A technical indicator is a series of data points that are derived by applying a formula to the price data of a security. Price data includes any combination of the open, high, low or close over a period of time. Some indicators may use only the closing prices, while others incorporate volume and open interest into their formulas. The price data is entered into the formula and a data point is produced. Millennium Trader 4 supports a wide range of indicator as follow:

• Accelerator/Decelerator Oscillator — AC
  

  The price is the last element to change. The price only changes after the driving force of the market has changed, and before changing direction, the acceleration of the driving force is to slow down and drop to nought. After that it starts accelerating in the opposite direction until the price makes a move that way too.

  Accelerator/Decelerator Oscillator - AC measures acceleration and deceleration of the current driving force.

  Accelerator/Decelerator Oscillator - AC will change direction before any changes in the driving force, which, it its turn, will change its direction before the price. If you realize that Accelerator Oscillator is a signal of an earlier warning, it gives you evident advantages.

  The nought line is basically the spot where the driving force is at balance with the acceleration. If AC is higher than nought, then it is usually easier for the acceleration to continue the upward movement (and vice versa in cases when it is below nought). Unlike in case with Awesome Oscillator, it is not regarded as a signal when the nought line is crossed. The only thing that needs to be done to control the market and make decisions is to watch for changes in color. To save yourself serious reflections, you must remember: you can not buy with the help of Accelerator Oscillator, when the current column is colored red, and you can not sell, when the current column is colored green.

  If you enter the market in the direction of the driving force (Accelerator Oscillator is higher than nought, when buying, or it is lower than nought, when selling), then you need only two green columns to buy (two red columns to sell). If the driving force is directed against the position to be opened (indicator below nought for buying, or higher than nought for selling), a confirmation is needed, hence, an additional column is required. In this case the indicator is to show three red columns over the nought line for a short position and three green columns below the nought line for a long position.

  

  Calculation

  AC bar chart is the difference between the value of 5/34 of the driving force bar chart and 5-period simple moving average, taken from that bar chart.

  AO = SMA(median price, 5)-SMA(median price, 34)
  AC = AO-SMA(AO, 5)

  Where:
  SMA — Simple Moving Average ;
  AO — Awesome Oscillator.
  

• Accumulation/Distribution — A/D
  

  The Accumulation/Distribution is really a variation of the more popular On Balance Volume indicator. Both of these indicators attempt to confirm changes in prices by comparing the volume associated with prices.

  When the Accumulation/Distribution moves up, it shows that the security is being accumulated, as most of the volume is associated with upward price movement. When the indicator moves down, it shows that the security is being distributed, as most of the volume is associated with downward price movement.

  Divergences between the Accumulation/Distribution and the security's price imply a change is imminent. When a divergence does occur, prices usually change to confirm the Accumulation/Distribution. For example, if the indicator is moving up and the security's price is going down, prices will probably reverse.

  

  Calculation

  A portion of each day's volume is added or subtracted from a cumulative total. The nearer the closing price is to the high for the day, the more volume added to the cumulative total. The nearer the closing price is to the low for the day, the more volume subtracted from the cumulative total. If the close is exactly between the high and low prices, nothing is added to the cumulative total.

  
  
• Alligator
  

  "Most of the time the market remains stationary. Only for some 15–30% of time the market generates trends, and traders who are not located in the exchange itself derive most of their profits from the trends. My Grandfather used to repeat: "Even a blind chicken will find its corns, if it is always fed at the same time". We call the trade on the trend "a blind chicken market". It took us years, but we have produced an indicator, that lets us always keep our powder dry until we reach the blind chicken market"

  Bill Williams

  In principle, Alligator Technical Indicator is a combination of Balance Lines (Moving Averages) that use fractal geometry and nonlinear dynamics.

  • The blue line (Alligator's Jaw) is the Balance Line for the timeframe that was used to build the chart (13-period Smoothed Moving Average, moved into the future by 8 bars);

  • The red line (Alligator's Teeth) is the Balance Line for the value timeframe of one level lower (8-period Smoothed Moving Average, moved by 5 bars into the future);

  • The green line (Alligator's Lips) is the Balance Line for the value timeframe, one more level lower (5-period Smoothed Moving Average, moved by 3 bars into the future).

  Lips, Teeth and Jaw of the Alligator show the interaction of different time periods. As clear trends can be seen only 15 to 30 per cent of the time, it is essential to follow them and refrain from working on markets that fluctuate only within certain price periods.

  When the Jaw, the Teeth and the Lips are closed or intertwined, it means the Alligator is going to sleep or is asleep already. As it sleeps, it gets hungrier and hungrier — the longer it will sleep, the hungrier it will wake up. The first thing it does after it wakes up is to open its mouth and yawn. Then the smell of food comes to its nostrils: flesh of a bull or flesh of a bear, and the Alligator starts to hunt it. Having eaten enough to feel quite full, the Alligator starts to lose the interest to the food/price (Balance Lines join together) — this is the time to fix the profit.

  

  Gator Oscillator

  Gator Oscillator is based on the Alligator and shows the degree of convergence/divergence of the Balance Lines (Smoothed Moving Averages). The top bar chart is the absolute difference between the values of the blue and the red lines. The bottom bar chart is the absolute difference between the values of the red line and the green line, but with the minus sign, as the bar chart is drawn top-down.

• Average Directional Movement Index — ADX
  

  Developed by J. Welles Wilder, the Average Directional Movement Index (ADX) is an indicator for use with the Directional Movement Index and quantifies the strength and direction of a trend. The ADX consists of three components: the plus Directional Indicator (+DI), the minus Directional Indicator (-DI) and the Average Directional Indicator. The ADX is simply a modified moving average of DX.

