Builtin Studies Reference Guide
The following document outlines the technical analysis theory for popular builtin studies.
Table of contents
 ADX/DMS
 Alligator and Gator Oscillator
 Aroon and Aroon Oscillator
 ATR Bands
 Average True Range (ATR)
 Average True Range (ATR) Trailing Stop
 Awesome Oscillator
 Beta
 Bollinger Bands®
 Bollinger Bandwidth
 Bollinger %B
 Chaikin Money Flow
 Commodity Channel Index (CCI)
 Compare (Price Overlay)
 Coppock Curve
 Detrended Price Oscillator
 Donchian Channel
 Elder Impulse System
 Ichimoku Cloud (intro)
 Keltner Channel
 MACD
 Momentum
 Money Flow Index
 Moving Average
 Moving Average Envelope
 OnBalance (Cumulative) Volume
 Parabolic SAR
 Pivot Points
 Price Momentum Oscillator
 Price Rate of Change
 Price Relative (Relative Strength)
 RSI
 STARC Bands
 Stochastics
 Stochastic Momentum (SMI)
 Supertrend
 Typical Price
 Volume
 Volume Profile
 Williams %R
 Zig Zag
Supertrend
Indicator Type
Trend following indicator
Formula
The upper band is the average price plus the volatilitybased multiplier (usually average true range (ATR)). The lower band is the average price minus the volatilitybased multiplier. Only one band is drawn for any period and it switches when price crosses it similar to the parabolic stopandreverse. Similar to any trailing stop, the upper band can never move higher once established and the lower band can never move lower once established. Each is continued at the same price level as the previous period. Arrows are drawn pointing to the close of the bar when direction changes.
Math
Supertrend Upper = ((high + low / 2) + Multiplier * ATR …Only if price < upper Lower = ((high + low / 2) – Multiplier * ATR …Only if price > lower
ATR (Average True Range) TR (True Range) is defined as the greatest of the following:
 Current high minus the current low
 Current high minus the previous close (absolute value)
 Current low minus the previous close (absolute value) ATR = simple moving average of TR
Donchian Channel
Indicator Type
Trend following indicator
Formula
The channel is formed by taking the highest high and the lowest low of the prior n periods. The median line is the average of the upper and lower band for each period and not a moving average of price.
Math
 Directional Movement (DM) is defined as the largest part of the current period’s price range that lies outside the previous period’s price range.
 PDM = current high minus the previous high (called plus DM)
 MDM = current low minus the previous low (called minus DM)
 If PDM > MDM then MDM is set to zero
 If MDM > PDM then PDM is set to zero
 If current range lies within or is equal to the previous range then set both PDM and MDM to zero

Calculate the value of the Plus and Minus Directional Indicators:
PDI(n) =PDM(n) * 100
ATR(n)
MDI(n) = MDM(n) * 100
ATR(n)
Where:
n = Number of periods
ATR = Average True Range 
Calculate the absolute value of the Directional Movement Index (DMI):
DMI = (PDI – MDI)
(PDI + MDI)

Calculate the Average Directional Movement (DMIA a.k.a. ADX):
DMIA(n) = Simple Moving Average of DMI
Alligator and Gator Oscillator
Indicator Type
Trend following indicator
Formula
The indicator uses three smoothed moving averages, each one offset forward (into the future).
Math
Calculate three moving averages and offsets them into the future.
 The Jaw line is a 13period Smoothed Moving Average (SMMA), moved into the future by 8 bars;
 The Teeth line is an 8period Smoothed Moving Average (SMMA), moved by 5 bars into the future;
 The Lips line is a 5period Smoothed Moving Average, moved by 3 bars into the future.
Smoothed Moving Average – Same calculation as an exponential moving average except the smoothing constant is different.
P + wP1 + w^{2}P2 + … + w^{(n1)}P(n1)
1 + w + w^{2} + … + w^{(n1)}
Exponential smoothing constant: 2/(n+1)
Wilder smoothing constant: 1/n
Therefore, the Wilder average reacts slower than an exponential average. Also, the Wilder average can be converted into an exponential average with the formula 2n1. For example, a 26day Wilder average will draw the exact same plot as a 51day exponential average.
