tags:Mathematical Trading Methods,Indicators,Moving Averages,arithmetic,linearly weighted,Oscillators,Stochastics,stochastics ,exponentially smoothed,Trading Signals
The mathematical trading methods provide a more objective view of price activity. In addition, these methods tend to provide signals prior to their occurrence on the currency charts. The tools of the mathematical methods are moving averages and oscillators.
A moving average is an average of a predetermined number of pricesover a number of days, divided by the number of entries. The higher the number of days in the average, the smoother the line is. A moving average makes it easier to visualize currency activity without daily statistical noise. It is a common tool in technical analysis and is used either by itself or as an oscillator.
As one can see from Figure 5.35., a moving average has a smootherline than the underlying currency. The daily closing price is commonly included in the moving averages. The average may also be based on the midrange level or on a daily average of the high, low, and closing prices.
It is important to observe that the moving average is a follower rather than a leader. Its signals occur after the new movement has started, not before.
There are three types of moving averages:
Traders have the option of using a linearly weighted moving average (See Figure 5.36.). 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.
Single moving averages are frequently used as price and time filters. As a price filter, a short-term moving average has to be cleared by the currency closing price, the entire daily range, or a certain percentage (chosen at the discretion of the trader).
The envelope model (See Figure 5.38.) serves as a price filter. It consists of a short-term (perhaps 5-day) closing price based moving average to which a small percentage (2 percent is suggested for foreign currencies.) are added and substracted. The two winding parallel lines above and below the moving average will create a band bordering most price fluctuations. When the upper band is penetrated, a selling signal occurs. When the lower band is penetrated, a buying signal occurs. Because the signals generated by the envelope model are very short-term and they occur many times against the ongoing direction of the market, speed of execution is paramount. The high-low band is set up the same way, except that the moving average is based on the high and low prices. As a time filter, a short number of days may be used to avoid any false signals.
A buying signal on a two-moving average combination occurs when the shorter term of two consecutive averages intersects the longer one upward. A selling signal occurs when the reverse happens, and the longer of two consecutive averages intersects the shorter one downward. (See Figure 5.39.)
Oscillators are designed to provide signals regarding overbought and oversold conditions. Their signals are mostly useful at the extremes of their scales and are triggered when a divergence occurs between the price of the underlying currency and the oscillator. Crossing the zero line, when applicable, usually generates direction signals. Examples of the major types of oscillators are moving averages convergence-divergence (MACD), momentum and relative strength
index (RSI).
Stochastics generate trading signals before they appear in the price itself. Its concept is based on observations that, as the market gets high, the closing prices tend to approach the daily highs; whereas in a bottoming market, the closing prices tend to draw near the daily lows.
The 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 stochastics are:
The mathematical trading methods provide a more objective view of price activity. In addition, these methods tend to provide signals prior to their occurrence on the currency charts. The tools of the mathematical methods are moving averages and oscillators.
Moving Averages
A moving average is an average of a predetermined number of pricesover a number of days, divided by the number of entries. The higher the number of days in the average, the smoother the line is. A moving average makes it easier to visualize currency activity without daily statistical noise. It is a common tool in technical analysis and is used either by itself or as an oscillator.
As one can see from Figure 5.35., a moving average has a smootherline than the underlying currency. The daily closing price is commonly included in the moving averages. The average may also be based on the midrange level or on a daily average of the high, low, and closing prices.
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| Figure 5.35. Examples of three simple moving averages—5-day (white), 20-day (red) and 60-day (green) |
There are three types of moving averages:
1. The simple moving average or arithmetic mean.
2. The linearly weighted moving average.
3. The exponentially smoothed moving average.
As described, the simple moving average or arithmetic mean is the average of a predetermined number of prices over a number of days, divided by the number of entries.