  To calculate up or down directional movement in a trend, a range is determined by comparing today's high and low with yesterdays close. If the largest part of today's range is above yesterday's range, the directional movement is plus. If the largest part of today's range is below yesterday's range, the directional movement is minus. If today's range is within yesterday's range, then directional movement is defined as zero. The average of the directional movement indicators is the ADX.

  Read the ADX like an oscillator. A high positive value would be bullish. A low negative value is interpreted as bearish.

  

  Calculation

  ADX = SUM[(+DI-(-DI))/(+DI+(-DI)), N]/N

• Average True Range — ATR
  

  The Average True Range ("ATR") is a measure of volatility. It was introduced by Welles Wilder in his book, New Concepts in Technical Trading Systems , and has since been used as a component of many indicators and trading systems.

  The Average True Range can be interpreted using the same techniques that are used with the other volatility indicators.

  

  Calculation The True Range indicator is the greatest of the following:

  • The distance from today's high to today's low.
  • The distance from yesterday's close to today's high.
  • The distance from yesterday's close to today's low.

  The Average True Range is a moving average (typically 14-days) of the True Ranges.

• Awesome Oscillator — AO
  

  Awesome Oscillator Technical Indicator (AO) is a 34-period simple moving average, plotted through the middle points of the bars (H+L)/2, which is subtracted from the 5-period simple moving average, built across the central points of the bars (H+L)/2. It shows us quite clearly what's happening to the market driving force at the present moment.

  Signals to buy

  Saucer

  This is the only signal to buy that comes when the bar chart is higher than the nought line. One must bear in mind:

  the saucer signal is generated when the bar chart reversed its direction from the downward to upward. The second column is lower than the first one and is colored red. The third column is higher than the second and is colored green.

  • for the saucer signal to be generated the bar chart should have at least three columns.

  • Keep in mind, that all Awesome Oscillator columns should be over the nought line for the saucer signal to be used.

  Nought line crossing

  The signal to buy is generated when the bar chart passes from the area of negative values to that of positive. It comes when the bar chart crosses the nought line. As regards this signal:

  • for this signal to be generated, only two columns are necessary;

  • the first column is to be below the nought line, the second one is to cross it (transition from a negative value to a positive one);

  • simultaneous generation of signals to buy and to sell is impossible.

  Two pikes

  This is the only signal to buy that can be generated when the bar chart values are below the nought line. As regards this signal, please, bear in mind:

  • the signal is generated, when you have a pike pointing down (the lowest minimum) which is below the nought line and is followed by another down-pointing pike which is somewhat higher (a negative figure with a lesser absolute value, which is therefore closer to the nought line), than the previous down-looking pike.

  • the bar chart is to be below the nought line between the two pikes. If the bar chart crosses the nought line in the section between the pikes, the signal to buy doesn't function. However, a different signal to buy will be generated — nought line crossing.

  • each new pike of the bar chart is to be higher (a negative number of a lesser absolute value that is closer to the nought line) than the previous pike.

  • if an additional higher pike is formed (that is closer to the nought line) and the bar chart has not crossed the nought line, an additional signal to buy will be generated.

  Signals to sell

  Awesome Oscillator signals to sell are identical to the signals to buy. The saucer signal is reversed and is below zero. Nought line crossing is on the decrease — the first column of it is over the nought, the second one is under it. The two pikes signal is higher than the nought line and is reversed too.

  

  Calculation

  AO is a 34-period simple moving average, plotted through the central points of the bars (H+L)/2, and subtracted from the 5-period simple moving average, graphed across the central points of the bars (H+L)/2.

  MEDIAN PRICE = (HIGH+LOW)/2
  AO = SMA(MEDIAN PRICE, 5)-SMA(MEDIAN PRICE, 34)

  Where:
  SMA — Simple Moving Average.

• Bollinger Bands — BB
  

  Bollinger Bands are similar to moving average envelopes. The difference between Bollinger Bands and envelopes is envelopes are plotted at a fixed percentage above and below a moving average, whereas Bollinger Bands are plotted at standard deviation levels above and below a moving average. Since standard deviation is a measure of volatility, the bands are self-adjusting: widening during volatile markets and contracting during calmer periods.

  Bollinger Bands was created by John Bollinger.

  Bollinger Bands are usually displayed on top of security prices, but they can be displayed on an indicator. These comments refer to bands displayed on prices.

  As with moving average envelopes, the basic interpretation of Bollinger Bands is that prices tend to stay within the upper- and lower-band. The distinctive characteristic of Bollinger Bands is that the spacing between the bands varies based on the volatility of the prices. During periods of extreme price changes (i.e., high volatility), the bands widen to become more forgiving. During periods of stagnant pricing (i.e., low volatility), the bands narrow to contain prices.

  Mr. Bollinger notes the following characteristics of Bollinger Bands.

  • Sharp price changes tend to occur after the bands tighten, as volatility lessens.
  • When prices move outside the bands, a continuation of the current trend is implied.
  • Bottoms and tops made outside the bands followed by bottoms and tops made inside the bands call for reversals in the trend.
  • A move that originates at one band tends to go all the way to the other band. This observation is useful when projecting price targets.

  

  Calculation

  Bollinger Bands are displayed as three bands. The middle band is a normal moving average. In the following formula, "n" is the number of time periods in the moving average (e.g., 20 days).

  

  The upper band is the same as the middle band, but it is shifted up by the number of standard deviations (e.g., two deviations). In this next formula, "D" is the number of standard deviations.

  

  The lower band is the moving average shifted down by the same number of standard deviations (i.e., "D").