Price Relative (Relative Strength)
Indicator Type
Relative performance Indicator
Formula
A simple ratio of A / B. Select the item to be used as “B.” Select the “Result” box to bring up a color pallet.
Math
A simple ratio of the first item to the second: A / B
Chaikin Money Flow
Indicator Type
Buying/Selling Pressure Gauge
Formula
Similar to onbalance or cumulative volume, CMF uses price times volume. However, there are two main differences. Whereas onbalance volume calculates each period’s value and plots the running total, CMF acts more like a moving window. It sums up price times volume for a user defined span of periods and then calculates a fresh value for the next period. The second difference is that instead of close price, CMF calculates the percentage of where the close price falls within that period’s range. Called a “multiplier” instead of simply price, it ranges from 1 for a close at the low to +1 for a close at the high.
Math
Find the Money Flow Multiplier:
(Close – Low) – (High – Close)
(High – Low)
Calculate Money Flow Volume:
(Money Flow Multiplier) x Volume
Calculate the CMF:(NPeriod Sum of Money Flow Volume)
(NPeriod Sum of Volume)
Keltner Channel
Indicator Type
Moving average envelope
Formula
The upper and lower lines form an envelope drawn a number of Average True Ranges (ATRs) above and below a moving average.
Math
Center Line: 20day exponential moving average
Upper Channel Line: 20day EMA + (2 x ATR (10period))
Lower Channel Line: 20day EMA – (2 x ATR (10period))
Awesome Oscillator
Indicator Type
Momentum Oscillator
Formula
The difference between two simple moving averages using the median price instead of the close price. The result does not have high or low limits.
Math
Fast Period: Simple Moving Average (Highest Price + Lowest Price)/2
Slow Period: Simple Moving Average (Highest Price + Lowest Price)/2
Aroon and Aroon Oscillator
Indicator Type
Trend Finder
Formula
The Aroon indicators are shown in percentage terms and fluctuate between 0 and 100. Aroon Up is based on recent highs and Aroon Down is based on recent lows. The Aroon Oscillator is simply a plot of Aroon Up minus Aroon Down.
Math
Aroon Up: 100 x (n Days Since nday High)/n
Aroon Down: 100 x (n – Days Since nday Low)/n
Aroon Oscillator: Aroon Up – Aroon Down
Money Flow Index
Indicator Type
Momentum Oscillator
Formula
The formula is essentially a volumeweighted relative strength index (RSI). However, instead of using simple close prices, MFI uses the typical price multiplied by volume. The result is then used in the RSI calculation as a ratio of average volume weighted size of the upcloses over the past “n” periods and compared to the average volume weighted size of the downcloses. The result is indexed between 0 and 100.
Math
Calculate Money Flow = Typical Price x Volume
Typical Price = (High + Low + Close)/3
Find positive money flow = sum of the volume weighted “up” typical price changes for the past nperiods
Find negative money flow = sum of the volume weighted “down” typical price changes for the past nperiods
Calculate Money Flow ratio = (nperiod positive Money Flow)/ (nperiod negative Money Flow)
Calculate Money Flow Index = 100 – 100/ (1 + Money Flow Ratio)
Bollinger Bandwidth
Indicator Type
Volatility Oscillator
Formula
Bollinger Bands form an envelope drawn a number of standard deviations above and below a moving average. Bandwidth measures the percentage difference between the upper and lower bands and therefore the volatility level.
Math
Bandwidth = (Upper Band – Lower Band) / Central Moving Average * 100
Bollinger %B
Indicator Type
Momentum Oscillator
Formula
Bollinger Bands form an envelope drawn a number of standard deviations above and below a moving average. %B is simply a percentage measure of a security’s location between the bands. %B can be lower than 0 or higher than 100 if price moves outside the bands.
Math
%B = (Price – Lower Band) / (Upper Band – Lower Band)
Williams %R
Indicator Type
Momentum oscillator
Formula
The calculation tells us where price is in its recent range.
Math
Calculates where price is within a recent range.
