Among our over 230 Indicators are – Advance/Decline Indicators, Comparative Indicators, and General Indicators.

Below is a brief summary of the three varieties of Indicator, followed by a thorough description of each.

We calculate these indicators for all of our exchanges and for our list of Global Indices.

**ADVANCE/DECLINE INDICATORS**

Advance/Decline Indicators pertain to an entire exchange, or to a categorized list of securities, indices, markets, mutual funds etc.… Advance-Decline indicators can be divided into two groups: issue-based indicators, which count the number of advancing issues, declining issues and unchanged issues on a given exchange, and volume-based indicators, which total the volume of advancing issues, the volume of declining issues and the volume of unchanged issues. Issues are mostly common stocks, preferred stocks or closed-end funds.

We calculate these indicators for all of our exchanges and for our list of Global Indices.

**Absolute Breadth Index**

The Absolute Breadth Index (ABI) the absolute value of the difference between the number of advancing issues and the number of declining issues. The values are always positive. Higher values indicate higher market volatility, that is, a greater spread between the advances and declines.**Advance/Decline Line**

The Advance/Decline Line is the most popular advance/decline indicator. It is a cumulative total of the Advancing-Declining Issues indicator. The Advance/Decline Line of a market (such as the NYSE or NASDAQ) moves with the price of the market index. Look for agreement/divergence to confirm/deny price trends.**Advance/Decline Line Breadth**

The Advance/Decline Line Breadth indicator displays the number of advancing issues as a percentage of the total advancing and declining issues. The values range from zero to 100. Because it is not cumulative, the indicator is often smoothed with a moving average. See also Breadth Thrust.**Advance/Decline Ratio**

The Advance/Decline Ratio is the ratio of the number of advancing issues to the number of declining issues. The values can be read easily. For instance, a value of two means that there were twice as many advancing issues as declining issues. Numbers below one mean that there were more declining issues than advancing issues. For instance, a value of 0.5 means that there were half as many advancing issues as declining issues. The A/D Ratio is often smoothed with a moving average.**Advancing-Declining Issues**

The Advancing-Declining Issues indicator is the simplest of the advance/decline indicators. It is simple the difference between the number of advancing issues and the number of declining issues. The values oscillate around zero. Extreme highs indicate overbought conditions, and extreme lows indicate oversold conditions. It is often smoothed with a moving average that can also act as a signal line.**Arms Index (TRIN)**

The Arms Index calculates the ratio of the Advance/Decline Ratio to the Upside/Downside Ratio. It shows whether volume is moving into advancing or declining issues. Values below 1.0 indicate more volume in advancing issues, while values above 1.0 indicate more volume in declining issues. A 10 period moving average of the Arms Index is often used. Values over 1.2 indicate oversold conditions, values under 0.7 indicate overbought.

The Arms Index is also known as the short-term Trading Index or TRIN.**Bolton-Tremblay**

The Bolton-Tremblay Indicator is a more complex version of the basic advance to decline ratio indicators. The indicator is created by taking the ratio of advancing issues to unchanged issues and the declining issues to unchanged issues. The square root of the absolute differences between the ratios is added to the previous BT value. This indicator is used to spot trend changes in the overall market and general market strength and weakness.**Breadth Thrust**

The Breadth Thrust indicator is a ten period simple moving average of the Advance/Decline Line Breadth. A Breadth Thrust formation is defined as when the Breadth Thrust indicator moves from below 40% to above 61.5 % within a ten day period. This indicates that the market is rapidly moving from an oversold condition to a strong up trend. A Breadth Thrust formations are rare and are a very good indicator of a bull market.**Bretz TRIN-5**

The Bretz TRIN-5 indicator is a five period moving sum of the TRIN. To interpret the Bretz TRIN-5, a buy signal is generated when it reaches a high above 6 then turns down, and a sell signal is generated when it reaches a low below 4 then turns up.**Cumulative Volume Index (CVI)**

The Cumulative Volume Index (CVI) is a cumulative total of the issues with up-volumes vs issues with down-volumes. It is a market momentum indicator that indicates whether money is flowing into or out of the market.**McClellan Oscillator**

McClellan Oscillator is the difference between two exponential moving averages of the advance decline spread. The time periods are typically 19 and 39 days. The values of the indicator oscillate around zero, and generally range from -100 to +100.

Overbought/oversold conditions are found above +70 and below -70. Values above +100 or below -100 indicate the continuation of the current trend. Buy/sell signals are generated by zero line crossovers.**McClellan Summation**

The McClellan Summation is a cumulative total of the McClellan Oscillator. The interpretation is similar to the McClellan Oscillator, but the Summation indicates longer term trends. Market bottoms occur when the Summation drops below -1300. Market tops occur when the Summation rises above +1600. Major Bull markets are signaled by a move above +1900 from a low.**Open-10 TRIN**

The Open-10 TRIN is a variation on the TRIN. The basic formula of advances divided by declines over up volume divided by down volume is the same, but the Open-10 TRIN uses 10 day moving sums of each of the numbers. The interpretation is the same as for the TRIN. The Open-10 TRIN is also known as the Open Trading Index.**Overbought/Oversold**

The Overbought/Oversold indicator is a 10 period exponential moving average of the Advance-Decline Spread. Values over +200 are considered bearish, and values under -200 are considered bullish. When the indicator falls below +200 a sell signal is generated, when it rises above -200 a buy signal is generated. Values around zero indicate market congestion.**STIX**

The STIX (an acronym of Short Term Index) is a short-term market momentum indicator. It is calculated by taking a 21 period exponential moving average of the Advance/Decline ratio. Values over 50 are generated when there are more advancing than declining issues, values under 50 mean more decliners. Values over 56 are considered overbought and values over 58 are extremely overbought. Values under 45 are considered oversold, and values under 42 are extremely oversold.**Upside/Downside Ratio**

The Upside/Downside Ratio is the ratio of up volume to down volume. A value of one means that there is a balance between up and down volume. Sustained high/low values indicate overbought/oversold conditions. Big market moves are often signaled by big buying or selling frenzies. The ratio is often smoothed with a moving average to show longer term trends.**Upside/Downside Volume**

The Upside/Downside Volume is the difference between the up volume and the down volume. The values oscillate around zero (balance). Look for zero line crossovers to give short-term buy/sell signals. Look at the overall trend of the line to indicate buy-ups or sell-offs.