  

  Mr. Bollinger recommends using "20" for the number of periods in the moving average, calculating the moving average using the "simple" method (as shown in the formula for the middle band), and using 2 standard deviations. He has also found that moving averages of less then 10 periods do not work very well.

• Commodity Channel Index — CCI
  

  The Commodity Channel Index (CCI) measures the variation of a security's price from its statistical mean. High values show that prices are unusually high compared to average prices whereas low values indicate that prices are unusually low. Contrary to its name, the CCI can be used effectively on any type of security, not just commodities.

  The CCI was developed by Donald Lambert.

  There are two basic methods of interpreting the CCI: looking for divergences and as an overbought/oversold indicator.

  • Finding the divergences

    A divergence occurs when the security's prices are making new highs while the Commodity Channel Index is failing to surpass its previous highs. This classic divergence is usually followed by a correction in the security's price.

  • As an indicator of overbuying/overselling

    The Commodity Channel Index typically oscillates between ±100. To use the Commodity Channel Index as an overbought/oversold indicator, readings above +100 imply an overbought condition (and a pending price correction) while readings below -100 imply an oversold condition (and a pending rally).

  

  Calculation

  A complete explanation of the Commodity Channel Index calculation is beyond the scope of this book. The following are basic steps involved in the calculation:

  1. Add each period's high, low, and close and divide this sum by 3. This is the typical price .

  2. Calculate an n-period simple moving average of the typical prices computed in Step 1.

  3. For each of the prior n-periods, subtract today's Step 2 value from Step 1's value n days ago. For example, if you were calculating a 5-day CCI, you would perform five subtractions using today's Step 2 value.

  4. Calculate an n-period simple moving average of the absolute values of each of the results in Step 3.

  5. Multiply the value in Step 4 by 0.015.

  6. Subtract the value from Step 2 from the value in Step 1.

  7. Divide the value in Step 6 by the value in Step 5.

  Further details on the contents and interpretation of the Commodity Channel Index can be found in an article by Donald Lambert that appeared in the October 1980 issue of Commodities (now known as Futures ) Magazine.

• DeMarker — DeM
  

  This study is designed to function as an oscillator and helps to identify high and low risk buy and sell areas. Unlike REI which makes price comparisons every other bar, DeMarker evaluates price movement from one bar to the next. This oscillator uses an 8 bar average for smoothing price action. It is suggested to use both a short and long term version of this indicator. The long term version helps you get a fix on the long term trend of the current market environment. The short term version allows you to identify low risk entry points and to fine tune your entry within the context of the longer term trend.

  When the indicator falls below 30, the bullish price reversal should be expected. When the indicator rises above 70, the bearish price reversal should be expected.

  If you use periods of longer duration, when calculating the indicator, you'll be able to catch the long term market tendency. Indicators based on short periods let you enter the market at the point of the least risk and plan the time of transaction so that it falls in with the major trend.

  

  Calculation

  The value of the DeMarker for the "i" interval is calculated as follows:

  • The DeMax(i) is calculated: If high(i) > high(i-1) , then DeMax(i) = high(i)-high(i-1), otherwise DeMax(i) = 0

  • The DeMin(i) is calculated:
    If low(i) < low(i-1), then DeMin(i) = low(i-1)-low(i), otherwise DeMin(i) = 0

  • The value of the DeMarker is calculated as:
    DMark(i) = SMA(DeMax, N)/(SMA(DeMax, N)+SMA(DeMin, N))

  Where:
  SMA — Simple Moving Average ;
  N — the number of periods used in the calculation.

• Elder-rays
  

  Developed in 1989, the Elder Ray is an extremely accurate and effective means of identifying divergences between bull or bear power and prices and helping time the best trading opportunities.

  The Elder Ray index actually consists of two indicators:

  • "Bull Power" (Daily High - n period moving average)
  • "Bear Power" (Daily Low - n period moving average).

  Bull Power is used to measure the potential for the price to increase above the moving average, while Bear Power is used to measure the potential for the price to decrease below the moving average. Long positions are taken when the Bear Power is below zero and there is a bullish divergence while Short positions are assumed when the Bull Power is above zero and there is a bearish divergence.

  

• Envelopes
  

  An envelope is comprised of two moving averages. One moving average is shifted upward and the second moving average is shifted downward. Envelopes define the upper and lower boundaries of a security's normal trading range. A sell signal is generated when the security reaches the upper band whereas a buy signal is generated at the lower band. The optimum percentage shift depends on the volatility of the security--the more volatile, the larger the percentage. The logic behind envelopes is that overzealous buyers and sellers push the price to the extremes (i.e., the upper and lower bands), at which point the prices often stabilize by moving to more realistic levels. This is similar to the interpretation of Bollinger Bands.

  

  Calculation

  Envelopes are calculated by shifted moving averages. In the above example, one 25-day exponential moving average was shifted up 6% and another 25-day moving average was shifted down 6%.

• Force Index — FRC
  

  Developed by Dr. Alexander Elder, the Force Index combines price movements and volume to measure the market. Unmodified Force Index results can be rather erratic, better results are achieved by smoothing with an moving average. A 2-day exponential moving average of the Force Index may be used to track the strength of buyers and sellers in the short term while a 13-day exponential moving average better measures the strength of intermediate cycles.

  Force Index combines three essential pieces of market information – the direction of price change, its extent, and trading volume. It provides a new, practical way of using volume to make trading decisions.

  Force Index can be used raw, but it works better if you smooth it with a moving average. Force Index smoothed with a short MA helps pinpoint entry and exit points. Force Index smoothed with a long MA reveals major changes in the force of bulls and bears.

