). It consists of not one but three ESSs and is graphically represented by two lines, the intersections of which give game signals.

Initially, the MACD indicator consisted of two lines: solid (MACD line) and dotted (called the signal line) (signal line). The MACD line is the difference between two exponential moving averages, i.e., from the EMA with a shorter period, the EMA with a longer period is subtracted. It reacts faster to price fluctuations. The signal line is the moving average of the MACD line, which reacts more slowly to price fluctuations.

Buy or sell signals are given when the fast MACD line crosses the slow signal line; in other words, the crossovers indicate a change in stock sentiment. If the fast line rises above the slow one, it means that the bulls are setting the tone in the market, and it is better to trade on the rise. If the fast line falls below the slow one, it means that the bears have seized the exchange power, and it is worth playing for a fall. To carry out trading operations in the direction of such intersections means to go with the flow of the exchange. This system will produce fewer zigzags than mechanically following a single moving average.

It should also be taken into account that the location of the lines above zero characterizes the market as bullish below zero – as bearish. The greater the values ​​accepted by the MACD line in relation to the zero level, the stronger the corresponding stock sentiment.

The most significant signals in the forecast plan are the so-called bullish divergence (divergence) or bearish convergence (convergence). Suppose we connect the two nearest extremums of the fast MACD line. In that case, two options are possible: either the direction of the straight line on the MACD coincides with the direction of the straight line connecting similar extremums on the price chart, or there are opposite directions of the corresponding lines. In the latter case, they speak of a bullish divergence (straight price up, straight MACD down) or bearish convergence (straight price down, straight MACD up)—a moment of the trend to reversal.

The meaning of divergence/convergence signals is quite transparent and is as follows. If the next MACD high on a bullish trend is lower than the previous one, this means that the result of the difference between the EMA of a smaller order and the EMA of a higher order began to decrease, i.e., The EMA of a smaller order came closer to the EMA of a higher order. Hence, the activity of the bulls decreased during this period. The explanation for this decrease in bullish activity may be different in different situations. Still, in general, it can be argued that everyone who wanted to buy on a bullish trend bought, and the entry of new traders into the market caused bulls to decrease. The price continued to move in accordance with the bullish trend only because the activity of the bears in this market was still lower than the activity of the bulls. Still, the gap began to narrow, and perhaps in the near future, the current trend will change direction.

bullish divergence	bear convergence
a signal of either a reversal of the bullish trend, or its temporary attenuation	a signal of either a reversal of the bearish trend, or its temporary attenuation

The standard parameters of the MACD indicator for the hourly chart are:

• – Fast EMA: 12 – EMA of a shorter period
• – Slow EMA: 26 – longer period EMA
• – MACD SMA: 9 – Signal, smoothing moving average

Many traders try to optimize the MACD by changing its parameters using other moving averages. The variants of 5, 34, and 7 are quite popular. Changing the parameters in order to obtain the desired (but not necessarily correct) signal is not a good practice. It can lead either to an increase in false signals or to a large delay in the applied signals. The parameters of the indicator are selected in accordance with the chosen trading strategy. Therefore, frequent optimization of the indicator will rather give you a signal that you do not have a trading strategy.

Histogram of moving average divergence. (Moving Average of Oscillator – OsMA)

The Technical Indicator Moving Average of Oscillator (OsMA) is the difference between the oscillator and the smoothing of the oscillator. In this case, as the oscillator, the main MACD line is used, and as the smoothing, the signal line is used.

The signals are slightly different:

BUY – the histogram value is above zero,

SELL – the value of the histogram is below zero.

The “no signal” state will only be in those rare cases when the OsMA value is zero.

OsMA is plotted as the difference between the MACD line and the MACD signal line, which is graphically represented by a series of vertical dashes, i.e., histogram.

OsMA allows you to assess the balance of power between bulls and bears deeper than the standard MACD. It shows which group is dominant and whether that group is getting stronger or weaker. This is one of the best indicators in stock traders’ arsenal.

OsMA reflects the difference between long-term and short-term agreements of exchange participants about the value of the market.

OSMA Features:

– The OsMA slope direction shows which stock group is dominating. An ascending OsMA is a sign of the rising strength of the bulls, while a falling OsMA is a sign of the growing strength of the bears.