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**COMPARATIVE INDICATORS**

Comparative Indicators are used to analyze the relationship between two or more securities, indices or markets. They compare prices, volume, and/or volatility, determining which instrument is relatively stronger or weaker over the chosen time frame. This type of analysis elicits a series of convergence and divergence signals, with the leading instrument generating a bullish divergence when it gets even stronger compared to the lagging instrument, and a bearish convergence when it gets even weaker compared to the lagging instrument. For each security on each of our exchanges, we compare the security with the generally accepted equivalent of the S&P 500 for that exchange. For example,

Comparative_Performance_vs_Bitcoin

Comparative_Performance_vs_HangSeng

Comparative_Performance_vs_BSE500**Beta Coefficient**

A beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market. A security’s beta is calculated by dividing the product of the covariance of the security’s returns and the market’s returns by the variance of the market’s returns over a specified period.

**Comparative Performance**

Comparative Performance compares two sets of bars and calculates their relative performance. The calculation is based on the ratio of the two prices compared to the ratio at the beginning of the set of bars. Usually, a security is compared to a market index such as the S&P 500, however, you can compare any two sets of bars.**Comparative Strength**

Comparative Strength compares two sets of bars and calculates their ratio by dividing one by the other. Usually, a security is compared to a market index such as the S&P 500, however, you can compare any two sets of bars.

Do not confuse the Comparative Strength with the RSI (Relative Strength Index), which is an entirely different calculation and also does not compare two sets of bars.**Comparative Relative Strength Index**

Comparative Relative Strength Index (RSIC) compares two sets of bars and calculates their relative strength. Mathematically, it is the rate of change of the Comparative Strength. Usually, a security is compared to a market index such as the S&P 500, however, you can compare any two sets of bars.

Do not confuse the RSIC with the RSI (Relative Strength Index), which is an entirely different calculation and also does not compare two sets of bars.**Moving Correlation Coefficient**

The Moving Correlation Coefficient calculates a correlation coefficient of two data series over the last n periods. This statistical calculation is used to determine if two series of numbers are related. The closer the value is to 1, the closer the data is related.**Moving Covariance**

The Moving Covariance calculates the covariance of two data series over the last n periods.

* Both covariance and correlation measure the relationship and the dependency between two variables. Covariance indicates the direction of the linear relationship between variables while correlation measures both the strength and direction of the linear relationship between two variables. Correlation is a function of the covariance.

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**GENERAL INDICATORS**

Unlike Comparative Indicators or Advance/Decline indicators which compare securities to indices, or pertain to an entire Exchange, these general indicators are heuristic or pattern-based signals produced by the price, volume, and/or open interest of a single security.**Accumulate or Running Total**

The Accumulate function calculates the running total of the input data. This is especially useful if the input data contains both positive and negative values so that the output will vary around zero. We use volume as input.**Accumulation Swing Index**

The Accumulation Swing Index is a running total of the Swing Index. The Swing Index is calculated using only the two most recent bars. By summing it the Accumulation Swing Index shows long-term trends. It will be positive in a long-term uptrend, negative in a long-term down trend and it will hover around zero if the market is flat. The shape of the Accumulation Swing Index line closely matches the shape of the price line. It can be interpreted by comparing it to the price and looking for divergence or confirmation.**Aroon**

The word Aroon is Sanskrit for “dawn’s early light.” The Aroon indicator attempts to show when a new trend is dawning. The indicator consists of two lines (Up and Down) that measure how long it has been since the highest high/lowest low has occurred within an n period range.

When the Aroon Up is staying between 70 and 100 then it indicates an upward trend. When the Aroon Down is staying between 70 and 100 then it indicates a downward trend. A strong upward trend is indicated when the Aroon Up is above 70 while the Aroon Down is below 30. Likewise, a strong downward trend is indicated when the Aroon Down is above 70 while the Aroon Up is below 30. Also look for crossovers. When the Aroon Down crosses above the Aroon Up, it indicates a weakening of the upward trend (and vice versa).**Aroon Oscillator**

The Aroon Oscillator is calculated by subtracting the Aroon Down from the Aroon Up. The resultant number will oscillate between 100 and -100. The Aroon Oscillator will be high when the Aroon Up is high and the Aroon Down is low, indicating a strong upward trend. The Aroon Oscillator will be low when the Aroon Down is high and the Aroon Up is low, indicating a strong downward trend. When the Up and Down are approximately equal, the Aroon Oscillator will hover around zero, indicating a weak trend or consolidation. See the Aroon indicator for more information.**Average Directional Movement Index (ADX)**

The ADX is a Welles Wilder style moving average of the Directional Movement Index (DX).The values range from 0 to 100, but rarely get above 60. To interpret the ADX, consider a high number to be a strong trend, and a low number, a weak trend.**Average Directional Movement Rating (ADXR)**

The ADXR is equal to the current ADX plus the ADX from n bars ago divided by 2. In effect, it is the average of the two ADX values. The ADXR smoothes the ADX, and is therefore less responsive, however, the ADXR filters out excessive tops and bottoms. To interpret the ADXR, consider a high number to be a strong trend, and a low number, a weak trend.**Average True Range (ATR)**

The ATR is a Welles Wilder style moving average of the True Range. The ATR is a measure of volatility. High ATR values indicate high volatility, and low values indicate low volatility, often seen when the price is flat. The ATR is a component of the Welles Wilder Directional Movement indicators (+/-DI, DX, ADX, and ADXR).**Average Price**

The Average Price is the average of the open + high + low + close of a bar. It can be used to smooth an indicator that normally takes just the closing price as input.

See also Median Price, Typical Price, and Weighted Close.**Balance of Power – BOP**

The Balance of Power indicator measures the market strength of buyers against sellers by assessing the ability of each side to drive prices to an extreme level. The calculation is: Balance of Power = (Close price – Open price) / (High price – Low price). The resulting value can be smoothed by a moving average.**Bollinger Bands**

Bollinger Bands consist of three lines. The middle band is a simple moving average (generally 20 periods) of the typical price (TP). The upper and lower bands are F standard deviations (generally 2) above and below the middle band. The bands widen and narrow when the volatility of the price is higher or lower, respectively. Bollinger Bands do not in themselves, generate buy or sell signals; they are an indicator of overbought or oversold conditions. When the price is near the upper or lower band it indicates that a reversal may be imminent. The middle band becomes a support or resistance level. The upper and lower bands can also be interpreted as price targets. When the price bounces off of the lower band and crosses the middle band, then the upper band becomes the price target. See also Bollinger Width, Envelope, Price Channels, and Projection Bands.**Bollinger Band Width**

The Bollinger Band Width indicator is the distance between the upper and lower Bollinger Bands. It is a measure of volatility. The Band Width value is higher when volatility is high and lower when volatility is low. High Band Width values indicate that the current trend may be about to end. Low Band Width values indicate that a new trend may be about to start.**Chaikin Accumulation/Distribution Line**

The Accumulation/Distribution Line is similar to the On Balance Volume (OBV), which sums the volume times +1/-1 based on whether the close is higher than the previous close. The Accumulation/Distribution indicator however multiplies the volume by the close location value (CLV). The CLV is based on the movement of the issue within a single bar and can be +1, -1 or zero.