 Fast calculation (%K) uses raw value with a simple moving average
 Slow (smoothed) version (%D) uses the simple average with another simple average of the first
%R = (Highest High – Current) / (Highest High – Lowest Low)
The result is multiplied by 100 and is plotted on a scale of 100 to zero
Lowest Low = lowest low for the past Nperiods including current
Highest High = highest high for the past Nperiods including current
Ichimoku Cloud (intro)
Indicator Type
Trend finder
Formula
There are five components:
 Tenkan Sen (Conversion Line) – Calculated as the sum of the highest high over the past nine periods and the lowest low divided by two
 The Kijun Sen (Base Line) – Calculated as the sum of the highest high over the past 22 periods and the lowest low divided by two.
 Senkou Span A (leading) – The sum of the Tenkan Sen and the Kijun Sen divided by two. The calculation is then plotted 26 time periods ahead of the current price action.
 Senkou Span B (leading) – The sum of the highest high and the lowest low over the past 52 periods divided by two. It is also plotted 26 periods ahead.
 Chikou (lagging)) – The same and Senkou Span B leading but plotted 26 periods in the past.
Math
coming soon!
Average True Range (ATR) Trailing Stop
Indicator Type
Trade trigger
Formula
Calculate the Average True Range and then multiply by the multiplier. For an up trend, subtract from previous close. For a down trend, add to previous close.
Math
TR=True Range = defined as the greatest of the following:
 Current high minus the current low
 Current high minus the previous close (absolute value)
 Current low minus the previous close (absolute value)
ATR = simple moving average of TR
ATR Trailing Stop in a rising trend is highest price over the userdefined span minus (multiplier * ATR). If prices continue to rise, the stop will continue to rise. However, if prices flatten out or pull back the stop will be flat. Only when price dips below the flat stop line will it flip to the inverse with the stop above prices.
Moving Average Envelope
Indicator Type
Trend follower
Formula
Lines are drawn a percentage or number of points above and below a moving average.
Math
Envelopes start with any moving average type (see Moving Averages for formulas) and then creates an offset x% above or below the average or an offset Y points above or below the average.
For percentage envelopes:
Upper band = moving average + x%(moving average)
Lower band = moving average – x%(moving average)
For points envelopes:
Upper band = moving average + constant
Lower band = moving average – constant
Stochastic Momentum (SMI)
Indicator Type
Momentum oscillator
Formula
The calculation tells us where price with regard the median of its recent range and runs a smoothing average through the result. Most traders smooth the smoothed line again to create a slower version of the indicator.
Math
coming soon!
Typical Price
Indicator Type
Price indicator
Formula
The formula is a simple average of the period’s open, high and low. ChartIQ allows you to calculate a moving average based on the typical price over a user defined span. It works the same way as a simple average of the other data points (open, high, low or close) works.
Math
Typical Price = ( high + low + close ) / 3
The moving average is calculated as a simple moving average
Mov Avg =
P + P1 + … + P(n1)
n
Volume Profile
Indicator Type
Activity indicator
Formula
Volume data is reported as is.
Math
None
Average True Range (ATR)
Indicator Type
Volatility measure
Formula
The True Range is the largest of (high – previous close), (previous close – low) or (high – low).
Math
TR=True Range = defined as the greatest of the following:
 Current high minus the current low
 Current high minus the previous close (absolute value)
 Current low minus the previous close (absolute value)
ATR = simple moving average of TR
RSI
Indicator Type
Momentum oscillator
Formula
The RSI looks at a ratio of average size of the upcloses over the past “n” periods and compares to the average size of the downcloses. The result is indexed between 0 and 100. RSI values are smoothed exponentially using the same “n” period parameter.
Math
RSI = 100 – 100/(1 + RS)
RS =
Average of the up closes over nperiods
Average of the down closes over nperiods
The average of the “up closes” refers to the total changes higher over the past “n” periods (not the last “n” upperiods) divided by “n.” The average of “down closes” refers to the total changes lower over the same span. RSI values are smoothed in an exponential manner after the initial calculation whereby the averages of up closes and down closes are each divided by n1 and the new period’s up or down close is added. The result is then divided by n. As follows: Average up close = (previous average up close x (n1) + current up close).Average down close = (previous average down close x (n1) + current down close).