  A 2-day EMA of Force Index provides a minimal degree of smoothing. It is useful for finding entry points into the markets. It pays to buy when the 2-day EMA is negative and sell when it is positive, as long as you trade in the direction of the 13-day EMA of prices.

  A 13-day EMA of Force Index tracks longer term changes in the force of bulls and bears. When it crosses above its centerline, it shows the bulls are in control. When it turns negative, it shows that bears are in control. Divergences between 13-day EMA of Force Index and prices identify important turning points.”

  

  Calculation

  The Force index is calculated by subtracting yesterday's close from today's close, then multiplying by volume.

  FI:=(C-Ref(C,-1))*V;Mov(FI,13,E)

• Fractals
  

  All markets are characterized by the fact that on the most part the prices do not change too much, and only short periods of time (15–30 percent) account for trend changes. Most lucrative periods are usually the case when market prices change according to a certain trend.

  A Fractal is one of five indicators of Bill Williams' trading system, which allows to detect the bottom or the top.

  Fractal Technical Indicator it is a series of at least five successive bars, with the highest HIGH in the middle, and two lower HIGHs on both sides. The reversing set is a series of at least five successive bars, with the lowest LOW in the middle, and two higher LOWs on both sides, which correlates to the sell fractal. The fractals are have High and Low values and are indicated with the up and down arrows.

  The fractal needs to be filtrated with the use of Alligator. In other words, you should not close a buy transaction, if the fractal is lower than the Alligator's Teeth, and you should not close a sell transaction, if the fractal is higher than the Alligator's Teeth. After the fractal signal has been created and is in force, which is determined by its position beyond the Alligator's Mouth, it remains a signal until it gets attacked, or until a more recent fractal signal emerges.

  

  : All rights on these materials are reserved by MetaQuotes Software Corp. Copying or reprinting of these materials in whole or in part is prohibited.

• Gator Oscillator — Gator
• Ichimoku Kinko Hyo
  

  Ichomoku Kinko Hyo is a Japanese charting technique developed by a Japanese journalist who wrote under the name "Ichimoku Sanjin" prior to World War II. This study shows where a market is headed and provides entry and exit points.

  Ichimoku means "glance", Kinko translates "balance" or "equalibrium", and Hyo is Japanese for "chart".

  Ichimoku Kinko Hyo consists of the following lines:

  1. Tenkan Sen is the conversion line.

  2. Kijun Sen is the base line.

  3. Chikou Span is the lagging span.

  4. Senkou Span 1 is the first leading span.

  5. Senkou Span 2 is the second leading span.

  The Kumo, or Cloud, is the area between Senkou Span 1 and Senkou Span 2.

  

  Ichimoku analysis is similar to Moving Average analysis. Buy and sell signals are given by cross-overs. A bullish signal is issued when the Tenkan Sen crosses Kijun Sen from below. Conversely, a bearish signal is given when Tenkan Sen crosses Kijun Sen from above.

  Ichimoku rates the strength of bullish and bearish cross overs, too. A bullish crossover signal that occurs above the Kumo is a very strong signal. Similarly, a bearish cross over below the Kumo is considered strong.

  The Kumo indicate support and resistance levels.

• Market Facilitation Index — BW MFI
  

  Developed by Dr. Bill Williams, the Market Facilitation Index synthesizes both price and volume data in an effort to improve trading accuracy.

  The combination of lowered volume with a rising MFI is known as a "Fake." As there is no real foundation for change behind a stock except for market activity on the floor, the price eventually reverses itself.

  A "Fade" is when volume is down and the MFI is also down. In essence, the market is bored and interest in the stock fades. Expect the price to move in the opposite direction.

  When volume is up while the MFI is down, the condition is referred to as a "Squat." Think of the stock crouching down like a sprinter before a race. Movement after the squat gives a clue to future to direction.

  When volume and the MFI are both up, the situation is "Green." This is a strong signal to follow the trendline.

  

  Calculation

  The calculation for the MFI is:

  [High] - [Low] / Volume

• Momentum
  

  The Momentum Technical Indicator measures the amount that a security's price has changed over a given time span.

  There are basically two ways to use the Momentum indicator:

  • You can use the Momentum indicator as a trend-following oscillator similar to the MACD. Buy when the indicator bottoms and turns up and sell when the indicator peaks and turns down. You may want to plot a short-term (e.g., 9-period) moving average of the indicator to determine when it is bottoming or peaking.

    If the Momentum indicator reaches extremely high or low values (relative to its historical values), you should assume a continuation of the current trend. For example, if the Momentum indicator reaches extremely high values and then turns down, you should assume prices will probably go still higher. In either case, only trade after prices confirm the signal generated by the indicator (e.g., if prices peak and turn down, wait for prices to begin to fall before selling).

  • You can also use the Momentum indicator as a leading indicator. This method assumes that market tops are typically identified by a rapid price increase (when everyone expects prices to go higher) and that market bottoms typically end with rapid price declines (when everyone wants to get out). This is often the case, but it is also a broad generalization.

    As a market peaks, the Momentum indicator will climb sharply and then fall off-- diverging from the continued upward or sideways movement of the price. Similarly, at a market bottom, Momentum will drop sharply and then begin to climb well ahead of prices. Both of these situations result in divergences between the indicator and prices.

  

  Calculation

  Momentum is calculated as a ratio of today's price to the price several (N) periods ago.

  MOMENTUM = CLOSE(i)/CLOSE(i-N)*100

• Money Flow Index — MFI
  

  The Money Flow Index ("MFI") is a momentum indicator that measures the strength of money flowing in and out of a security. It is related to the Relative Strength Index , but where the RSI only incorporates prices, the Money Flow Index accounts for volume

  The interpretation of the Money Flow Index is as follows:

  • Look for divergence between the indicator and the price action. If the price trends higher and the MFI trends lower (or vice versa), a reversal may be imminent.