The Accumulation/Distribution Line is interpreted by looking for a divergence in the direction of the indicator relative to price. If the Accumulation/Distribution Line is trending upward it indicates that the price may follow. In addition, if the Accumulation/Distribution Line becomes flat while the price is still rising (or falling) then it signals an impending flattening of the price.**Chaikin Money Flow**

The Chaikin Money Flow compares the total volume over the last n time periods to the total of volume times the Closing Location Value (CLV) over the last n time periods. The CLV calculates where the issue closes within its trading range. When the Chaikin Money Flow is above 0.25 it is a bullish signal, when it is below -0.25, it is a bearish signal. If the Chaikin Money Flow remains below zero while the price is rising, it indicates a probable reversal.**Chaikin Oscillator**

The Chaikin Oscillator (AKA Chaikin A/D Oscillator) is essentially a momentum of the Accumulation/Distribution Line. It is calculated by subtracting a 10 period exponential moving average of the A/D Line from a 3 period exponential moving average of the A/D Line. When the Chaikin Oscillator crosses above zero, it indicates a buy signal, and when it crosses below zero it indicates a sell signal. Also look for price divergence to indicate bullish or bearish conditions.**Chaikin Volatility**

The Chaikin Volatility indicator is the rate of change of the trading range. The indicator defines volatility as an increasing of the difference between the high and low. A rapid increase in the Chaikin Volatility indicates that a bottom is approaching. A slow decrease in the Chaikin Volatility indicates that a top is approaching.**Chande Momentum Oscillator (CMO)**

The Chande Momentum Oscillator is a modified RSI. Where the RSI divides the upward movement by the net movement (up / (up + down)), the CMO divides the total movement by the net movement ((up – down) / (up + down)).

There are several ways to interpret the CMO. Values over 50 indicate overbought conditions, while values under -50 indicate oversold conditions. High CMO values indicate strong trends. When the CMO crosses above a moving average of the CMO, it is a buy signal, crossing down is a sell signal.**Chicago Floor Trading Pivotal Point**

This function is used by floor traders on Chicago Mercantile Exchange to calculate short term support and resistance levels for commodities. It consists of two support and two resistance levels.**Commodity Channel Index (CCI)**

The CCI is designed to detect beginning and ending market trends. The range of 100 to -100 is the normal trading range. CCI values outside of this range indicate overbought or oversold conditions. You can also look for price divergence in the CCI. If the price is making new highs, and the CCI is not, then a price correction is likely.**Commodity Selection Index (CSI)**

The Commodity Selection Index is a composite indicator calculated by multiplying the ADXR (Average Directional Movement Rating) and the ATR (Average True Range) by a constant that incorporates the move value, commission, and margin. The CSI selects commodities that are suitable for short term trading (those with high CSI values).**Correl – Pearson Product Momentum Correlation Coefficient**

The Pearson coefficient is a type of correlation coefficient that represents the relationship between two variables that are measured on the same interval or ratio scale. It is a measure of the strength of the association between two continuous variables. Pearson coefficients range from +1 to -1, with +1 representing a positive correlation, -1 representing a negative correlation, and 0 representing no relationship.**Darvas Boxes (Bullish and Bearish Breakouts)**

The Darvas box theory is type of momentum strategy. The Darvas box theory uses market momentum theory along with technical analysis to determine when to enter and exit the market. Darvas boxes are a fairly simple indicator created by drawing a line along lows and highs to make the box.**DEMA**

The DEMA is a smoothing indicator with less lag than a straight exponential moving average. DEMA is an acronym for Double Exponential Moving Average, but the calculation is more complex than just a moving average of a moving average.**Demand Index**

The Demand Index is a market strength indicator based on price and volume that calculates a ratio buying pressure to selling pressure. It can be a leading indicator of price moves. A rising Demand Index suggests increasing buying pressure, while a falling Demand Index indicates increasing selling pressure. The Demand Index can be interpreted by looking for divergence with price to indicate impending price moves. Peaks in the Demand Index signal a coming peak in price. When the Demand Index hovers around zero, it indicates weak price moves.**De-trended Price**

The De-trended Price first calculates a regression line for a time series, then subtracts the slope of the line from the price. By removing the trend from the time series, the result is a series of de-trended prices. It has the effect of flattening out the trend to make oscillations more visible.**De-trended Price Oscillator (DPO)**

The De-trended Price Oscillator removes the trend in prices by subtracting a moving average of the price from the price. The De-trended Price shows cycles and overbought/oversold conditions. It highlights peaks and troughs in price, which are used to estimate buy and sell points in line with the historical cycle.**Directional Movement Index (DX)**

The DX is usually smoothed with a moving average (i.e. the ADX). The values range from 0 to 100, but rarely get above 60. To interpret the DX, consider a high number to be a strong trend, and a low number, a weak trend.

The DX was developed by J. Welles Wilder and is described in his 1978 book New Concepts in Technical Trading Systems. See also +/-DI, ADX, and ADXR.**Directional Movement Index aka Directional Indicator (+DI and -DI)**

Also known as Positive or Negative Directional Indicator, or PLUS_DI/MINUS_DI

The +DI is the percentage of the true range that is up. The -DI is the percentage of the true range that is down. A buy signal is generated when the +DI crosses up over the -DI. A sell signal is generated when the -DI crosses up over the +DI. You should wait to enter a trade until the extreme point is reached. That is, you should wait to enter a long trade until the price reaches the high of the bar on which the +DI crossed over the -DI, and wait to enter a short trade until the price reaches the low of the bar on which the -DI crossed over the +DI. The DI was developed by J. Welles Wilder and is described in his 1978 book New Concepts in Technical Trading Systems.

The Negative Directional Indicator (-DI) measures the presence of a downtrend and is part of the Average Directional Index (ADX). If -DI is sloping upward, it’s a sign that the price downtrend is getting stronger. This indicator is nearly always plotted along with the Positive Directional Indicator (+DI).

The Positive Directional Indicator (+DI) is a component of the Average Directional Index (ADX) and is used to measure the presence of an uptrend. When the +DI is sloping upward, it is a signal that the uptrend is getting stronger. This indicator is nearly always plotted along with the Negative Directional Indicator (-DI).

