In technical analysis, lines and various geometric figures to be plotted in price charts or in indicator charts are called line studies. Those include the Support/Resistance Lines and Trend Lines described above, along with:

Fibonacci Instruments [Top]

Leonardo Fibonacci was an important mathematician who was born in Italy around the year 1170. It is rumored that Fibonacci discovered the relationship of what are now referred to as Fibonacci numbers while studying the Great Pyramid of Giza in Egypt.

Fibonacci numbers are a sequence of numbers in which each successive number is the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, etc. These numbers possess an intriguing number of interrelationships, such as the fact that any given number is approximately 1.618 times the preceding number and any given number is approximately 0.618 times the following number.

These numbers are interrelated with a series of curious correlations. For example, each number in the series is approximately 1.618 times more than the previous one, and each preceding one makes approximately 0.618 of the consequent one.

There are several widespread instruments of technical analysis based on Fibonacci Numbers. The general interpretation principle of these instruments consists in the fact that, when the price approximates to lines built with their help, the changes in trend development should be expected.

• Fibonacci Arcs
  

  Fibonacci Arcs are used to draw circular arcs that are probable values of support and resistance based on a market range.

  

  They are displayed by first drawing a trend line between two extreme points, for example, a trough and opposing peak. Three arcs are then drawn, centered on the second extreme point, so they intersect the trend line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%. The interpretation of Fibonacci Arcs involves anticipating support and resistance as prices approach the arcs.

  A common technique is to display Fibonacci Arcs and Fibonacci Fan Lines and to anticipate support/resistance at the points where the Fibonacci studies cross.
  
  

• Fibonacci Fan
  

  Fibonacci Fan Lines are displayed by drawing a trend line between two extreme points, for example, a trough and opposing peak. Then an "invisible" vertical line is drawn through the second extreme point. Three trend lines are then drawn from the first extreme point so they pass through the invisible vertical line at the Fibonacci levels of 38.2%, 50.0%, and 61.8%.

  Fibonacci Fan is a charting technique consisting of three diagonal lines that use Fibonacci ratios to help identify key levels of support/resistance.

  
  
  

• Fibonacci Retracement
  

  Fibonacci Retracements are displayed by first drawing a trend line between two extreme points, for example, a trough and opposing peak. A series of nine horizontal lines are drawn intersecting the trend line at the Fibonacci levels of 0.0%, 23.6%, 38.2%, 50%, 61.8%, 100%, 161.8%, 261.8%, and 423.6%. (Some of the lines will probably not be visible because they will be off the scale.)

  After a significant price move (either up or down), prices will often retrace a significant portion (if not all) of the original move. As prices retrace, support/resistance levels often occur at or near the Fibonacci Retracement levels.

  
  
  

• Fibonacci Time Zones
  

  Fibonacci Time Zones are a series of vertical lines that are spaced at the Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc. The first line is placed at an extreme point on the chart and the lines that follow are spaced at increasingly wider intervals in accord with the Fibonacci sequence. Interpretation of Fibonacci Time Zones involves looking for significant changes in price at or near the vertical lines.

  To build this instrument, it is necessary to specify two points to determine the length of a unit interval. All other lines are built on base of this unit interval according to Fibonacci Numbers.

  

  Note that Time Zones are most applicable to a long-term analysis of price action and are probably of limited value when studying short-term charts.Users inexperienced with Fibonacci Studies should consider this type of analysis only when viewing charts that span multiple years.
  

• Fibonacci Expansion
  

  Fibonacci expansion targets require a wave and a correction of that wave, and assume the following (projected) wave will conclude in the same direction of the first wave. They require 3 points to calculate: A completed wave high and low, and a correction of the wave from which the point is taken for the expansion projection. If the expansion targets are not realized, then the wave count is brought into question.

  The Fibonacci retracement targets require the correct identification of the current trend. Keep in mind that trend is "time frame dependent." The yearly, monthly, weekly, daily, and hourly trends can all be in conflict. Therefore, it is important to identify time frame when identifying the trend, particularly when using the retracement levels.