  • Look for market tops to occur when the MFI is above 80. Look for market bottoms to occur when the MFI is below 20.

  

  Calculation

  The Money Flow Index requires a series of calculations. First, the period's Typical Price is calculated.

  

  Next, Money Flow (not the Money Flow Index) is calculated by multiplying the period's Typical Price by the volume.

  

  If today's Typical Price is greater than yesterday's Typical Price, it is considered Positive Money Flow. If today's price is less, it is considered Negative Money Flow.

  Positive Money Flow is the sum of the Positive Money over the specified number of periods. Negative Money Flow is the sum of the Negative Money over the specified number of periods.

  The Money Ratio is then calculated by dividing the Positive Money Flow by the Negative Money Flow.

  

  Finally, the Money Flow Index is calculated using the Money Ratio

• Moving Average — MA
  

  A Moving Average is an indicator that shows the average value of a security's price over a period of time. When calculating a moving average, a mathematical analysis of the security's average value over a predetermined time period is made. As the security's price changes, its average price moves up or down.

  There are five popular types of moving averages: simple (also referred to as arithmetic), exponential, triangular, variable, and weighted. Moving averages can be calculated on any data series including a security's open, high, low, close, volume, or another indicator. A moving average of another moving average is also common.

  The only significant difference between the various types of moving averages is the weight assigned to the most recent data. Simple moving averages apply equal weight to the prices. Exponential and weighted averages apply more weight to recent prices. Triangular averages apply more weight to prices in the middle of the time period. And variable moving averages change the weighting based on the volatility of prices

  The most popular method of interpreting a moving average is to compare the relationship between a moving average of the security's price with the security's price itself. A buy signal is generated when the security's price rises above its moving average and a sell signal is generated when the security's price falls below its moving average.

  

  This type of moving average trading system is not intended to get you in at the exact bottom nor out at the exact top. Rather, it is designed to keep you in line with the security's price trend by buying shortly after the security's price bottoms and selling shortly after it tops.

  The critical element in a moving average is the number of time periods used in calculating the average. When using hindsight, you can always find a moving average that would have been profitable (using a computer, I found that the optimum number of months in the preceding chart would have been 43). The key is to find a moving average that will be consistently profitable. The most popular moving average is the 39-week (or 200-day) moving average. This moving average has an excellent track record in timing the major (long-term) market cycles.

  The length of a moving average should fit the market cycle you wish to follow. For example if you determine that a security has a 40-day peak to peak cycle, the ideal moving average length would be 21 days calculated using the following formula:

  

  You can convert a daily moving average quantity into a weekly moving average quantity by dividing the number of days by 5 (e.g., a 200-day moving average is almost identical to a 40-week moving average). To convert a daily moving average quantity into a monthly quantity, divide the number of days by 21 (e.g., a 200-day moving average is very similar to a 9-month moving average, because there are approximately 21 trading days in a month).

  Moving averages can also be calculated and plotted on indicators. The interpretation of an indicator's moving average is similar to the interpretation of a security's moving average: when the indicator rises above its moving average, it signifies a continued upward movement by the indicator; when the indicator falls below its moving average, it signifies a continued downward movement by the indicator.

  Indicators which are especially well-suited for use with moving average penetration systems include the MACD, Price ROC, Momentum, and Stochastics.

  Some indicators, such as short-term Stochastics, fluctuate so erratically that it is difficult to tell what their trend really is. By erasing the indicator and then plotting a moving average of the indica-tor, you can see the general trend of the indicator rather than its day-to-day fluctuations.

  Whipsaws can be reduced, at the expense of slightly later signals, by plotting a short-term moving average (e.g., 2-10 day) of oscillating indicators such as the 12-day ROC, Stochastics, or the RSI. For example, rather than selling when the Stochastic Oscillator falls below 80, you might sell only when a 5-period moving average of the Stochastic Oscillator falls below 80.

  Calculation

  Simple A simple, or arithmetic, moving average is calculated by adding the closing price of the security for a number of time periods (e.g., 12 days) and then dividing this total by the number of time periods. The result is the average price of the security over the time period. Simple moving averages give equal weight to each daily price.

  

  Where:

  

  Exponential

  An exponential (or exponentially weighted) moving average is calculated by applying a percentage of today's closing price to yesterday's moving average value. Exponential moving averages place more weight on recent prices.

  

  Because most investors feel more comfortable working with time periods, rather than with percentages, the exponential percentage can be converted into an approximate number of days. For example, a 9% moving average is equal to a 21.2 time period (rounded to 21) exponential moving average.

  The formula for converting exponential percentages to time periods is:

  

  You can use the above formula to determine that a 9% moving average is equivalent to a 21-day exponential moving average:

  

  The formula for converting time periods to exponential percentages is:

  

  You can use the above formula to determine that a 21-day exponential moving average is actually a 9% moving average:

  

  Triangular

  Triangular moving averages place the majority of the weight on the middle portion of the price series. They are actually double-smoothed simple moving averages. The periods used in the simple moving averages varies depending on if you specify an odd or even number of time periods.

  The following steps explain how to calculate a 12-period triangular moving average.

  1. Add 1 to the number of periods in the moving average (e.g., 12 plus 1 is 13).

  2. Divide the sum from Step #1 by 2 (e.g., 13 divided by 2 is 6.5).

  3. If the result of Step #2 contains a fractional portion, round the result up to the nearest integer (e.g., round 6.5 up to 7).

  4. Using the value from Step #3 (i.e., 7), calculate a simple moving average of the closing prices (i.e., a 7-period simple moving average).