See also DX, ADX, and ADXR.**Down Average**

The Down Average is a Welles Wilder style moving average of the decreases between consecutive prices. Used in the calculation of the RSI.**Dynamic Momentum Index (DMI)**

The Dynamic Momentum Index is a variable term RSI. The RSI term varies from 3 to 30. The variable time period makes the RSI more responsive to short-term moves. The more volatile the price is the shorter the time period is. It is interpreted in the same way as the RSI, but provides signals earlier. See also RSI.**Ease of Movement**

The EMV emphasizes days in which the stock is moving easily and minimizes the days in which the stock is finding it difficult to move. This indicator is used frequently with equivolume charts to identify market formations. A buy signal is generated when the EMV crosses above zero, a sell signal when it crosses below zero. When the EMV hovers around zero, there are small price movements and/or high volume, which is to say, the price is not moving easily. The volume is divided by a volume increment (typically 10,000) to make the resultant numbers larger and easier to work with. The EMV is usually smoothed with a moving average.**Envelope Hi & Low with Bollinger Bandwidth**

The Envelope function creates plus and minus bands around series of numbers, based on a second series (bollinger bands). A common use is creating support/resistance bands around the close.**Envelope Hi & Low with Projection Bandwidth**

The Envelope function creates plus and minus bands around series of numbers, based on a second series (projection bands). A common use is creating support/resistance bands around the close.**Exponential Moving Average**

EMA 9, 12, 26, 50, 100, 200

The Exponential Moving Average is a staple of technical analysis and is used in countless technical indicators. In a Simple Moving Average, each value in the time period carries equal weight, and values outside of the time period are not included in the average. However, the Exponential Moving Average is a cumulative calculation, including all data. Past values have a diminishing contribution to the average, while more recent values have a greater contribution. This method allows the moving average to be more responsive to changes in the data.

See also Least Squares MA, Simple MA, Triangular MA, Weighted MA, Welles MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3**Following Adaptive Moving Average – FAMA**

What is the following adaptive moving average (FAMA)?

An interesting set of indicators result if the MAMA (Mesa Adaptive Moving Average) is applied to the first MAMA line to produce a Following Adaptive Moving Average (FAMA). By using an alpha in FAMA that is half the value of the alpha in MAMA, the FAMA has steps in time synchronization with MAMA, but the vertical movement is not as great.

See also MAMA – Mesa Adaptive Moving Average**Forecast Oscillator**

The Forecast Oscillator calculates the percentage difference between the actual price and the Time Series Forecast (the endpoint of a linear regression line). When the price and the forecast are equal, the Oscillator is zero. When the price is greater than the forecast, the Oscillator is greater than zero. When the price is less than the forecast, the Oscillator is less than zero. If the Forecast Oscillator stays below zero, it indicates that prices are about to fall, and if the Oscillator stays above zero, it indicates that prices are about to rise.**Forecast Oscillator Signal**

The Forecast Oscillator signal is an exponential moving average of the Forecast Oscillator. When the Oscillator crosses above/below the signal line, then prices are expected to rise/fall.**General Stochastic Calculation**

This is a general form of the Lane Stochastic calculation that works on any Array, instead of Bars. This is very useful for building composite indicators. The general Stochastic theory still applies, that is, that as prices decrease, they tend to accumulate near the extreme lows, and when rising, they tend to accumulate near the extreme highs.**Herrick Payoff Index**

The Herrick Payoff Index measures the money flowing in and out of a futures contract based on the trading range, volume and open interest. The HPI is interpreted by looking for divergence with the price.

The Herrick Payoff Index was developed by John Herrick.**Hilbert Transform****Hilbert_Transform_Dominant_Cycle_Period****Hilbert_Transform_Dominant_Cycle_Phase****Hilbert_Transform_Phasor_In_Phase****Hilbert_Transform_Phasor_Quadrature****Hilbert_Transform_Sine_Lead_Sine****Hilbert_Transform_Sine_Sine****Hilbert_Transform_Instantaneous_Trendline****Hilbert_Transform_Trend_vs_Cycle_Mode**

The Hilbert Transform is a technique used to generate inphase and quadrature components of a de-trended real-valued “analytic-like” signal (such as a Price Series) in order to analyze variations of the instantaneous phase and amplitude.**Hilbert_Transform_Dominant_Cycle_Period: **

Based on closing prices (or the array provided), this function returns the period (length) of the most dominant waveform it detects. This period is useful because a number of other standard indicators operate at their very best (quicker detection, maximum gain) when set to a period that matches the length of the dominant cycle period (divided by two or by four in some cases). In the case of RSIs and stochastics, these are said to work best when set to half of the current HT_DC_Period.

Things to keep in mind when using HT_DC_Period:

1. The values produced by the HT_DC_Period function are (approximately) 5 to 50. You may want to be aware of this if you’re using HT_DC_Period for other uses, or if you just wanted to know the range.

2. HT_DC_Period does not provide a single value that describes a stock, bond, currency pair, etc. Instead, for each and every point along price series (such the daily stock chart for MSFT), it provides a new value. If you were to plot HT_DC_Period, each column should have a different value (assuming you were working with an ordinary stock price chart).

3. When given a long enough series of price data to work with, even if it is not able to detect a dominant cycle at the current position, it will pull in some of the price data that’s before or after the present time in order to provide a reasonable and stable HT_DC_Period value to work with.**Hilbert_Transform_Dominant_Cycle_Phase: **

Returns the phase of the dominant cycle. Output ranges from -45 to 315 (representing 360 degrees).

A rapid transition from the largest value to the smallest value is used to detect the start of a new cycle (when in cyclic mode).**Hilbert_Transform_Sine_Lead_Sine:**

“The sine of the phase angle advanced by 45 degrees.” Quoting from Market Mode Strategies.doc by John Ehlers from MESA Software, “A clear, unequivocal cycle mode indicator can be generated by plotting the Sine of the measured phase angle advanced by 45 degrees. This leading signal crosses the sinewave 1/8th of a cycle BEFORE the peaks and valleys of the cyclic turning points, enabling you to make your trading decision in time to profit from the entire amplitude swing of the cycle.” This indicator by itself can be treated as an overbought/oversold indicator when above 0.85 and below -0.85. Range is from -1 to 1.**Hilbert_Transform_Sine_Sine: **

The sine of the DC Phase. Crossover of HT_Sine AND HT_Lead_Sine anticipates a turning point during cycle mode.**Hilbert_Transform_Instantaneous_Trendline: **

Also known as the MESA Instantaneous Trendline. Appears much like a Moving Average, but with minimal lag compared to ordinary moving averages. Created by removing the Dominant Cycle (the primary sine wave detected by the Hilbert Transform) from the price series.**Hilbert_Transform_Trend_vs_Cycle_Mode: **

Uses the Hilbert Transform to determine when the provided data is in Cycle Mode (value = 0) or Trend Mode (value = 1). According to Ehlers, a market will switch back and forth between Trend Mode and Cycle Mode, and as it does, your tools and your trading strategy should change with it. Some algorithms disable their Hilbert Transform functions while trend mode is active.**Ichimoku Kinko Hyo**

Ichimoku Kinko Hyo is Japanese for “one glance cloud chart.” It consists of five lines called Tenkan-sen, Kijun-sen (sen is Japanese for line), Senkou Span A, Senkou Span B and Chinkou Span. The calculation uses four different time periods which we call termT, termK, termS, and termC.

