Gaps

Mathematical Tools And Technical Indicators

The quantitative or mathematical tools for the technical analysis called the technical indicators

are being obtained as a result of the mathematical processing of prices averaged in time as well as

other characteristics of market movements. They are applied to get signals for an additional

evaluation of trade channels and patterns analysis by means of the indicators charts. The main

groups of technical indicators are moving averages and oscillators.

Moving Averages. A moving average is an average price of a certain currency over a certain time

interval (in days, hours, minutes etc) during an observation period divided by these time intervals.

This averaged price is being determined for each regular interval beginning from the first. A

moving average has a smoother line than the underlying currency because statistical ‘noises’ are

excluded to provide more convenient visualization of the currency activity. A moving average

may be used as a special indicator or to create an oscillator. The moving average may be based

on the midrange level or on a daily average of the high, low, and closing prices. The charts of

moving averages are being plotted within same coordinates with an underlying price chart (See

Figures 4.53 – 4.56). Technical analysis uses the next three types of moving averages:

1. The simple moving average or arithmetic mean (SMA).

2. The linearly weighted moving average (LMA). This type of average assigns more

weight to the more recent closings. This is achieved by multiplying the last day's price by

one, and each closer day by an increasing consecutive number. In our previous example,

the fourth day's price is multiplied by 1, the third by 2, the second by 3, and the last one

by 4; then the fourth day's price is deducted. The new sum is divided by 9, which is the

sum of its multipliers.

3. The exponentially smoothed moving average (EMA) which provides the best

smoothing of data averaged taking into account the previous price information of the

underlying currency.

In Figure 4.53 is shown the difference in reading of different types of moving averages.

Trading signals of moving averages. Trade signals which occur by the use of one moving

average is a buy signal by the crossing of the underlying price chart by the moving average chart

from below up and a sell signal by the crossing of the underlying price chart by the moving

average chart from above down (see Figure 4.54).

For technical analysis application usually consists of two or three moving averages charts

constructed for different periods – long term, middle term and short term. For example, to use

two charts, a combination of moving averages for 4 and 9 days may be used and to use three

charts, three moving averages – for 4, 9 and 18 days may be applied. Other often-applied

combinations of three moving averages are 5, 20 and 60 days and 7, 21 and 90 days. A buying

signal on a two-moving average combination, for example, for 4 and 9 days, occurs when the

shorter term of two consecutive averages (4 days) intersects the longer (9 days) upward. A selling

signal occurs when the reverse happens, and the longer of two consecutive averages intersects the

shorter one downward (see Figure 4.55).

A signal involving three moving averages is generated by a moving averages combination of 4, 9,

and 18 days. The buying warning occurs when the 4-day moving average crosses upward

through both the 9-day and 18-day averages, and the buying signal is confirmed when the 9-day

moving average also crosses upward through the 18-day average (see Figure 4.56). The reverse is

true for the selling signal.

Envelopes The envelope model consists of a short-term (perhaps 5-day) closing price based

moving average to which you add and subtract a small percentage (2 percent is suggested for

foreign currencies). An example for the envelope using the averaging along 14 days intervals is

shown in figure 4.57. The crossing of the underlying chart price by the envelope chart from above

down is a buy signal.

Bollinger Bands The Ballinger bands combine a moving average with the instrument's volatility.

The bands were designed to gauge whether prices are high or low on a relative basis via volatility.

The two are plotted two standard deviations above and below a 20-day simple moving average.

The bands look a lot like an expanding and contracting envelope model. When the band contracts

drastically, the signal is that volatility is low and thus likely to expand in the near future. An

additional signal is a succession of two top formations, one outside the band followed by one

inside. If it occurs above the band, it is a selling signal. When it occurs below the band, it is a

buying signal (See Figure 4.58).

Median Price The Median Price indicator chart is being plotted using arithmetical averages of

high and low for trade period prices. An example of that indicator is shown in Figure 4.59. The

superposition of an underlying price chart with the indicator chart gives a visual representation

about the grade and direction of the deviation of close prices from the averaged prices during an

observation interval.

Average True Range The Average True Range indicator denoted in the USA as ATR is a grade

of the volatility. Minimal and maximal values of the volatility are signals warning about a

possible reversal.