Traders have the option of using a linearly weighted moving average (See Figure 5.36.). 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.
 |
| Figure 5.36. Example of a 20-day simple moving average (red) as compared to a 20-day weighted moving average (white) |
The most sophisticated moving average available is the exponentially smoothed moving average. (See Figure 5.37.) In addition to assigning different weights to the previous prices, the exponentially smoothed moving average also takes into account the previous price information of the underlying currency.
 |
| Figure 5.37. Example of a 20-day simple moving average (red) as compared to a 20-day exponential moving average (white) |
Trading Signals of Moving Averages
Single moving averages are frequently used as price and time filters. As a price filter, a short-term moving average has to be cleared by the currency closing price, the entire daily range, or a certain percentage (chosen at the discretion of the trader).
The envelope model (See Figure 5.38.) serves as a price filter. It consists of a short-term (perhaps 5-day) closing price based moving average to which a small percentage (2 percent is suggested for foreign currencies.) are added and substracted. The two winding parallel lines above and below the moving average will create a band bordering most price fluctuations. When the upper band is penetrated, a selling signal occurs. When the lower band is penetrated, a buying signal occurs. Because the signals generated by the envelope model are very short-term and they occur many times against the ongoing direction of the market, speed of execution is paramount. The high-low band is set up the same way, except that the moving average is based on the high and low prices. As a time filter, a short number of days may be used to avoid any false signals.
 |
| Figure 5.38. An envelope model define the edges of the band. A close above the upper band sends a buying signal and one below the lower band gives a selling signal |
Usually traders choose a number of averages to use with a currency. A suggested number is three, as more signals may be available. It may be helpful to use intervals that better encompass short-term, medium-term, and long-term periods, to arrive at a more complex set of signals. Some of the more popular periods are 4, 9, and 18 days; 5, 20, and 60 days; and 7, 21, and 90 days. Unless you focus on a specific combination of moving averages (for instance, 4, 9, and 18 days), the exact number of days for each of the averages is less important, as long as they are spaced far enough apart from each other to avoid insignificant signals.
A buying signal on a two-moving average combination occurs when the shorter term of two consecutive averages intersects the longer one upward. A selling signal occurs when the reverse happens, and the longer of two consecutive averages intersects the shorter one downward. (See Figure 5.39.)
Oscillators
Oscillators are designed to provide signals regarding overbought and oversold conditions. Their signals are mostly useful at the extremes of their scales and are triggered when a divergence occurs between the price of the underlying currency and the oscillator. Crossing the zero line, when applicable, usually generates direction signals. Examples of the major types of oscillators are moving averages convergence-divergence (MACD), momentum and relative strength
index (RSI).
 |
| Figure 5.39. Examples of a sell signal (first and third crossovers) and a buy signals (second crossover) provided by the 5-day (red) and 20-day (white) moving averages |
Stochastics
Stochastics generate trading signals before they appear in the price itself. Its concept is based on observations that, as the market gets high, the closing prices tend to approach the daily highs; whereas in a bottoming market, the closing prices tend to draw near the daily lows.
The 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 stochastics are:
%K = [(CCL -L9)I(H9 - L9)] * 100, where
CCL = current closing price
L9 - the lowest low of the past 9 days
H9 - the highest high of the past 9 days
and
%D=(H3/L3~) * 100,
where H3 = the three-day sum of (CCL - L9)
L3 = the three-day sum of (H9 - L9)
The resulting lines are plotted on a 1 to 100 scale, with overbought and oversold warning signals at 70 percent and 30 percent, respectively. The buying (bullish reversal) signals occur under 10 percent, and conversely the selling (bearish reversal) signals come into play above 90 percent after the currency turns. (See Figure 5.40.) In addition to these signals, the oscillator-currency price divergence generates significant signals.
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| Figure 5.40. An example of the stochastic |
The intersection of the %D and %K lines generates further trading signals.
There are two types of intersections between the %D and %K lines
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.
%D line.
2. The right crossing, when the %K line occurs after the peak of the %D
line.
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