  

  Since the trend in different time frames can be in conflict, it's useful to look at targets from different time frames and different directions. I.e., an expansion level from a shorter time frame can find confluence with a retracement in a longer time frame (or visa versa). In addition, multiple retracements (corrections) from different time frames can also add confluence, for instance, when a 61.8% retracement on a shorter time frame closely matches a 38.2% retracement on a longer time frame. The same is true with expansion targets (impulses) from different time frames. These confluence areas support each other, and give the targets increased credibility. When there are other supporting areas on the charts, i.e., moving averages and congestion areas, then the credibility of the target becomes significant.

  Looking at both techniques, you could say for every A-B-C move, after the initial “A” move: the “B” move is projected using a retracement and the “C” move is projected with an expansion.
  

• Fibonacci Channel
  

  Fibonacci Channels are drawn by consecutive parallel trend lines based on a user selected channel range. The intervals are then calculated using fibonacci values from the selected range, beginning with 0.618-fold size of the channel, then 1.000-fold, 1.618-fold, 2.618-fold, 4.236-fold, etc. As soon as the fifth wave finishes, correction in the direction opposite to the trend can be expected.

  
  
  

Gann Instruments [Top]

W. D. Gann (1878-1955) designed several unique techniques for studying price charts. Central to Gann's techniques was the use of geometric angles in conjunction with time and price.

Gann believed that specific geometric patterns and angles had unique characteristics that could be used to predict price action. All of Gann's techniques require that equal time and price intervals be used on the charts, so that a rise/run of 1 x 1 will always equal a 45 degree angle. Gann believed that the ideal balance between time and price exists when prices rise or fall at a 45 degree angle relative to the time axis. This is also called a 1 x 1 angle (i.e., prices rise one price unit for each time unit).

• Gann Fan
  

  Gann watched for important tops and bottoms to form on a daily, weekly, or monthly chart and drew his angles from these changes in trend. When the trend is up and the price stays in the space above an ascending angle without breaking below it, the market is strong; when the trend is down and the price remains below a descending angle without breaking above it, the market is weak. The market shows its relative strength or weakness according to the angle it is above or below.

  Gann Angles are drawn between a significant bottom and top (or vice versa) at various angles. Deemed the most important by Gann, the 1 x 1 trend line signifies a bull market if prices are above the trend line or a bear market if below.

  The ideal balance between time and price exists when prices move identically to time, which occurs when the Gann angle is at 45 degrees. In total, there are nine different Gann angles that are important for identifying trend lines and market actions. When one of these trend lines is broken, the following angle will provide support or resistance with the 1 x 1 being the most important:

  • 1 x 8 - 82.5 degrees
  • 1 x 4 - 75 degrees
  • 1 x 3 - 71.25 degrees
  • 1 x 2 - 63.75 degrees
  • 1 x 1 - 45 degrees
  • 2 x 1 - 26.25 degrees
  • 3 x 1 - 18.75 degrees
  • 4 x 1 - 15 degrees
  • 8 x 1 - 7.5 degrees

  

  Note that in order for the rise/run values (e.g., 1 x 1, 1 x 8, etc.) to match the actual angles (in degrees), the x- and y-axes must have equally spaced intervals. This means that one unit on the x-axis (i.e., hour, day, week, month, etc.) must be the same distance as one unit on the y-axis. The easiest way to calibrate the chart is make sure that a 1 x 1 angle produces a 45 degree angle. Gann observed that each of the angles can provide support and resistance depending on the trend. For example, during an up-trend the 1 x 1 angle tends to provide major support. A major reversal is signaled when prices fall below the 1 x 1 angled trend line.

  According to Gann, prices should then be expected to fall to the next trend line (i.e., the 2 x 1 angle). In other words, as one angle is penetrated, expect prices to move and consolidate at the next angle. Gann developed several techniques for studying market action.
  
  

• Gann Line
  

  Gann believed that the ideal balance between time and price exists when prices rise or fall at a 45 degree angle relative to the time axis. This is also called a 1 x 1 angle (i.e., prices rise one price unit for each time unit).

  If prices are above the ascending line, the market holds bull directions. If prices hold below the descending line, the market is characterized as a bear one.