  5. Again using the value from Step #3 (i.e., 7) calculate a simple moving average of the moving average calculated in Step #4 (i.e., a moving average of a moving average).

  Variable

  A variable moving average is an exponential moving average that automatically adjusts the smoothing percentage based on the volatility of the data series. The more volatile the data, the more sensitive the smoothing constant used in the moving average calculation. Sensitivity is increased by giving more weight given to the current data.

  Most moving average calculation methods are unable to compensate for trading range versus trending markets. During trading ranges (when prices move sideways in a narrow range) shorter term moving averages tend to produce numerous false signals. In trending markets (when prices move up or down over an extended period) longer term moving averages are slow to react to reversals in trend. By automatically adjusting the smoothing constant, a variable moving average is able to adjust its sensitivity, allowing it to perform better in both types of markets.

  A variable moving average is calculated as follows:

  

  Where:

  

  The variable moving average was defined by Tushar Chande in an article that appeared in Technical Analysis of Stocks and Commodities in March, 1992.

  Weighted

  A weighted moving average is designed to put more weight on recent data and less weight on past data. A weighted moving average is calculated by multiplying each of the previous day's data by a weight. The following table shows the calculation of a 5-day weighted moving average.

  The weight is based on the number of days in the moving average. In the above example, the weight on the first day is 1.0 while the value on the most recent day is 5.0. This gives five times more weight to today's price than the price five days ago.

• Moving Average Convergence/Divergence — MACD
  

  The MACD ("Moving Average Convergence/Divergence") is a trend following momentum indicator that shows the relationship between two moving averages of prices. The MACD was developed by Gerald Appel.

  The MACD is the difference between a 26-day and 12-day exponential moving average. A 9-day exponential moving average, called the "signal" (or "trigger") line is plotted on top of the MACD to show buy/sell opportunities. (Appel specifies exponential moving averages as percentages. Thus, he refers to these three moving averages as 7.5%, 15%, and 20% respectively.)

  The MACD proves most effective in wide-swinging trading markets. There are three popular ways to use the MACD: crossovers, overbought/oversold conditions, and divergences.

  Crossovers

  The basic MACD trading rule is to sell when the MACD falls below its signal line. Similarly, a buy signal occurs when the MACD rises above its signal line. It is also popular to buy/sell when the MACD goes above/below zero.

  Overbought/Oversold Conditions

  The MACD is also useful as an overbought/oversold indicator. When the shorter moving average pulls away dramatically from the longer moving average (i.e., the MACD rises), it is likely that the security price is overextending and will soon return to more realistic levels. MACD overbought and oversold conditions exist vary from security to security.

  Divergences

  A indication that an end to the current trend may be near occurs when the MACD diverges from the security. A bearish divergence occurs when the MACD is making new lows while prices fail to reach new lows. A bullish divergence occurs when the MACD is making new highs while prices fail to reach new highs. Both of these divergences are most significant when they occur at relatively overbought/oversold levels.

  

  Calculation

  The MACD is calculated by subtracting the value of a 26-day exponential moving average from a 12-day exponential moving average. A 9-day dotted exponential moving average of the MACD (the "signal" line) is then plotted on top of the MACD.

  Moving Average of Oscillator

  Moving Average of Oscillator is the difference between the oscillator and oscillator smoothing. In this case, Moving Average Convergence/Divergence base-line is used as the oscillator, and the signal line is used as the smoothing.

• Moving Average of Oscillator — OsMA
• On Balance Volume — OBV
  

  On Balance Volume is a running total of volume. It shows if volume is flowing into or out of a security. When the security closes higher than the previous close, all of the day's volume is considered up-volume. When the security closes lower than the previous close, all of the day's volume is considered down-volume.

  A full explanation of OBV is beyond the scope of this book. If you would like further information on OBV analysis, I recommend that you read Granville's book, New Strategy of Daily Stock Market Timing for Maximum Profits .

  The basic assumption, regarding OBV analysis, is that OBV changes precede price changes. The theory is that smart money can be seen flowing into the security by a rising OBV. When the public then moves into the security, both the security and the OBV will surge ahead.

  If the security's price movement precedes OBV movement, a "non-confirmation" has occurred. Non-confirma-tions can occur at bull market tops (when the security rises without, or before, the OBV) or at bear market bottoms (when the security falls without, or before, the OBV).

  The OBV is in a rising trend when each new peak is higher than the previous peak and each new trough is higher than the previous trough. Likewise, the OBV is in a falling trend when each successive peak is lower than the previous peak and each successive trough is lower than the previous trough. When the OBV is moving sideways and is not making successive highs and lows, it is in a doubtful trend.

  

  Once a trend is established, it remains in force until it is broken. There are two ways in which the OBV trend can be broken. The first occurs when the trend changes from a rising trend to a falling trend, or from a falling trend to a rising trend.

  The second way the OBV trend can be broken is if the trend changes to a doubtful trend and remains doubtful for more than three days. Thus, if the security changes from a rising trend to a doubtful trend and remains doubtful for only two days before changing back to a rising trend, the OBV is consid-ered to have always been in a rising trend.

  When the OBV changes to a rising or falling trend, a "breakout" has occurred. Since OBV breakouts normally precede price breakouts, investors should buy long on OBV upside breakouts. Likewise, investors should sell short when the OBV makes a downside breakout. Positions should be held until the trend changes (as explain-ed in the preceding paragraph).

  This method of analyzing On Balance Volume is designed for trading short-term cycles. According to Granville, investors must act quickly and decisively if they wish to profit from short-term OBV analysis.

  Calculation

  On Balance Volume is calculated by adding the day's volume to a cumulative total when the security's price closes up, and subtracting the day's volume when the security's price closes down.