Price Rate of Change
Indicator Type
Momentum indicator
Formula
( (Current Price – Price nperiods ago) / Price nperiods ago) * 100
Math
ROC = Current Price – Price (nperiods ago) * 100 1
Price nperiods ago
Pivot Points
Indicator Type
Support/Resistance
Formula
The pivot point and its support and resistance pairs are defined as follows:
 Pivot point (P) = (H + L + C) / 3
 Third resistance level (R3) = P + 2*(H – L)
 Second resistance level (R2) = P + (H – L)
 First resistance level (R1) = (2 * P) – L
 First support level (S1) = (2 * P) – H
 Second support level (S2) = P – (H – L)
 Third support level (S3) = P – 2*(HL)
where H, L, C are the previous period’s high, low and close
Math
Plots 7 horizontal lines for each period, one for Pivot line, 3 for Support, and 3 for Resistance Period is determined as follows:
 Intraday chart from 1 minute up to but not including 30 minutes – Period=daily
 Intraday chart from 30 minutes upwards – Period=weekly
 Daily charts – Period=monthly
 Weekly and Monthly charts – Period=yearly
Daily periods begin at midnight ET for equities, 5PM for forex, 6PM for metals
MACD
Indicator Type
Momentum oscillator
Formula
The Moving Average ConvergenceDivergence (MACD) indicator makes use of three moving averages, usually of the exponential variety. Two are averages of price and the third is an average of the difference of the other two. The MACD line is generated from the first two averages, subtracting the longer from the shorter. The Signal Line is simply a moving average of the MACD line.
Math
MACD line – short moving average minus long moving average
Signal line – a moving average of the MACD line
Histogram – same as MACD line but in a different visual format
Averages are usually based on the close and are exponentially smoothed.
OnBalance (Cumulative) Volume
Indicator Type
Volume study
Formula
Cumulative total of daily volume on up days minus daily volume on down days. Each day’s volume may also be weighted by the price change for that day so that volume on days with large price moves is counted more heavily.
Math
A running total of volume on upperiods minus volume on down periods. Periods with no change have no effect.
∑ volume * (direction of price change ) Value will change depending on span chosen but plot will look the same.
ADX/DMS
Indicator Type
Trend finder
Formula
Directional Movement (DM) is defined as the largest part of the current period’s price range that lies outside the previous period’s price range. Each period will either be positive (larger range above previous range), negative (larger range below previous range) or zero if moves above and below the previous period’s range are the same or price stay within the previous day’s range. The value of the Plus Directional Indicator (+DI) is the DM, if above the previous range) divided by the average true range. The value of the Minus Directional Indicator (DI) is the DM (if below the previous range) divided by the average true range. Each period with have only one result, either plus, minus or zero. Calculate the Average Directional Index by taking a simple moving average of the past +DI and DI values. ChartIQ defaults to 14 periods. You can also select colors for the ADX, +DI and –DI lines by selecting the appropriate box to bring up a color palette. Green and red are often used for +DI and –DI, respectively.
Math

Directional Movement (DM) is defined as the largest part of the current period’s price range that lies outside the previous period’s price range.
 PDM = current high minus the previous high (called plus DM)
 MDM = current low minus the previous low (called minus DM)
 If PDM > MDM then MDM is set to zero
 If MDM > PDM then PDM is set to zero
 If current range lies within or is equal to the previous range then set both PDM and MDM to zero

Calculate the value of the Plus and Minus Directional Indicators:
PDI(n) = PDM(n) * 100
ATR(n)
MDI(n) = MDM(n) * 100
ATR(n)
Where: n = Number of periods ATR = Average True Range 
Calculate the absolute value of the Directional Movement Index (DMI):
DMI = (PDI – MDI)
(PDI + MDI)

Calculate the Average Directional Movement (DMIA a.k.a. ADX):
DMIA(n) = Simple Moving Average of DMI
Volume
Indicator Type
Activity indicator
Stochastics
Indicator Type
Momentum oscillator
Formula
The calculation (fast) tells us where price is in its recent range. It is then smoothed with a 3period moving average (slow) leaving both lines on the chart. Most traders smooth the smoothed line again to create a slower version of the indicators.
Math
Calculates where price is within a recent range.