  On intersection of Gann Line usually signals of the basic trend break. If prices go down to this line during an ascending trend, time and price become fully balanced. The further intersection of Gann Line is the evidence of breaking of this balance and possible changing the trend.

  

  Note that it is necessary to define two points for building a Gann Line.
  

• Gann Grid
  

  Gann Angles are drawn between a significant bottom and top (or vice versa) at various angles. Deemed the most important by Gann, the 1 x 1 trend line signifies a bull market if prices are above the trend line or a bear market if below.

  According to Gann, prices should then be expected to fall to the next trend line (i.e., the 2 x 1 angle). In other words, as one angle is penetrated, expect prices to move and consolidate at the next angle. Gann developed several techniques for studying market action.

  

  Note that t o build a Gann Grid, it is necessary to define two points determining sizes of cells.
  

Other analytical instruments [Top]

There are line studies being largely used in technical analysis and helping to define channels and trend changes. These instruments are:

• Linear Regression Channel
  

  Linear Regression Channel consists of two parallel lines, equidistant up and down from the line of linear regression trend. The distance between frame of the channel and regression line equals to the value of maximum close price deviation from the regression line. All price changes take place within Regression Channel, where the lower frame works as support line , and the upper one does as resistance line . Prices usually exceed the channel frames for a short time. If they keep outside of the channel frames for a longer time than usually, it forecasts the possibility of trend turn.

  

  There are two conventional interpretations for the linear regression line:

  The first interpretation is to use the linear regression as the overall trendline for that given period. If the line is positive, it may suggest a buying opportunity, whereas a turn downwards suggests one may consider selling the financial instrument. Price divergences below the line indicate a possible buying opportunity, for the market is oversold, while divergences above the line indicate the market is potentially overbought. Linear regression will work best when the period being studied is similar to the cycle length or typical trend length of the security in question.

  A second interpretation is to construct a Linear Regression Channel, consisting of two parallel lines at fixed distances above and below the Linear Regression Line. These lines can be used as support and resistance lines, which are used to watch the battle between buyers and sellers.

  Support and resistance lines are drawn as the upper and lower limits of a trading range, whereby the support line is the bottom line, and is the point at which "bulls" will not let the price fall below, and the resistance line is the top line, the point above which the "bears" will not let the price rise above.

  Conventionally, a breakout above resistance or below support indicates that there is either a) some news about the company which justifies recreating the upper and lower trading limits or b) there is about to be a correction towards the range as trader's are hesitant about the stock's new value.

  Using the Linear Regression Channel can assist in finding support and resistance levels from the Linear Regression.
  

• Equidistant Channel
  

  Equidistant Channel , this new line study represents two parallel trend lines connecting extreme maximum and minimum close prices.

  
  
  

• Standard Deviation Channel
  

  Standard Deviation Channels are calculated by plotting two parallel lines above and below an x-period linear regression trendline. The lines are plotted x standard deviations away from the Linear Regression Trendline.

  Markets tend to have an equilibrium point (i.e., a point towards which prices tend to be drawn). Linear regression analysis is helpful in determining where this "balancing point" lies. On the other hand, standard deviation analysis is helpful in determining where the "extremes" lie.

  Elementary statistical analysis states that approximately 67% of future price movement should be contained within one standard deviation and approximately 95% within two standard deviations. However, this assumes random, trendless data. Since most markets show overwhelming evidence of non-random, trending behavior, these 67% and 95% values are not as accurate. Standard Deviation channels, however, incorporate the trend (as measured by the middle linear regression plot). Therefore, they provide a trend-biased assessment of expected price movement.

  

  Note that Standard Deviation Channels can be used to enhance several types of technical analysis techniques. Here are some ideas:

  • Validate candlestick patterns : Enter long on bullish engulfing lines only if they form below the bottom channel line.
  • Validate overbought/oversold signals : Close long (or enter short) when the Stochastic falls below 80, volume is above average, and prices have recently fallen below the top channel line.
  • Validate support/resistance breakouts : If prices have broken above a long-term resistance level, yet volume is suspiciously light, wait until the prices break above the upper channel on above average volume.

  
  

• Andrews` Pitchfork
  

  Andrews' Pitchfork is an instrument consisting of three parallel Trend Lines. This instrument was developed by Dr. Alan Andrews.