-If OsMA moves in the same direction as prices, the trend is resilient. If OsMA is tilted in the opposite direction, then the stability of the trend is doubtful. It is better to speculate in the direction of the slope of the OsMA histogram, as it shows who now sets the tone – bulls or bears.

-The magnitude of the crests and bottoms shows the relative strength of the trends at that time.

The signal to buy is the moment when the histogram, having fallen below zero, begins to rise. A protective stop is placed below the recent price bottom. And vice versa, a signal to sell will be the moment when the OsMA histogram, having risen above zero, starts to fall. Protective stop above the recent high. In this case, it is always necessary to take into account the strength of the dominant group in terms of the size of the previous ridges and bottoms.

Both OsMA and all indicators give the most reliable signals when they diverge from prices. Bottom divergences form when prices fall to a new bottom, and the indicator does not follow suit. This means that the bears are losing strength, prices are falling only out of inertia, and the bulls are ready to seize power. Bottom divergences often herald the end of downtrends.

Ridge divergences are observed in uptrends: they reveal the market’s readiness for a downward reversal. These divergences form when prices rise to new highs, and the indicator does not follow suit. This means that the bulls run out of steam, prices rise only out of inertia, and the bears are ready to seize power.

If the price remains in place and the MACD retreats to the middle, then the trend that was in effect before this will continue with a very high probability.

Average directional movement index. (Average Directional Movement Index – ADX)

The Technical Indicator Average Directional Movement Index (ADX) helps to determine the existence of a price trend. It is based on the approaches described in Wells Wilder`s book “New concepts of technical trading systems.”

The strategy of signals from the directory.
This signal can receive two types of signals for the opening.
If ADXLevel = 0, then the following strategy is used:
Wilder suggests buying if + DI crosses above -DI and selling when + DI crosses below -DI.
If ADXLevel is not = 0, then the following strategy is used:
Wilder suggests buying if + DI crosses above -DI with ADX above ADXLevel and selling when + DI crosses below -DI with ADX above ADXLevel.
When using ADX as a filter, the position of the lines is used + DI> -DI = only BUY, + DI <-DI = only SELL,

If ADXLevel is 0, then the permission to open SELL is DI-> DI +
If ADXLevel is 0, then the permission to open BUY is DI +> DI-
If ADXLevel is not equal to 0, then the permission to open SELL is DI-> DI + and ADX> ADXLevel
If ADXLevel is not equal to 0, then the permission to open BUY is DI +> DI- and ADX> ADXLevel

The Average Directional Index (ADX) belongs to a group of analytical methods for capturing trends. It was developed in the mid-70s by J. Wells Wilder Jr. This system allows you to detect trends and determine by their speed whether it is worth playing in their direction. ADX helps you profit from big trends.
The indicator consists of three lines. Two lines of directional change indicators, +DI and -DI, ​​and a line of probable directionality indicator, the value of which is calculated using the readings of +DI and -DI.

The +DI (red) and -DI (blue) lines very clearly show the long-term trend and the pace of its development, comparing the high and low prices of the emerging candle with similar prices of the previous candle. If there is a trend, there is a divergence of these curves, and the stronger the trend, the stronger the divergence. In a bullish trend, the +DI curve is above the -DI curve, and in a bearish trend, on the contrary, the -DI curve is above the +DI curve. When moving sideways, the values ​​of both lines are close and seem to intertwine.
Signals to buy and hold a buy position when +DI is above -DI and sell signals with hold a sell position when -DI is above +DI. The third ADX line called the probable direction indicator, is calculated as the modulus of the difference between two values ​​, +DI and -DI. As a result, it turns out that the larger the ADX, the more “overheated the market is.” If ADX is in the zone of its minimum values, then this means that the market is weak and is flat or consolidating. When the ADC value increases, this means that the current trend is strengthening, and positions can be opened in accordance with the current trend. When the indicator reaches its maximum value, you need to be careful because the market is overheated, and it is risky to be in it due to the uncertainty of further developments.
ADX works well on daily charts because it represents well the part of today’s range (the distance between the top and bottom points) that extends beyond the previous day’s range.