 Fast calculation (%K) uses raw value with a simple moving average
 Slow (smoothed) version (%D) uses the simple average with another simple average of the first
Fast %K = (Current Price – Lowest Low) / (Highest High – Lowest Low)
Fast %D = 3period simple moving average of Fast %K
Slow %K = Fast %D
Slow %D = 3period simple moving average of Slow %K
Lowest Low = lowest low for the past Nperiods including current
Highest High = highest high for the past Nperiods including current
Parabolic SAR
Indicator Type
Trend following system
Formula
The initial SAR (stop and reverse point) is set at the end of the previous trend. For new rising trend, to calculate the next SAR, the acceleration factor is multiplied by the difference between the current high for the new trend and the prior period’s SAR. This is then added to the prior period’s SAR.
Math
The initial SAR (stop and reverse point) is set at the extreme price of the previous trend. After the initial SAR is set, the next interval’s SAR is adjusted in the direction of the trend by the distance between the high for the new trend and the previous SAR then multiplied by an acceleration factor. The acceleration factor typically starts at .02 and increases by .02 to a typical maximum of .20 each period the market makes a new high/low for the move. For a rising trend:
 Previous SAR: The SAR value for the previous period.
 Extreme Point (EP): The highest high of the current uptrend.
 Acceleration Factor (AF): Starting at .02
Current SAR = Previous SAR + Previous AF(Previous EP – Previous SAR)
When price moves through the SAR point, the entire calculation starts over but the extreme point becomes the lowest low of the new trend and the AF becomes a negative number.
Current SAR = Previous SAR – Previous AF(Previous EP – Previous SAR)
Moving Average
Indicator Type
Trend follower
Formula
Moving averages can be calculated from open, high, low, close or some combination of these data. Simple averages are means of the data. Other averages assign higher significance to recent data than to older data. Technician allows you to calculate the average based on open, high, low, close or adjusted close data. You also have a choice of several average types as follows.
 Simple: mean (average) of the data.
 Exponential: newer data are weighted more heavily geometrically.
 Time Series: Calculates a linear regression trendline using the “least squares fit” method.
 Triangular: Weighted average where the middle data are given the most weight, decreasing linearly to the end points.
 Variable: An exponential moving average with a volatility index factored into the smoothing formula. The Variable Moving average uses the Chande Momentum Oscillator as the volatility index.
 VIDYA: An exponential moving average with a volatility index factored into the smoothing formula. The VIDYA moving average uses the Standard Deviation as the volatility index. (Volatility Index DYnamic Average)
 Weighted: newer data are weighted more heavily arithmetically.
 Welles Wilder: The standard exponential moving average formula converts the time period to a fraction using the formula EMA% = 2/(n + 1) where n is the number of days. For example, the EMA% for 14 days is 2/(14 days +1) = 13.3%. Wilder, however, uses an EMA% of 1/14 (1/n) which equals 7.1%. This equates to a 27day exponential moving average using the standard formula.
Math
Moving Averages
Simple =
P + P1 + … + P(n1)
n
Weighted =
n*P + (n1)*P1 + (n2)*P2 + … + P(n1)
1 + 2 + 3 + … + n
Exponential =
P + aP1 + a^{2}P2 + … + a^{(n1)} P(n1)
1 + a + a^{2} + … + a^{(n1)}
Welles Wilder =
P + wP1 + w^{2}P2 + … + w^{(n1)} P(n1)
1 + w + w^{2} + … + w^{(n1)}
Variable =
P + (a*b)P1 + (a*b)^{2}P2 + … + (a*b)^{(n1)} P(n1)
1 + (a*b) + (a*b)^{2} + … + (a*b)^{(n1)}
Vidya =
P + (a*bv)P1 + (a*bv)^{2}P2 + … + (a*bv)^{(n1)} P(n1)
1 + (a*bv) + (a*bv)^{2} + … + (a*bv)^{(n1)}
Triangular = Same as weighted average except the middle data gets the highest weight and the ends get arithmetically lower weights
Where:
P = current price
P1 = price 1 period ago
P2 = price 2 periods ago
a = smoothing constant 2/(n+1)
w = smoothing constant 1/n
v = a * b and is variable
b = absolute value (F(P)/100)
F = Chande Momentum Oscillator (CMO) with Period 9
n = userdefined number of periods for the average
Momentum
Indicator Type
Momentum indicator
Formula
Current Price – Price nperiods ago
Commodity Channel Index (CCI)
Indicator Type
Momentum indicator
Formula
The CCI starts with the average of the high, low and close for the period and subtracts the “n” period moving average. The goal is to measure the current price level relative to an average price level over a given period of time, normalized for the average price over time.