  If today's close is greater than yesterday's close then:

  

  If today's close is less than yesterday's close then:

  

  If today's close is equal to yesterday's close then:

  
• Parabolic SAR
  

  The Parabolic Time/Price System, developed by Welles Wilder, is used to set trailing price stops and is usually referred to as the "SAR" (stop-and-reversal). This indicator is explained thoroughly in Wilder's book, New Concepts in Technical Trading Systems .

  The Parabolic SAR provides excellent exit points. You should close long positions when the price falls below the SAR and close short positions when the price rises above the SAR.

  If you are long (i.e., the price is above the SAR), the SAR will move up every day, regardless of the direction the price is moving. The amount the SAR moves up depends on the amount that prices move.

  

  You should be long when the SAR is below prices and short when it is above prices.

  The Parabolic SAR is plotted as shown in Wilder's book. Each SAR stop level point is displayed on the day in which it is in effect. Note that the SAR value is today's, not tomorrow's stop level.

  Calculation

  SAR(i) = SAR(i-1)+ACCELERATION*(EPRICE(i-1)-SAR(i-1))

  Where:

  SAR(i-1) — is the value of the indicator on the previous bar;
  ACCELERATION — is the acceleration factor;
  EPRICE(i-1) — is the highest (lowest) price for the previous period (EPRICE=HIGH for long positions and EPRICE=LOW for short positions).

  It is beyond the scope of this book to explain the calculation of the Parabolic SAR. Refer to Wilder's book New Concepts in Technical Trading , for detailed calculation information.

• Relative Strenght Index — RSI
  

  The Relative Strength Index ("RSI") is a popular oscillator. It was first introduced by Welles Wilder in an article in Commodities (now known as Futures ) Magazine in June, 1978. Step-by-step instructions on calculating and interpreting the RSI are also provided in Mr. Wilder's book, New Concepts in Technical Trading Systems .

  The name "Relative Strength Index" is slightly misleading as the RSI does not compare the relative strength of two securities, but rather the internal strength of a single security. A more appropriate name might be "Internal Strength Index." Relative strength charts that compare two market indices, which are often referred to as Comparative Relative Strength .

  When Wilder introduced the RSI, he recommended using a 14-day RSI. Since then, the 9-day and 25-day RSIs have also gained popularity. Because you can vary the number of time periods in the RSI calculation, I suggest that you experiment to find the period that works best for you. (The fewer days used to calculate the RSI, the more volatile the indicator.)

  The RSI is a price-following oscillator that ranges between 0 and 100. A popular method of analyzing the RSI is to look for a divergence in which the security is making a new high, but the RSI is failing to surpass its previous high. This divergence is an indication of an impending reversal. When the RSI then turns down and falls below its most recent trough, it is said to have completed a "failure swing." The failure swing is considered a confirmation of the impending reversal.

  In Mr. Wilder's book, he discusses five uses of the RSI in analyzing commodity charts. These methods can be applied to other security types as well.

  • Tops and Bottoms.

    The RSI usually tops above 70 and bottoms below 30. It usually forms these tops and bottoms before the underlying price chart.

  • Chart Formations.

    The RSI often forms chart patterns such as head and shoulders (page 215) or triangles (page 216) that may or may not be visible on the price chart.

  • Failure Swings .

    (also known as support or resistance penetrations or breakouts). This is where the RSI surpasses a previous high (peak) or falls below a recent low (trough).

  • Support and Resistance.

    The RSI shows, sometimes more clearly than price themselves, levels of support and resistance.

  • Divergences.

    As discussed above, divergences occur when the price makes a new high (or low) that is not confirmed by a new high (or low) in the RSI. Prices usually correct and move in the direction of the RSI.

  For additional information on the RSI, refer to Mr. Wilder's book.

  

  Calculation

  The RSI is a fairly simple formula, but is difficult to explain without pages of examples. Refer to Wilder's book for additional calculation information. The basic formula is:

  

  Where:

  
• Relative Vigor Index — RVI
  

  In 1972, Jim Waters and Larry Williams published a description of their A/D Oscillator. In this case, A/D means accumulation/distribution rather than the usual advance/decline.

  The Relative Vigor Index (RVI) is appropriate for the occasion because it uses concepts dating back to the beginning of the magazine and also uses modern filter and digital signal processing theory to realize those concepts as a practical and useful indicator. Just like the magazine, the RVI merges the old concepts with the new technologies.

  

  Calculation

  The basic idea of the RVI is that the prices tend to close higher than they open in up markets and tend to close lower than they open in down markets. The vigor of the move is thus established by where the prices reside at the end of the day. To make the index normalized to the daily trading range, the change of price is divided by the maximum range of prices for the day. Thus, the basic equation for the RVI is:

• Standard Deviation
  

  Standard Deviation is a statistical measure of volatility. Standard Deviation is typically used as a component of other indicators, rather than as a stand-alone indicator. For example, Bollinger Bands are calculated by adding a security's Standard Deviation to a moving average.

  High Standard Deviation values occur when the data item being analyzed (e.g., prices or an indicator) is changing dramatically. Similarly, low Standard Deviation values occur when prices are stable.

  Many analysts feel that major tops are accompanied with high volatility as investors struggle with both euphoria and fear. Major bottoms are expected to be calmer as investors have few expectations of profits.

  

  Calculation

  Where:

  

  Standard Deviation is derived by calculating an n-period simple moving average of the data item (i.e., the closing price or an indicator), summing the squares of the difference between the data item and its moving average over each of the preceding n-time periods, dividing this sum by n, and then calculating the square root of this result.