Oscillators

Inertia. (Momentum)

The inertia indicator allows you to monitor the pace of the trend – its acceleration, deceleration, or smooth
progress. Typically, these indicators reach a crest, bottom, or reversal before prices do.
While it is gaining altitude, you can safely hold bullish positions. In the meantime, it is falling lower and lower; you can also safely hold positions for the fall. Having reached a new height, the signaller indicates the acceleration of the upward trend and the likelihood of its continuation. Turning around at a lower level, the signalman shows that the acceleration has stopped: the trend is now moving like a rocket that is running out of fuel. And since it moves only by inertia, you need to prepare for the moment of reversal.
The situation with the bottoms of the signalman with downward trends is assessed according to the same logic.
It is calculated simply as the change in price over a certain period.

Each price reflects the agreement on the value of the market reached by all traders at the time of the transaction.
Inertia is based on the comparison of today’s price (today’s value agreement) with the previous price (previous value agreement). It measures changes in the level of mass optimism or pessimism.
If the momentum indicator reaches a new height, it reflects increased optimism in the market and the likelihood of further price increases. If the momentum indicator falls to a new depth, it indicates increased
pessimism and the possibility of further price declines.
If prices rise and momentum falls, he warns that a ridge is approaching: consider closing bull positions or tightening suspensions. If prices reach a new height and the ridge of inertia or rate of change is lower than the previous one, this divergence of the hills will give a strong sell signal. For downward trends, do the same, but in the opposite direction.
In an uptrend, buy whenever the momentum indicator falls below the zero line and begins to rise. If there is a downward trend, sell when the momentum indicator rises above the zero line and falls again.
On the charts of the inertia indicator, you can draw trend lines of the indicator itself. A breakout of a trend
line or a reflection from a trend line gives fairly reliable signals to buy or sell.

Commodity Channel Index (CCI)

The technical indicator of the Commodity Channel Index (CCI) measures the deviation of the instrument`s price from its average statistical price. High values ​​of the index indicate that the price is unusually high compared with the average, and low – that it is too understated. Despite the name, the Commodity Channel Index is applicable to any financial instrument, not just to goods.

Also, all three signals are used, but the ground state is still “no signal”.

BUY – the intersection of the top level from the top down

SELL. – the intersection of the lower level from the bottom up

The value of the external parameters CCIHighLevel and CCILowLevel determines the upper and lower levels.

The period and price of calculating the indicator are determined by the values CCIPeriod and CCIPrice.

Normalizes the Momentum chart by dividing its value by the largest amplitude achieved:

CCI = [ X – SMA(X, n) ] / [0.015 x dX ], where X = [ Close + High + Low ] / 3,

• Close –closing price,
• High and Low – max and min price for the analyzed period,
• dX = Sum [ Xi – SMA(X, n) ] / n,
• n – period length
• Xi is the price value at the time I,
• SMA(X, n) is the moving average for period n. 

Recommended n = 8.
The Commodity Channel Index (CCI) measures the deviation of a security’s price from its average price. High index values ​​indicate that the price is unusually high compared to the average, while low values ​​indicate that the price is too low. Despite the name, CCI is applicable to any financial instrument, not just commodities.
There are two main ways to use the CCI:

To find divergences
A divergence occurs when the price makes a new high, and the CCI fails to rise above
previous highs. A price correction usually follows this classic divergence.
As an overbought/oversold indicator,
the CCI usually fluctuates in the range of ±100. Values ​​above +100 indicate an overbought condition (and
the likelihood of a corrective decline), while values ​​below 100 indicate an oversold condition (and the possibility of a corrective rise).

Relative Strength Index (RSI)

Technical Indicator Relative Strength Index (RSI) is the next oscillator that oscillates in the range from 0 to 100. By introducing the Relative Strength Index, W. Wilder recommended using its 14-period variant. Later, 9 and 25-period indicators were also disseminated. One of the most common methods for analyzing the Relative Strength Index is to find discrepancies in which the price forms a new high, and the RSI can not overcome its previous high. This discrepancy indicates the probability of a price reversal. If the indicator then turns down and falls below its cavity, it completes the so-called “failure swing”. This failed swing is considered a confirmation of an early reversal of prices.