Math
CCI =
Typical Price (TP) – (nperiod simple moving average of TP)
(0.015 * Mean Deviation)
Typical Price =
(high + low + close) / 3
Mean Deviation =
∑ (absolute value of difference of TP and its Npd simple moving average)
N
Bollinger Bands®
Indicator Type
Moving average envelope
Formula
The bands form an envelope drawn a number of standard deviations above and below a moving average.
Math
An envelope based with width determined by standard deviations above and below a moving average.
 Middle Band = Nperiod moving average
 Upper Band = Nperiod moving average + (Nperiod standard deviation of price x multiple)
 Lower Band = Nperiod moving average – (Nperiod standard deviation of price x multiple)
Multiple = user defined number of deviations above and below middle band (typically 2.0)
Nperiod = typically 20
Standard Deviation =
 Calculate the average (mean) price for N periods
 Subtract each price over N periods from the average price over N periods
 Square each difference.
 Sum these squares
 Divide this sum by N
 Standard deviation = the square root of that number.
Compare (Price Overlay)
Indicator Type
Relative performance measure
Formula
The main chart does not have a formula but the optional correlation pane shows how each item compares to the main item using a correlation coefficient. The end result varies between 1 (trades exactly the opposite) and +1 (trades exactly the same).
Math
Correlation Coefficient is used in statistics to calculate the strength and direction of the linear relationship or the statistical relationship (correlation) between two data sets. For charting, it is between two traded instruments, and the result is recalculated for each period in the same way a moving average “moves” through time using fresh data.
In the formula, the symbols μ_{x} and μ_{y} represent the mean of the two data sets X and Y respectively. The σ_{x} and σ_{y} represent the sample standard deviation of the two data sets X and Y respectively.
Step by step calculation:
 Find the sample mean μ_{x} for data set X.
 Find the sample mean μ_{y} for data set Y.
 Estimate the standard deviation σ_{x} for sample data set X.
 Estimate the sample deviation σ_{y} for data set Y.
 Find the covariance (cov(x, y)) for the data sets X and Y.
 Apply the values in the formula for correlation coefficient to get the result.
The value ranges between 1 to +1. The positive and negative correlation coefficient represents the direct (positive) and inverse (negative) linear correlation or statistical relationship between the data sets. If it is close to zero or equal to zero, then the data sets have no correlation (uncorrelated). If the value is between 1 to +1, then there is a linear correlation between the two data sets.
Coppock Curve
Indicator Type
Momentum indicator
Formula
The Coppock Curve is calculated by first determining the sum of the rates of change of a long and a short period. Then, a Weighted Moving Average of this sum is taken over another period. This average is the result for the indicator.
The defaults for the periods are 11 for the Short period, 14 for the Long period, and 10 for the WMA period. The rate of change is usually calculated on the Close.
Math

SP=Short Period, LP=Long Period, N=WMA Period, X=data field

sumi=100 * ( Xi / XiSP + Xi / XiLP  2 )

Coppocki: WMA(i,sum,N)
Price Momentum Oscillator
Indicator Type
Momentum indicator
Formula
The Price Momentum Oscillator is a twice smoothed rate of change of the price from the previous price. The smoothing is an EMA with a period one less than specified. There is also a signal which is an EMA of the oscillator result.
The defaults for the periods are 35 for the first smoothing, 20 for the second smoothing, and 10 for the signal period. The rate of change is usually calculated on the Close.
Math
 SM=smoothing period, DSM=double smoothing period, SG=signal period, X=data field
 ai=1000* ( Xi / Xi1  1 )
 smi=EMA(i, a, SM  1)
 PMOi=EMA(i, sm, DSM  1)
 Signali=EMA(i, PMO, SG)
Elder Impulse System
Indicator Type
Trendmomentum crossover indicator
Formula
The Elder Impulse System combines an exponential moving average with the moving average convergence/divergence (MACD) to produce bullish and bearish signals on the chart. The result is a colored bar chart where the colors represent bullish, bearish or neutral signals.