The Ichimoku Kinko Hyo is graphed over the closing price line.

The space between the Senkou spans is called the Cloud, and is usually graphed in a hatched pattern.

The Senkou Spans are support and resistance lines. When the price is in the Cloud, the market is non-trending. When the price is above the Cloud, the higher Span is the first support level and the lower Span is the second support level. When the price is below the Cloud, the lower Span is the first resistance level and the higher Span is the second resistance level.

Kijun-sen and Tenkan-sen are trend indicators. When the price is above the Kijun-sen, prices will likely continue to go up, when the price is below the Kijun-sen, prices will likely continue to go down. The direction of the Tenkan-sen indicates the direction of the trend. If the Tenkan-sen is flat, the market is in a non-trending channel. A buy signal is generated when the Chinkou Span crosses over the price, or when the Tenkan-sen crosses over the Kijun-sen. A sell signal is generated when the Chinkou Span crosses under the price, or when the Tenkan-sen crosses under the Kijun-sen. Look for confirmation when both crosses occur.**Inertia**

The Inertia indicator is the Relative Volatility Index (RVI) smoothed with a Least Squares Moving Average. Like the RVI, the Inertia ranges from 0 to 100. Inertia signals long-term trends. Positive Inertia is indicated by values above 50, while values below 50 indicate negative inertia (slowing).**Intraday Momentum Index (IMI)**

The Intraday Momentum Index is similar to the RSI, but uses the movement between the open and close whereas the RSI uses the movement between the close and the previous close. IMI values over 70 indicate an overbought condition, and values under 30 indicate oversold.**Klinger Oscillator**

The Klinger Oscillator uses a combination of high-low trading range, volume and accumulation/distribution to find trading tops and bottoms. The KO is used with a signal line which is a 13 period Exponential Moving Average of the KO.

To interpret the KO, look for divergence with the price to signal the coming end of a trend, or to indicate that rising/falling prices are not forming a new trend. A buy signal is generated when the KO rises from below zero to cross above the trigger line. A sell signal is generated when the KO falls from its high and crosses below the trigger line. The Klinger Oscillator is also known as the Klinger Volume Oscillator or KVO.**Klinger Oscillator Trigger**

The signal line (or trigger line) of the Klinger Oscillator.**KAMA – Kaufman Adaptive Moving Average**

KAMA 10, 14, 20, 50, 100, 200

Developed by Perry Kaufman, Kaufman’s Adaptive Moving Average (KAMA) is a moving average designed to account for market noise or volatility. KAMA will closely follow prices when the price swings are relatively small and the noise is low. KAMA will adjust when the price swings widen and follow prices from a greater distance. This trend-following indicator can be used to identify the overall trend, time turning points and filter price movements.

NOTE: The KAMA function has an unstable period.**Least Squares Moving Average**

LSMA 10, 14, 20, 50, 100, 200

The Least Squares Moving Average first calculates a least squares regression line over the preceding time periods, and then projects it forward to the current period. In essence, it calculates what the value would be if the regression line continued.

The Least Squares Moving Average is also known as an Endpoint Moving Average, a Time Series Moving Average, or a Time Series Forecast. See also Exponential MA, Simple MA, Triangular MA, Weighted MA, Welles MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3. The default time period for this indicator is 14 days.**Linear Regression**

The Linear Regression Indicator plots the ending value of a Linear Regression Line for a specified number of bars; showing, statistically, where the price is expected to be. For example, a 20 period Linear Regression Indicator will equal the ending value of a Linear Regression line that covers 20 bars.**Linear Regression Angle**

Linear Regression Angle is a directional movement indicator which defines a trend at the moment of its birth, and additionally defines trend weakening. The indicator calculates the angle of the linear regression channel and displays it in a separate window in the form of histogram. The signal line is a simple average of the angle.

The angle is the difference between the right and left edges of regression (in points), divided by its period.

The angle value above 0 indicates an uptrend. The higher the value, the stronger the trend. A value below 0 indicates a downtrend. The lower the value, the stronger the downtrend.**Linear Regression Intercept**

Linear regression is a statistical tool used to help predict future values from past values. It is commonly used as a quantitative way to determine the underlying trend and when prices are overextended. A linear regression trendline uses the least squares method to plot a straight line through prices so as to minimize the distances between the prices and the resulting trendline. This linear regression intercept indicator plots the **intercept** for the trendline for each data point.**Linear Regression Slope**

Linear regression is a statistical tool used to help predict future values from past values. It is commonly used as a quantitative way to determine the underlying trend and when prices are overextended. A linear regression trendline uses the least squares method to plot a straight line through prices so as to minimize the distances between the prices and the resulting trendline. This linear regression indicator plots the **slope** of the trendline value for each given data point.**Line Oscillator – Open to Close**

The Line Oscillator is the difference between the Simple Moving Averages of two input data series. It is a generic function that can be used in conjunction with other indicators.**Market Facilitation Index (MFI)**

Market Facilitation Index (MFI) is the trading range divided by the volume. The MFI measures the price movement per unit of volume. To interpret the MFI, compare it to the volume. When the MFI is high and volume is low, it signals a fake trend which will soon reverse. When the MFI is low and volume is high, it signals a new trend in either direction is about to occur. When the MFI is low and volume is also low, it signals a fading market and an impending trend reversal. When the MFI is high and volume is also high, it signals a strong trend.**Mass Index**

The Mass Index is a moving sum of a 9 period Exponential Moving Average of the trading range (high minus low) divided by the double smoothed moving average of the range. The Mass Index is intended to identify trend reversals. Higher Mass Index values are created by widening trading ranges, which indicate a trend reversal. The Mass Index is often used to identify potential trend reversal points when it rises above a certain threshold. A common signal is when the Mass Index rises above 27 and then falls back below 26.5**Max 30 days**