Similar to CCI and DeMarker. Signals are the exit from overbought (RSIHighLevel) and oversold zones (RSILowLevel).

BUY signal appears when RSI goes up from a lower value and crosses (RSILowLevel).
SELL signal appears when RSI goes down from a higher value and crosses (RSILowLevel)
The default state is “no signal”.

The period of the indicator can be set in the RSIPeriod parameter, and the settlement price can be placed in the RSIPrice parameter.

Developed by J. Wheeler Jr. In 1978, it is currently one of the most popular oscillators.
RSI = 100 – [ 100 / ( 1 + RS) ], where RS = AUx / ADx, x is the number of days in the analysis period (RSI order), 8 is recommended, AUx is the sum of positive price changes for the period, ADx is the sum of negative changes prices for the period. The recommended order is 8 (for any period). The author used to order 14 in his calculations because I saw its main application on daily charts. The relative strength index is a price-following oscillator that ranges from 0 to One common method of analyzing RSI is to look for divergences where the price makes a new high. Still, the RSI fails to break above its previous high. Similar divergence indicates the likelihood of a price reversal. If the RSI then turns down and falls
below its trough, it completes what is known as a ‘failure swing’. This failed swing is considered a confirmation of an imminent price reversal.

How to use RSI for chart analysis:
Tops and bottoms

RSI tops typically form above 70 and bottoms below 30, and they usually precede tops and bottoms on the price chart.

Chart Patterns
RSI often forms chart patterns – such as ‘head and shoulders’ or triangles – that may not appear on a price chart. A failed swing (breakout of support or resistance level) Occurs when the RSI rises
above a previous high (peak) or falls below a previous low (trough).

Support and Resistance Levels
On the RSI chart, support and resistance levels appear even more clearly than on the price chart.
Divergences
As mentioned above, divergences are formed when the price makes a new high (low), but it is
not confirmed by a new high (low) on the RSI chart. In this case, prices usually correct
in the direction of the RSI movement.

The same methods are used to analyze them when analyzing average prices on a chart. The advantage is that RSI fluctuations are limited and that signals from the RSI averages may outstrip the signals from the chart averages. 

Parabolic SAR

Indicator The Parabolic SAR indicator is built on a price chart. In its meaning, this indicator is similar to a moving average, with the only difference being that Parabolic SAR moves with greater acceleration. This indicator is often used as a moving stop signal line. The parabolic system is excellent at identifying market exit points. Long positions should be closed when the price falls below the SAR line, and short positions should be closed when the price rises above the SAR line. If you have a long position (that is, the price is above the SAR line), then the SAR line will move up regardless of which direction prices are moving. The amount the SAR line moves depends on the size of the price movement. 

Williams’ Percent Range (%R) 

Technical Indicator Williams` Percent Range (% R) is a dynamic indicator that determines the state of overbought / oversold. Williams` Percent Range is very similar to the technical indicator Stochastic Oscillator . The difference between them is only that the first has an inverted scale, and the second one is constructed using internal smoothing.

Williams’ Percent Range Technical Indicator (%R) is a dynamic technical indicator, which determines whether the market is overbought/oversold. Williams’ %R is very similar to the Stochastic Oscillator. The only difference is that %R has an upside down scale and the Stochastic Oscillator has internal smoothing.
Indicator values ranging between -80% and -100% indicate that the market is oversold. Indicator values ranging between -0% and -20% indicate that the market is overbought. To show the indicator in this upside down fashion, one places a minus symbol before the Williams` Percent Range values (for example -30%). One should ignore the minus symbol when conducting the analysis (Meta Trader 5).

It is similar to RSI, CCI, and DeMarker.

Signal BUY – the intersection of the level of overbought (WPRHighLevel) from top to bottom,

Signal SELL – the intersection of the oversold level (WPRLowLevel) from the bottom up.

All the rest is “no signal”.

Only the parameter of the indicator period can be changed from outside – WPRPeriod.

Williams’ Percent Range (%R) is a dynamic indicator that determines overbought/oversold conditions. The (%R) indicator is very similar to the stochastic Oscillator.

The only difference between them is that the first has an inverted scale, and the second is constructed using internal smoothing. 