The EMA had a period of 13, computed on the Close. The MACD has a fast period of 12, a slow period of 26, and a signal period of 9.
Math
 MAi = EMA(i, Close, 13)
 MACD1 i= EMA(i, Close, 12)
 MACD2i = EMA(i, Close, 26)
 MACDi = MACD1MACD2
 MACDSigi = EMA(i, MACD, 9)
If MAi>MAi1 and MACDiMACDSigi>MACDi1MACDSigi1 then bar i is bullish
If Mai<MAi1 and MACDiMACDSigi<MACDi1MACDSigi1 then bar i is bearish
If neither of the above, bar i is neutral
Detrended Price Oscillator
Indicator Type
Price cycle
Formula
The Detrended Price Oscillator seeks to remove trend information from the dagta. It does this by taking a moving average and shifting it to the left. It then subtracts the average from the time period from the Close of that time period to arrive at the result.
The resulting DPO plot will emphasize the movement of the security above and below the moving average while filtering out the general trends.
Note that as the moving average is shifted to the left, the DPO will not compute to the present bar.
The Moving Average type defaults to Simple, and the moving average period defaults to 14, computed on the Close.
Math
In this section, xMA denotes any moving average chosen by the user. N is the period, and X is the data field.
 MAi = xMA(i, X, N)
 MAShiftedi = MA(i+int(N/2+1)) where "int" is the whole number portion of the formula within the parentheses. For example, int(16.5)=16.
 DPOi = Xi  MAShiftedi
Zig Zag
Indicator Type
Trend finder/ Elliot Wave finder
Formula
The ZigZag is used to identify trends in the price movement. It filters out noisy fluctuations in price while identifying larger trends.
Lines are drawn on a diagonal, up then down, when price movement exceeds a distance threshold percentage (default is 10). A lowest low point is recorded once a high price is reached which is the distance threshold percentage greater than that low, after which lowest low is sought once more. A highest high point is recorded once a low price is reached which is D less than that high, after which highest high is sought once more.
For OHLC data, the high and low values of the bar are considered. For line and mountain charts, only the close is considered.
The final leg of the ZigZag is a proposed line between the last extreme value encountered and the present price.
ATR Bands
Indicator Type
Moving average envelope
Formula
The Average True Range, or ATR, is a measure of the volatility of a security. ATR Bands creates an envelope around the data field being measured (usually the close) sby drawing a plot above and below the data offset vertically by a percentage of the ATR, forming a channel. When the data breaks out of the channel, it can be interpreted as a signal.
By default, the ATR Bands will use an ATR with period of 5, and a 3% shift, to compute the bands. The Close field is usually used as the median band.
Math
Where M is the ATR period
 Median Bandi = Xi (usually X is the Close)
 Top bandi = Median Bandi + %Shift * ATR(M)i
 Bottom Bandi= Median Bandi  %Shift * ATR(M)i
STARC Bands
Indicator Type
Moving average envelope
Formula
STARC Bands are a special type of ATR Bands. Instead of basing the envelope as a percentage shift off a data field such as the close, it is based instead on the simple moving average of the Close.
By default, the ATR Bands will use an ATR with period of 15, and a 1.3% shift, to compute the bands. The moving average has a period of 5.
Math
Where M is the ATR period, N is the SMA period.
 Median Bandi = SMA(i, Close, N)
 Top bandi = Median Bandi + %Shift * ATR(M)i
 Bottom Bandi= Median Bandi  %Shift * ATR(M)i
Beta
Indicator Type
Relative volatility measure
Formula
The Beta calculation is a statiscical formula which measures volatility of one security tvs a benchmark security, usually the S&P 500 Index.
Math
Where X is the Close of the measured security, Y is the Close of the benchmark security, and N is the period.
 XChgi = Xi – Xi1
 YChgi = Yi – Yi1
 XMAi = SMA(i, XChg, N)
 YMAi = SMA(i, YChg, N)
 COVARi = (XChgiXMAi) * (YChgiYMAi)
 VARi = (XChgiXMAi)2
 Betai = SMA(i, COVAR, N) / SMA(i, VAR, N)