Highest close over a specified period – 30 Days**Max Close Position 30 days**

Index of highest close over a specified period – 30 Days. Zero-based – Meaning that the value corresponds to the Row # + 1**Median Price**

The Median Price is the average of the high + low of a bar. It can be used to smooth an indicator that normally takes just the closing price as input. See also Average Price, Typical Price, and Weighted Close.**MESA Sinewave**

The Mesa Sine Wave calculates two sine curves. When the two curves resemble a sine wave, the market is in a cycle, otherwise the market is trending. Signals are generated only when the market is in a cycle. A buy signal is generated when the Sine crosses up over the Lead Sine and a sell signal when the Sine crosses down below the Lead Sine.**MESA Adaptive Moving Average – MAMA**

Developed by John Ehlers, the MESA Adaptive Moving Average is a technical trend-following indicator which, according to its creator, adapts to price movement “based on the rate change of phase as measured by the Hilbert Transform Discriminator”. This method of adaptation features a fast and a slow moving average so that the composite moving average swiftly responds to price changes and holds the average value until the next bars close.**Midpoint – Midpoint over period**

Over an n day period, (highest close + lowest close)/2**Midprice – Midpoint Price over period**

Over an n day period, (highest high + lowest low)/2**Min 30 days**

Lowest close over a specified period – 30 Days**Min Close Position 30 days**

Index of lowest close over a specified period – 30 Days. Zero-based – Meaning that the value corresponds to the Row # + 1**Momentum**

The Momentum is a measurement of the acceleration and deceleration of prices. It indicates if prices are increasing at an increasing rate or decreasing at a decreasing rate. The Momentum function can be applied to the price or to any other data series.**Money Flow Index**

The Money Flow Index calculates the ratio of money flowing into and out of a security. To interpret the Money Flow Index, look for divergence with price to signal reversals. Money Flow Index values range from 0 to 100. Values above 80/below 20 indicate market tops/bottoms.**Moving Average Envelope High & Low**

The MA Envelope function creates high and low bands around a moving average.**Moving Averages of the High and Low**

The MA High Low function creates exponential moving averages of the high and the low.**Moving Average Convergence/Divergence (MACD)**

The Moving Average Convergence Divergence (MACD) is the difference between two Exponential Moving Averages. The MACD signals trend changes and indicates the start of new trend direction. High values indicate overbought conditions, low values indicate oversold conditions. Divergence with the price indicates an end to the current trend, especially if the MACD is at extreme high or low values. When the MACD line crosses above the signal line a buy signal is generated. When the MACD crosses below the signal line a sell signal is generated.

To confirm the signal, the MACD should be above zero for a buy, and below zero for a sell. The time periods for the MACD are often given as 26 and 12. However the function actually uses exponential constants of 0.075 and 0.15, which are closer to 25.6667 and 12.3333 periods. To create a similar indicator with time periods other than those built into the MACD use the Price Oscillator function.**Moving Average Convergence/Divergence Signal**

The Signal line is an Exponential Moving Average of the MACD.**Moving Dispersion**

The Moving Dispersion calculates the absolute change between values over a given time period.**Moving Regression Line Slope and Constant of Least Squares Regression Line – 2 arrays**

The Moving Regression Line function fills two output arrays with the slope and constant of a least squares regression line of the input data series over the given time period. This function is used in the calculation of several indicators. It can be used to calculate the slope of the price or any indicator.**Moving Standard Deviation**

This function is used in the calculation of several indicators. Standard Deviation is often used as a measure of volatility. The default time period is 14 days although we also provide the 10, 20, 50, 100, and 200 day values. Standard Deviation is the square root of the variance.**Moving Standard Error**

The Moving Standard Error function fills the output Array with the standard error of the last n values of the input Array. This function is used in the calculation of several indicators. It can take price or the output of any indicator as its input.**Moving Summation**

The moving summation is the sum of the last n values. It is a Simple Moving Average without dividing the sum by n. The moving sum is used in the calculation of many indicators. It can also be used to modify any existing indicator.**Normalized Average True Range (NATR)**

Normalized Average True Range is a measure of volatility. Because Normalized Average True Range is normalized, it can be more useful than Average True Range when comparing across different price levels.

John Forman’s formula for Normalized ATR, or NATR, is:

NATR = ATR / Close * 100%

**Negative Volume Index (NVI)**

Negative Volume Index (NVI) attempts to identify bull markets by showing what the smart investors are doing. It is based on the assumption smart investors dominate trading on light volume days and uninformed investors dominate trading on active days. The NVI changes on days when the volume is down and stays flat on up volume days. Look for the NVI to rise above its one year moving average to signal a bull market. See also the Positive Volume Index.**Net Momentum Oscillator (NMO)**

The Net Momentum Oscillator (NMO) is a variation on the RSI. Whereas the RSI based on the ratio of up periods to down periods, the NMO is the ratio of the momentum (up – down) to the absolute momentum (up + down). The NMO is able to show overbought and oversold levels (greater than +50, less than -50) better than the RSI.**On Balance Open Interest (OBOI)**

The OBOi function returns the total On Balance Open Interest for the specified time period.**On Balance Volume (OBV)**

The On Balance Volume (OBV) is a cumulative total of the up and down volume. When the close is higher than the previous close, the volume is added to the running total, and when the close is lower than the previous close, the volume is subtracted from the running total.

To interpret the OBV, look for the OBV to move with the price or precede price moves. If the price moves before the OBV, then it is a non-confirmed move. A series of rising peaks or falling troughs in the OBV indicates a strong trend. If the OBV is flat, the market is not trending.**On Balance Volume, Expanded System**

The On Balance Volume, Expanded System calculates OBV and identifies the breakouts and field trends as described in Joseph Granville’s 1963 book New Strategy of Daily Stock Market Timing for Maximum Profit. The breakout Array is filled with the following codes: 1 = up, -1 = down, 0 = no breakout on this bar. The fieldtrend Array is filled with the following codes: 1 = rising, -1 = falling, 0 = doubtful.