  Interpretation of Andrews' Pitchfork is based on standard rules of interpretation of support and resistance lines.

  

  The The first trendline begins at the left-most point selected (either a major peak or trough) and is drawn so it passes directly between the two right-most points. This line is the "handle" of the pitchfork. The second and third trendlines are then drawn beginning at the two right-most points (a major peak and a major trough) and are drawn parallel to the first line. These lines are the "tines" of the pitchfork.
  

• Dow Theory
  

  In 1897, Charles Dow developed two broad market averages. The "Industrial Average" included 12 blue-chip stocks and the "Rail Average" was comprised of 20 railroad enterprises. These are now known as the Dow Jones Industrial Average and the Dow Jones Transportation Average.

  The Dow Theory resulted from a series of articles published by Charles Dow in The Wall Street Journal between 1900 and 1902. The Dow Theory is the common ancestor to most principles of modern technical analysis.

  Interestingly, the Theory itself originally focused on using general stock market trends as a barometer for general business conditions. It was not originally intended to forecast stock prices. However, subsequent work has focused almost exclusively on this use of the Theory.

  Interpretation

  The Dow Theory comprises six assumptions:

  1. The Averages Discount Everything.

  An individual stock's price reflects everything that is known about the security. As new information arrives, market participants quickly disseminate the information and the price adjusts accordingly. Likewise, the market averages discount and reflect everything known by all stock market participants.

  2. The Market Is Comprised of Three Trends.

  At any given time in the stock market, three forces are in effect: the Primary trend, Secondary trends, and Minor trends.

  The Primary trend can either be a bullish (rising) market or a bearish (falling) market. The Primary trend usually lasts more than one year and may last for several years. If the market is making successive higher-highs and higher-lows the primary trend is up. If the market is making successive lower-highs and lower-lows, the primary trend is down.

  Secondary trends are intermediate, corrective reactions to the Primary trend. These reactions typically last from one to three months and retrace from one-third to two-thirds of the previous Secondary trend. The following chart shows a Primary trend (Line "A") and two Secondary trends ("B" and "C").

  

  Minor trends are short-term movements lasting from one day to three weeks. Secondary trends are typically comprised of a number of Minor trends. The Dow Theory holds that, since stock prices over the short-term are subject to some degree of manipulation (Primary and Secondary trends are not), Minor trends are unimportant and can be misleading.

  3. Primary Trends Have Three Phases.

  The Dow Theory says that the First phase is made up of aggressive buying by informed investors in anticipation of economic recovery and long-term growth. The general feeling among most investors during this phase is one of "gloom and doom" and "disgust." The informed investors, realizing that a turnaround is inevitable, aggressively buy from these distressed sellers.

  The Second phase is characterized by increasing corporate earnings and improved economic conditions. Investors will begin to accumulate stock as conditions improve.

  The Third phase is characterized by record corporate earnings and peak economic conditions. The general public (having had enough time to forget about their last "scathing") now feels comfortable participating in the stock market--fully convinced that the stock market is headed for the moon. They now buy even more stock, creating a buying frenzy. It is during this phase that those few investors who did the aggressive buying during the First phase begin to liquidate their holdings in anticipation of a downturn.

  The following chart of the Dow Industrials illustrates these three phases during the years leading up to the October 1987 crash.

  

  In anticipation of a recovery from the recession, informed investors began to accumulate stock during the First phase (box "A"). A steady stream of improved earnings reports came in during the Second phase (box "B"), causing more investors to buy stock. Euphoria set in during the Third phase (box "C"), as the general public began to aggressively buy stock.

  4. The Averages Must Confirm Each Other.

  The Industrials and Transports must confirm each other in order for a valid change of trend to occur. Both averages must extend beyond their previous secondary peak (or trough) in order for a change of trend to be confirmed.

  The following chart shows the Dow Industrials and the Dow Transports at the beginning of the bull market in 1982.

  

  Confirmation of the change in trend occurred when both averages rose above their previous secondary peak.