To construct the %R indicator on an inverted scale, its values ​​are usually assigned a negative sign (for example -30%). When analyzing, the negative sign can be ignored. 

Indicator values ​​range from 80 to 100 %, indicating oversold conditions. Values ​​in the range from 0 to 20% indicate that the market is overbought. 

According to the rule common to all overbought/oversold indicators, it is best to act on their signals by waiting for prices to turn in the appropriate direction.

So, if the indicator overbought/oversold indicates an overbought state, then before selling the security, it is reasonable to wait for prices to turn downward. The %R indicator has a curious ability to anticipate price reversals mysteriously. It almost always peaks and turns down a certain amount of time before the price peaks and turns down. Likewise, the %R indicator usually forms a trough and turns upward in advance.

Rules for oscillator analysis:
Signal Trader’s actions Confirmations

• Values ​​following the max of the Oscillator for the min of the oscillator Warning for a trade Down Up at least two
• Intersection with a given boundary of upper-lower values ​​: It’s time for a trade. Sells Buys at least one.
• Intersection with the middle: You can be late at least two

• ·In a bullish market, the value limits must be raised, and in a bearish market, lowered
• analysis of oscillators gives good results in a flat market
• if, during a strong upward trend, the Oscillator shows downward, and the price does not move in the indicated direction, then the stronger the upward trend will be in the future; with a strong downward trend, it’s the other way around when the trend changes, the Oscillator can both greatly deceive and be the first to warn
• Interaction of oscillators with the price chart (from now on, in the figures, the price is on top, and the Oscillator is below)

Bearish convergence

1. medium signal
If the end of the Oscillator is close to the upper limit, then a price decrease is possible; if it is to the middle of the values, then the exchange rate may stabilize.

2. weak signal
We expect price stabilization followed by a change in trend.

3. medium signal
If the end of the Oscillator is close to the upper limit, then the trend may strengthen; if it is to the bottom, then an increase will most likely occur; if it is towards the middle, then both a fall and price stabilization are equally likely.

Bullish divergence

1. medium signal
If the end of the Oscillator is close to the lower boundary, then the price may rise; if it is towards the middle of the values, then depreciation is more likely.

2. strong signal
We expect price stabilization with a subsequent change in trend.

3. medium signal
If the end of the Oscillator is close to the lower border, then the trend may strengthen;

if – to the top, then stabilization of the exchange rate is possible; 

if – to the middle, then both price growth and price stabilization are equally likely.

Parallelism

Average signal
1. Strong upward trend

2. Expect a trend change

3. Strong downward trend

Final remarks
When working on a strong trend, treat oscillator signals with the utmost caution, while false oscillator signals, as a rule, indicate a strengthening of the trend. If the trend is upward, then the oscillators are in the overbought zone most of the time; if, on the contrary, then they are in the oversold zone.

Basic rules for volume analysis:

• · Decrease in volume – Decrease in interest in a given exchange rate dynamics, a change in trend, or temporary price stabilization
• · Increase in volume – increase in interest in a given exchange rate dynamics, or strengthening of the current dynamics, or the emergence of a new direction of price change
• · Sometimes, a gradual decrease in volumes is accompanied by a sharp change in price
• · Peaks in volumes signal a possible trend reversal

Plotting Japanese candlestick charts and analyzing candlestick patterns is a relatively new area of ​​technical analysis. The advantage of Japanese candlesticks is that they represent data in such a way that it is possible to see relationships within the data. Candlesticks create a clear psychological picture of trading.
Japanese candlesticks offer a picture of short-term trading (within the few candlesticks analyzed) by examining its results rather than its causes. This fact puts Japanese candlesticks into the category of technical analysis.

It cannot be ignored that prices are influenced by psychologically determined investor emotions: fear, greed, and hope. The general psychological atmosphere prevailing on the trading floor cannot be measured statistically; it is necessary to use some form of technical analysis to assess the changes occurring in psychology. Japanese candlesticks record changes in the nature of investors’ assessment of value. They are then reflected in price movements. Candlesticks are not just a method of recognizing patterns; they show how buyers and sellers interact.

Below, we provide a brief overview of candlestick patterns as a reference guide because… the entire versatility of this method cannot be considered within the confines of this summary.

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