Oscillators were designed to provide signals regarding overbought and oversold market

conditions. Therefore, the signals of oscillators are most useful at the extremes of their scales.

Crossing the zero line, when applicable, usually generates direction signals. The major types of

oscillators provided by the Trading Intl. program are considered below.

Commodity Channel Index The commodity channel index (CCI) consists of the difference

between the mean price of the currency and the average of the mean price over a predetermined

period of time. A buying signal is generated when the price exceeds the upper (+100) line, and a

selling signal occurs when the price dips under the lower (-100) line. An example of this indicator

is shown in Figure 4.61. As one can see in this Figure, the CCI oscillates around 0 in the interval

from -100 till +100. Values CCI>100 tells about an overbought (position sell likes to be rational),

a value CCI<100 is a feature of an oversold (position buy likes to be rational).

Directional Movement Index (DMI) provides a signal of a clear trend presence in the market.

The line simply rates the price directional movement on a scale of 0 to 100%. The higher the

number, the better the trend potential of a movement, and vice versa. An example of the DMI

indicator for 14 days is presented in Figure 4.62.

To construct a DMI indicator chart two lines are to be generated which measure the buying and

selling pressure. They are called +DI (that is the positive directional indicator which is shown in

Figure 4.62 by the green line) and-DI (that is the positive directional indicator which is shown in

Figure 4.62 by the black line). If +DI line is higher than –DI, a bullish situation exists, otherwise

– a bearish as in Figure 4.62. Lines +DI and -DI are a ground to create the third one – so called

directional movement line (ADX). The latter oscillates in limits from 0 till 50. Values of the ADX

below 20 correspond to the absence of any clear trend in the market. A rise of the ADX above 20

is a signal warning about the beginning of a trend formation. An ADX line, which was above 40

and is going to fall down, signals an exhaustion of the trend.

Stochastic. Stochastic generate trading signals before they appear in the price itself. The

stochastic concept is based on observations that, as the market gets toppish, the closing prices

tend to approach the daily highs; whereas in a bottoming market, the closing prices tend to draw

near the daily lows. This oscillator consists of two lines called %K and %D. Visualize %K as the

plotted instrument, and %D as its moving average. The formulas for calculating the stochastic

are: %K = [(CCL -L9) I (H9 -L9)] * 100, where CCL - current closing price; L9 - the lowest low

of the past 9 trade periods; H9 - the highest high of the past 9 trade periods and %D= (H3/L3) *

100, where H3 = CCL – L3; L3= H3 – L3. The resulting lines are plotted on a 1 to 100 scale,

with overbought and oversold warning signals at 70% and 30%, respectively. The buying (bullish

reversal) signals occur under 10%, and conversely the selling (bearish reversal) signals come into

play above 90% after the currency turns. (see Figure 4.67.) In addition to these signals, the

oscillator-currency price divergence generates significant signals. A real example of a stochastic

oscillator is presented in Figure 4.63. The intersection of the %D and %K lines generates

further trading signals. There are two types of intersections between the %D and %K lines:

1. The left crossing, when the %K line crosses prior to the peak of the %D line.

2. The right crossing, when the %K line occurs after the peak of the %D line.

Convergence – Divergence of Moving (MACD) oscillator is built on exponentially smoothed

moving averages. The MACD is a combination of charts (1) of the difference of two EMA (a

short one and a long one) and (2) of “the shortest” EMA which all are plotted against the zero

line. The zero line represents the times the values of the two moving averages are identical. A real

example of the MACD indicator is shown in Figure 4.64. In addition to the signals generated by

the averages' intersection with the zero line and by divergence, additional signals occur as the

shorter average line intersects the longer average line. The buying signal is displayed by an

upward crossover, and the selling signal by a downward crossover (see Figure 4.64).

Momentum is an oscillator designed to measure the rate of price change. This oscillator consists

of the net difference between the current closing price and the oldest closing price from a

predetermined period. The formula for calculating the momentum (M) is: M=CCP-OCP, where

CCP - current close price; OCP – the oldest close price for the predetermined period. The new

values thus obtained will be either positive or negative numbers, and they will be plotted around

the zero line. In the program Trading Intl. the algebraic addition of the difference obtained with

the figure 100 is being performed and a real indicator outputted from this program oscillates

around the 100 line. At values of the momentum M>100 one says “The market caught a

moment”, otherwise (M<100) “The market lost a moment”. A real example of the Momentum

indicator for 14 days is shown in Figure 4.65. Maximal values of the indicator show the

overbought, minimal – oversold market conditions. In terms of time frame, needless to say, the

shorter the number of days included in the calculations, the more responsive the momentum will

be to short-term fluctuations, and vice versa.

