Over the years numerous technical indicators have been developed to describe performance, as well as to predict future price movements. In this section we introduce five of the most useful indicators and explain how they are calculated.

Over the years numerous technical indicators have been developed to describe performance, as well as to predict future price movements. In this section we introduce five of the most useful indicators and explain how they are calculated.

**Moving Average**

A price/time series can be seen as a representation of a longer-term trend on which is superimposed on a shorter-term, random fluctuating “noise.” In order to obtain a clean trend signal, using moving averages can filter out shorter-term noises. The formula for calculating the p-interval moving-average time series is given by

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where,

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is the price time series, and n is the number of periods.

The moving average defined above assigns equal weight to every point in the averaging interval; consequently, it may not emphasize the most recent price behavior. To overcome this, some people use the p-period exponential moving average:

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In reality, it is good enough to run the summation through *j=i-2p, to j=i.*

**BollingerBand** Sometimes prices appear to remain in a range for extended periods of time. A good way to describe this situation is to define a moving range around the prices. Some people use an upper boundary and a lower boundary to define the range; the upper boundary is calculated as a moving average of a chosen period plus 5% of the price, and the lower boundary is the moving average minus 5%. These boundaries have the drawback of being too narrow to accommodate price levels when volatility is high and too wide when volatility is low. A better solution, recommended by John Bollinger, defines the upper boundary as a chosen moving average plus twice the corresponding standard deviation, with the lower boundary as the moving average minus twice the standard deviation. The method is described below:

The Bollinger Band includes 3 lines: the upper band, lower band, and the centerline. The centerline is simply the moving average, and the upper and lower bands are, respectively, the center line plus/minus twice the standard deviation. For a p-period Bollinger band:

Center Line = p-period moving average

Upper Band = Center Line + 2 x StdDev

Lower Band = Center Line – 2 x StdDev

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*Figure 5. Bollinger Band*

**RSI**

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**RSI** stands for Relative Strength Indicator. In order to compute the p-period RSI, one first computes the p one-period changes.

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Then one computes the average of the up changes U and down changes D:

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Then

RSI = 100% x U/(U+D)

We can see that, if the price goes up in every single period, RSI is 100%. If the price goes down in every period, RSI=0.

**Stochastics**

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*Figure 7. K/D*

**KD **stands for two Stochastic indicators K and D. In order to compute the p-period K, one needs to compute the p-period high Hp and low Lp,

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then the fast Stochastic K is given by

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The q-period slow Stochastic D is simply the q-period moving average of K. Many people simply refer to D by calling it KD.

**MACD**

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Figure 8. MACD

MACD stands for Moving Average Convergence and Divergence. It is simply the difference between a shorter period exponential moving average and a longer period exponential moving average. For example,

MACD(8, 17) = EMA(8) – EMA(17)

The MACD is often plotted together with a “Signal Line,” the 9-day moving average of the MACD. A basic MACD signal is to buy when the 9-day signal line moves above the MACD line and to sell if it crosses below the MACD line.

“Technical Indicators.” FXtrek University. . Copyright © 2001-2007 FXtrek.com. 17 Novemeber 2007