• Stochastic Oscillator
  

  The Stochastic Oscillator is displayed as two lines. The main line is called "%K." The second line, called "%D," is a moving average of %K. The %K line is usually displayed as a solid line and the %D line is usually displayed as a dotted line.

  There are several ways to interpret a Stochastic Oscillator. Three popular methods include:

  1. Buy when the Oscillator (either %K or %D) falls below a specific level (e.g., 20) and then rises above that level. Sell when the Oscillator rises above a specific level (e.g., 80) and then falls below that level.

  2. Buy when the %K line rises above the %D line and sell when the %K line falls below the %D line.

  3. Look for divergences . For example, where prices are making a series of new highs and the Stochastic Oscillator is failing to surpass its previous highs.

  

  Calculation

  The Stochastic Oscillator has four variables:

  1. %K Periods.
     This is the number of time periods used in the stochastic calculation.

  2. %K Slowing Periods.
     This value controls the internal smoothing of %K. A value of 1 is considered a fast stochastic; a value of 3 is considered a slow stochastic.

  3. %D Periods.
     This is the number of time periods used when calculating a moving average of %K. The moving average is called "%D" and is usually displayed as a dotted line on top of %K.

  4. %D Method.
     The method (i.e., Exponential, Simple, Time Series, Triangular, Variable, or Weighted) that is used to calculate %D.

  The formula for %K is:

  

  For example, to calculate a 10-day %K, first find the security's highest-high and lowest-low over the last 10 days. As an example, let's assume that during the last 10 days the highest-high was 46 and the lowest-low was 38--a range of 8 points. If today's closing price was 41, %K would be calculated as:

  

  The 37.5% in this example shows that today's close was at the level of 37.5% relative to the security's trading range over the last 10 days. If today's close was 42, the Stochastic Oscillator would be 50%. This would mean that that the security closed today at 50%, or the mid-point, of its 10-day trading range.

  The above example used a %K Slowing Period of 1-day (no slowing). If you use a value greater than one, you average the highest-high and the lowest-low over the number of %K Slowing Periods before performing the division.

  A moving average of %K is then calculated using the number of time periods specified in the %D Periods. This moving average is called %D.

  The Stochastic Oscillator always ranges between 0% and 100%. A reading of 0% shows that the security's close was the lowest price that the security has traded during the preceding x-time periods. A reading of 100% shows that the security's close was the highest price that the security has traded during the preceding x-time periods.

• Volume
  

  Volume is simply the number of shares (or contracts) traded during a specified time frame (e.g., hour, day, week, month, etc). The analysis of volume is a basic yet very important element of technical analysis. Volume provides clues as to the intensity of a given price move.

  Low volume levels are characteristic of the indecisive expectations that typically occur during consolidation periods (i.e., periods where prices move sideways in a trading range). Low volume also often occurs during the indecisive period during market bottoms.

  High volume levels are characteristic of market tops when there is a strong consensus that prices will move higher. High volume levels are also very common at the beginning of new trends (i.e., when prices break out of a trading range). Just before market bottoms, volume will often increase due to panic-driven selling.

  Volume can help determine the health of an existing trend. A healthy up-trend should have higher volume on the upward legs of the trend, and lower volume on the downward (corrective) legs. A healthy downtrend usually has higher volume on the downward legs of the trend and lower volume on the upward (corrective) legs.

  
• Williams' Percent Range — %R
  

  Williams' %R (pronounced "percent R") is a momentum indicator that measures overbought/oversold levels. Williams' %R was developed by Larry Williams.

  The interpretation of Williams' %R is very similar to that of the Stochastic Oscillator (page 244) except that %R is plotted upside-down and the Stochastic Oscillator has internal smoothing.

  To display the Williams' %R indicator on an upside-down scale, it is usually plotted using negative values (e.g., -20%). For the purpose of analysis and discussion, simply ignore the negative symbols.

  Readings in the range of 80 to 100% indicate that the security is oversold while readings in the 0 to 20% range suggest that it is overbought.

  As with all overbought/oversold indicators, it is best to wait for the security's price to change direction before placing your trades. For example, if an overbought/oversold indicator (such as the Stochastic Oscillator or Williams' %R) is showing an overbought condition, it is wise to wait for the security's price to turn down before selling the security. (The MACD is a good indicator to monitor change in a security's price.) It is not unusual for overbought/oversold indicators to remain in an overbought/oversold condition for a long time period as the security's price continues to climb/fall. Selling simply because the security appears overbought may take you out of the security long before its price shows signs of deterioration.

  An interesting phenomena of the %R indicator is its uncanny ability to anticipate a reversal in the underlying security's price. The indicator almost always forms a peak and turns down a few days before the security's price peaks and turns down. Likewise, %R usually creates a trough and turns up a few days before the security's price turns up.

  

  Calculation

  TBelow is the formula of the %R indicator calculation, which is very similar to the Stochastic Oscillator formula:

  
• Zig Zag
  

  The Zig Zag indicator filters out changes in an underlying plot (e.g., a security's price or another indicator) that are less than a specified amount. The Zig Zag indicator only shows significant changes.

  The Zig Zag indicator is used primarily to help you see changes by punctuating the most significant reversals.

  It is very important to understand that the last "leg" displayed in a Zig Zag chart can change based on changes in the underlying plot (e.g., prices). This is the only indicator in this book where a change in the security's price can change a previous value of the indicator. Since the Zig Zag indicator can adjust its values based on subsequent changes in the underlying plot, it has perfect hindsight into what prices have done. Please don't try to create a trading system based on the Zig Zag indicator--its hindsight is much better than its foresight!

  In addition to identifying significant prices reversals, the Zig Zag indicator is also useful when doing Elliot Wave counts .