  5. The Volume Confirms the Trend.

  The Dow Theory focuses primarily on price action. Volume is only used to confirm uncertain situations. Volume should expand in the direction of the primary trend. If the primary trend is down, volume should increase during market declines. If the primary trend is up, volume should increase during market advances.

  The following chart shows expanding volume during an up trend, confirming the primary trend.

  

  6. A Trend Remains Intact

  Until It Gives a Definite Reversal Signal. An up-trend is defined by a series of higher-highs and higher-lows. In order for an up-trend to reverse, prices must have at least one lower high and one lower low (the reverse is true of a downtrend).

  When a reversal in the primary trend is signaled by both the Industrials and Transports, the odds of the new trend continuing are at their greatest. However, the longer a trend continues, the odds of the trend remaining intact become progressively smaller. The following chart shows how the Dow Industrials registered a higher high (point "A") and a higher low (point "B") which identified a reversal of the down trend (line "C").

  
  
  

• Elliot Waves
  

  The Elliott Wave Theory is named after Ralph Nelson Elliott. Inspired by the Dow Theory and by observations found throughout nature, Elliott concluded that the movement of the stock market could be predicted by observing and identifying a repetitive pattern of waves. In fact, Elliott believed that all of man's activities, not just the stock market, were influenced by these identifiable series of waves.

  With the help of C. J. Collins, Elliott's ideas received the attention of Wall Street in a series of articles published in Financial World magazine in 1939. During the 1950s and 1960s (after Elliott's passing), his work was advanced by Hamilton Bolton. In 1960, Bolton wrote Elliott Wave Principle--A Critical Appraisal . This was the first significant work since Elliott's passing. In 1978, Robert Prechter and A. J. Frost collaborated to write the book Elliott Wave Principle.

  The underlying forces behind the Elliott Wave Theory are of building up and tearing down. The basic concepts of the Elliott Wave Theory are listed below.

  1. Action is followed by reaction.
  2. There are five waves in the direction of the main trend followed by three corrective waves (a "5-3" move).
  3. 5-3 move completes a cycle. This 5-3 move then becomes two subdivisions of the next higher 5-3 wave.
  4. The underlying 5-3 pattern remains constant, though the time span of each may vary.
  5. The basic pattern is made up of eight waves (five up and three down) which are labeled 1, 2, 3, 4, 5, a, b, and c on the following chart.

  

  Waves 1, 3, and 5 are called impulse waves. Waves 2 and 4 are called corrective waves. Waves a, b, and c correct the main trend made by waves 1 through 5.

  The main trend is established by waves 1 through 5 and can be either up or down. Waves a, b, and c always move in the opposite direction of waves 1 through 5.

  Elliott Wave Theory holds that each wave within a wave count contains a complete 5-3 wave count of a smaller cycle. The longest wave count is called the Grand Supercycle. Grand Supercycle waves are comprised of Supercycles, and Supercycles are comprised of Cycles. This process continues into Primary, Intermediate, Minute, Minuette, and Sub-minuette waves.

  Fibonacci numbers provide the mathematical foundation for the Elliott Wave Theory. Briefly, the Fibonacci number sequence is made by simply starting at 1 and adding the previous number to arrive at the new number (i.e., 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13, etc). Each of the cycles that Elliott defined are comprised of a total wave count that falls within the Fibonacci number sequence. For example, the preceding chart shows two Primary waves (an impulse wave and a corrective wave), eight intermediate waves (the 5-3 sequence shown in the first chart), and 34 minute waves (as labeled). The numbers 2, 8, and 34 fall within the Fibonacci numbering sequence.

  Elliott Wave practitioners use their determination of the wave count in combination with the Fibonacci numbers to predict the time span and magnitude of future market moves ranging from minutes and hours to years and decades.

  There is general agreement among Elliott Wave practitioners that the most recent Grand Supercycle began in 1932 and that the final fifth wave of this cycle began at the market bottom in 1982. However, there has been much disparity since 1982. Many heralded the arrival of the October 1987 crash as the end of the cycle. The strong recovery that has since followed has caused them to reevaluate their wave counts. Herein, lies the weakness of the Elliott Wave Theory--its predictive value is dependent on an accurate wave count. Determining where one wave starts and another wave ends can be extremely subjective.