See also On Balance Volume and On Balance Volume, Moving.**On Balance Volume, Moving**

This version of the On Balance Volume (OBV) is a moving total, not a cumulative total. That is, only the values from the past n days are totaled, as opposed to totaling all days from the beginning of the data series. See on Balance Volume for more information. Also see On Balance Volume, Expanded System.**Oscillator – Open to Close**

The Oscillator function calculates the difference between two data series. It is a generic function that can take any price or indicator data as input. It is used in the calculation of many indicators.**Oscillator (Percent) – Open to Close**

The OscillatorPct function calculates the difference between two data series as a percentage. It is a generic function that can take any price or indicator data as input. It is used in the calculation of many indicators.**Parabolic SAR (Parabolic Stop and Reverse)**

The Parabolic SAR calculates a trailing stop. Simply exit when the price crosses the SAR. The SAR assumes that you are always in the market and calculates the Stop and Reverse point when you would close a long position and open a short position or vice versa.**Parabolic SAR Position**

Represents the positions of the Parabolic SAR dots relative to the price line. The value will be 0,-1, or 1. When the dots flip, it indicates that a potential change in price direction is under way. For example, if the dots are above the price (-1), when they flip below the price (+1), it could signal a rise in price.**Percentage Volume Oscillator (PVO)**

The Percentage Volume Oscillator (PVO) is the percentage difference between two moving averages of volume. The PVO has a maximum of 100, but no minimum value.

PVO crosses over zero when the fast Exponential Moving Average (EMA) is greater than the slow EMA indicating that volume is above average. The PVO crosses below zero when the fast EMA is less than the slow EMA indicating that volume is below average. The direction of the PVO curve indicates rising or falling volume levels. Look for strong volume (rising PVO) to confirm price trends. A moving average of the PVO can be used as a signal line to indicate longer term movements and to look for crossovers.**Performance Indicator**

The Performance indicator displays the percentage difference between the price today and the price at the start of the data series. It is also known as a normalized price. It can be useful for comparing the performance of two securities or a security and an index. In our current implementation, we compare Close to the Close on the first day of the series for each asset.**Polarized Fractal Efficiency (PFE)**

The Polarized Fractal Efficiency indicator uses fractal geometry to determine how efficiently the price is moving. It fluctuates between -100 and 100 where the centerline is at zero. The price shows an upward trend if the PFE goes above zero and a downward trend if it drops below zero. The higher/lower the PFE value, the stronger the trend is.

The Polarized Fractal Efficiency indicator was developed by Hans Hannula and was introduced in the January, 1994 issue of Technical Analysis of Stocks & Commodities magazine.**Positive Volume Index (PVI)**

The Positive Volume Index (PVI) attempts to identify bull markets. The PVI shows what the uninformed investors are doing, while the Negative Volume Index shows what the smart investors are doing. It is based on the assumption smart investors dominate trading on light volume days and uninformed investors dominates trading on active days. The PVI changes on days when the volume is up and stays flat on down volume days.

See also the Negative Volume Index.**Price and Volume Trend (PVT)**

The Price Volume Trend (PVT) is similar to the On Balance Volume (OBV). The OBV is a cumulative total of the up and down volume based on whether the close is greater or less than the previous close. However, the PVT is a cumulative total of volume times the percentage change of the close from the previous close so it adds more of the volume to the total when the price makes greater moves. The PVT is interpreted in the same ways as the OBV.

See also On Balance Volume.**Price Channels**

The Price Channels indicator creates a high band of the highest high over the last n periods and a low band of the lowest low over the last n periods. The bands are support and resistance levels. See also Bollinger Bands, Envelope, and Projection Bands.**Price Oscillator**

The Price Oscillator shows the difference between two moving averages. It is basically a MACD, but the Price Oscillator can use any time periods. A buy signal is generated when the Price Oscillator rises above zero and a sell signal when it falls below zero. See also Price Oscillator Percent, MACD.**Price Oscillator, Percent**

The Price Oscillator Percent shows the percentage difference between two moving averages. A buy signal is generated when the Price Oscillator Percent rises above zero and a sell signal when it falls below zero.**Price Volume Rank**

The Price Volume Rank was developed as a simple indicator that could be calculated even without a computer. The basic interpretation is to buy when the PV Rank is below 2.5 and sell when it is above 2.5. Potential values are 1,2,3,4**Projection Bands**

Projection Bands are calculated by finding the highest high and lowest low over the last n periods and plotting them parallel to a regression line of the high/low. The Projection Bands are support and resistance levels. When the price reaches the upper band, it signals a price top and probable reversal. Likewise, when the price reaches the bottom band, it signals a bottom. The price will never actually break above or below the bands (unlike Bollinger Bands).

See also Projection Bandwidth and Projection Oscillator. For other types of bands, see Bollinger Bands, Envelope, and Price Channels.**Projection Bandwidth**

Projection Bandwidth is based on the Projection Bands indicator. It is the ratio of the width of the bands to the midpoint. A low number indicates that the bands are narrowing; a high number means that the bands are widening. The band width is a measure of volatility. Narrow bands mean a narrow trading range and low volatility; wide bands, wide range, high volatility. The calculation is as follows:

200 x (Projection_Bands_Hi – Projection_Bands_Low) / (Projection_Bands_Hi + Projection_Bands_Low)

See also Projection Bands and Projection Oscillator.

**Projection Oscillator**

The Projection Oscillator is based on the Projection Bands indicator. The Oscillator calculates where the close lies within the band as a percentage. Therefore, an Oscillator value of 50 would mean that the close is in the middle of the band. A value of 100 would mean that the close is equal to the top band, and zero means that it is equal to the low band. The calculation is similar to a Stochastic which uses the raw highest high and lowest low value, whereas the Projection Oscillator adds the regression line component, making it more sensitive.

The Projection Oscillator can be interpreted several ways. Look for divergence with price to indicate a trend reversal. Extreme values (over 80 or under 20) indicate overbought/oversold levels. A moving average of the oscillator can be used as a trigger line.

A buy/sell signal is generated when the Projection Oscillator to cross above/below the trigger line. The signal is stronger if it happens above 70 or below 30. See also Projection Bands and Projection Bandwidth.**Qstick**

The Qstick indicator is an 8 period exponential moving average of the difference between the open and close (close-open). The “stick” in the name comes from candlestick charting. The body of a candlestick is from the open to the close. A white candlestick is an up and a black candlestick is a down day. Positive Qstick values indicate a majority of up days; negative values, a majority of down days.

To interpret the Qstick, look for a buy signal when it crosses above zero and a sell signal when it crosses below zero. Also look for a buy signal when the Qstick is very low and turns up and a sell signal when it is very high and turns down. A moving average of the Qstick can be used as a trigger line (look for the Qstick to cross the trigger). You can also look for divergence between the Qstick and price to indicate the end of a trend or as a non-confirmation of a price move.**Random Walk Index (RWI)**

The Random Walk Index (RWI) is used to determine if an issue is trending or in a random trading range by comparing it to a straight line. The more random the price movement, the more the RWI fluctuates. The short-term (2 to 7 periods) RWI is an overbought/oversold indicator used by short-term traders, while the long-term (8 to 64 periods) RWI is a trend indicator used more by long-term investors. An issue is trending higher if the RWI of the highs is greater than 1, while a downtrend is indicated if the RWI of the lows is greater than 1.