Relative Strength Index (RSI) measures the relative changes between the highest and lowest

close prices (see Figure 4.66). The formula for calculating the RSI is: RSI=100-[100/(1+RS)],

where RS - average of predetermined number X trade periods value of all closes, which were

higher than all preceded closes divided by average of the same X periods value of all closes,

which were lower than all preceded closes. Most often RSI is calculated for 14 days. RSI charts

are plotted on a 0 to 100% scale. The 70% and 30% values are used as warning signals, whereas

values above 85% indicate an overbought condition (sell signal) and values under 15 indicate an

oversold condition (buy signal). By technical analysis, RSI is effectively used together with

Ballinger Bands. It is believed that a sell position should be open when by a high RSI value the

price chart touches with the upper Ballinger Band, and a buy position – when by a low RSI value

the price chart touches with the bottom band. A real example of an RSI indicator for 14 days

together with the Ballinger Bands indicator is shown in Figure 4.66.

Rate of Change (ROC) is another version of the Momentum oscillator. The difference consists in

the fact that, the Momentum's formula is based on subtracting the oldest close price from the most

recent, and the ROC's formula is based on dividing the oldest close price into the most recent one:

ROC = (CCP/OCP) * 100, where CCP - current close; OCP – the oldest close price for the

predetermined period. A real example of the ROC for 14 days is shown in Figure 4.67.

Larry Williams Percent Rate (Williams’s %R) is a version of the stochastic oscillator. It consists

of the difference between the highest high price of a predetermined number of days and the

current close price, which difference in turn is divided by the total range. This oscillator is plotted

on a reversed 0 to 100% scale (See a real example in Figure 4.68). Therefore, the bullish reversal

signals occur at fewer than 80%, and the bearish signals appear at above 20%. The interpretations

are similar to those discussed under stochastic.

It is rational to use, for a detailed technical analysis, a combination of different indicators from

those mentioned above (see Figure 4.69).

Ichimoku Kinko Hyo The Ichimoku Kinko Hyo (or simply - Ichimoku) indicator is appointed to

determine simultaneously a market trend direction, support and resistance levels and to trigger

buy and sell signals. In such a way, this indicator unites in itself a number of other indicators as

well as different approaches concerning the price movement prediction. To construct an Ichimoku

chart, four time intervals of different widths are used. On those intervals are grounded values of

the following lines constituting the Ichimoku which are the lines of median prices in a

corresponding interval:

Tenkan-sen – shows the average value of a price of the first time interval which is the

sum of a maximum and minimum of that time, divided by two;

Kijun-sen - shows the average value of a price of the second time interval;

Senkou Span À – shows the middle of a distance between two preceding lines moved

ahead on the value equal the second time interval;

Senkou Span B - shows the average value of a price of the third time interval moved

ahead on the value equal the second time interval;

Chinkou Span - shows the close of a current candlestick moved back on the value equal

the second time interval.

The area between Senkou lines is hatched and called the cloud. If the price chart is inside the

cloud the market is believed trendless, and Senkou lines form support and resistance levels. If the

price chart is above the cloud, the upper cloud border is the first support and the bottom – the

second. If the price chart is under the cloud then the bottom cloud border is the first resistance

and the upper – the second. The crossing of the price chart by the line Chinkou Span bottom-up is

a buy – signal, top-down - sell. Kijun-sen («main line») is used as a gauge of the market

movement. If the price is above this line, a growth of prices is to be expected. If the prices cross

this line then further trend reversal is likely to be expected. The other variant of the Kijun-sen use

is trade signals triggering. A signal buy is generated if the Tenkan-sen line crosses the Kijun-sen

line bottom-up and signal sell – by crossing otherwise. The Tenkan-sen ("reversal line") is being

used as an indicator of the market trend – a trend exists if this line is rising or falling. A real

example of the Ichimoku is presented in Figure 4.70.

Continue: Fibonacci & Elliot Wave Theory