When the RWI High is above the RWI Low, it means there is more upward strength than downward strength and vice versa. Readings below one mean movement could be random because there is not enough strength to indicate otherwise.

At OLAPTrader, we currently calculate a 64 period RWI. In the future, we may calculate a short-term RWI as well. If so, the following comparison may be made between the two:

A buy signal is generated when the long-term RWI of the highs is greater than 1 and the short-term RWI of the lows rises above 1. A sell signal is generated when the long-term RWI of the lows is greater than 1 and the short-term RWI of the highs rises above 1.

**Range Indicator**

The Range indicator compares the intraday range (high – low) to the inter-day (close – previous close) range. When the intraday range is greater than the inter-day range, the Range Indicator will be a high value. This signals an end to the current trend. When the Range Indicator is at a low level, a new trend is about to start.**Ratio – Open to Close**

The Ratio function measures relationships between two data series. It is used in the calculation of many indicators and can be used with the output of other indicators.**Rate of Change – ROC**

The Rate of Change function measures rate of change relative to previous periods. The function is used to determine how rapidly the data is changing. The factor is usually 100, and is used merely to make the numbers easier to interpret or graph. The function can be used to measure the Rate of Change of any data series, such as price or another indicator. When used with the price, it is referred to as the Price Rate of Change, or PROC.**Relative Momentum Index (RMI)**

The Relative Momentum Index (RMI) is a variation on the Relative Strength Index (RSI). To determine up and down days, the RSI uses the close compared to the previous close. The RMI uses the close compared to the close n days ago. An RMI with a time period of 1 is equal to the RSI. The RMI ranges from 0 to 100. Like the RSI, The RMI is interpreted as an overbought/oversold indicator when the value is over 70/below 30. You can also look for divergence with price. If the price is making new highs/lows, and the RMI is not, it indicates a reversal.**Relative Strength Index (RSI)**

The Relative Strength Index (RSI) calculates a ratio of the recent upward price movements to the absolute price movement. The RSI ranges from zero to 100. The RSI is interpreted as an overbought/oversold indicator when the value is over 70/below 30. You can also look for divergence with price. If the price is making new highs/lows, and the RSI is not, it indicates a reversal.**Relative Volatility Index (RVI)**

The Relative Volatility Index (RVI) is based on the Relative Strength Index (RSI). Whereas the RSI uses the average price change, the RVI uses a nine period standard deviation of the price. The RVI indicator is a revision of the original RVI. The original version of the RVI is calculated using the closing price. The revised version is calculated by taking the average of the original RVI of the high and the original RVI of the low. See Relative Volatility Index – Original Calculation for the original version.

The RVI is a volatility indicator. It was developed as a compliment to and a confirmation of momentum based indicators. When used to confirm other signals, only buy when the RVI is over 50 and only sell when the RVI is under 50. If a signal is ignored, buy when the RVI is over 60 and sell when the RVI is under 40. Exit a long position if the RVI drops below 40 and exit a short position when the RVI rises above 60.**Relative Volatility Index (RVI) Original Calculation**

The original version of the RVI is calculated using the closing price. The revised version is calculated by taking the average of the original RVI of the high and the original RVI of the low. See Relative Volatility Index for the revised version.**R-squared**

The r-squared indicator calculates how well the close price approximates a linear regression line. The indicator gets its name from the calculation which is the square of the correlation coefficient (referred to in mathematics by the Greek letter rho, or r). The range of the r-squared is from zero to one.

High r-squared values indicate a strong correlation, and an indication of a trend.

A high R-squared, between .85 and 1.0, indicates that the stock or fund’s performance strongly approximates a linear regression line. A fund with a low R-squared, at 0.7 or less, indicates the security does not generally approximate a linear regression line.

**Simple Moving Average**

SMA 10, 14, 20, 50, 100, 200

Moving Averages are used to smooth the data in an array to help eliminate noise and identify trends. The Simple Moving Average is literally the simplest form of a moving average. Each output value is the average of the previous n values. In a Simple Moving Average, each value in the time period carries equal weight, and values outside of the time period are not included in the average. This makes it less responsive to recent changes in the data, which can be useful for filtering out those changes.

See also Exponential MA, Least Squares MA, Triangular MA, Weighted MA, Welles MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3.**Standard Error Bands**

Standard Error Bands are a type of envelope. They look similar to Bollinger Bands, however the calculation and interpretation is different. The middle band is a Least Squares Moving Average. The high band is the middle band plus a factor times the n period standard error. The low band is the middle band minus a factor times the n period standard error. When the bands are close together, it means that there is a low standard error, which means that the price is in a trend. When the bands are farther apart, then the price is not trending. When the price is in a trend and the bands are close together, look for the bands to widen to signal the end of the trend.**Stochastic Momentum Index (SMI)**

The Stochastic Momentum Index (SMI) is based on the Stochastic Oscillator. The difference is that the Stochastic Oscillator calculates where the close is relative to the high/low range, while the SMI calculates where the close is relative to the midpoint of the high/low range. The values of the SMI range from +100 to -100. When the close is greater than the midpoint, the SMI is above zero, when the close is less than the midpoint, the SMI is below zero. The SMI is interpreted the same way as the Stochastic Oscillator. Extreme high/low SMI values indicate overbought/oversold conditions. A buy signal is generated when the SMI rises above -50, or when it crosses above the signal line. A sell signal is generated when the SMI falls below +50, or when it crosses below the signal line. Also look for divergence with the price to signal the end of a trend or indicate a false trend.**Stochastic Momentum Index Signal**

The signal line of the Stochastic Momentum Index.**Stochastic Oscillator**

The Stochastic Oscillator measures where the close is in relation to the recent trading range. The values range from zero to 100. %K values over 75 indicate an overbought condition; values under 25 indicate an oversold condition. When the Fast %K crosses above the Fast %D, it is a buy signal; when it crosses below, it is a sell signal. When a double-smoothed %K is available (aka Slow %D), a buy signal is triggered when the Fast %D crosses over the Slow %D.* Terminology:*Stochastic Oscillator K (%K or Fast K) refers to a 5 day Fast Stochastic Oscillator where %K is un-smoothed.

Stochastic Oscillator D (%D) refers to a 3 day moving average of the %K. This may also be called a Slow %K or Fast %D.

Slow %D is a 3 period moving average of a smoothed %K, in effect: a double smoothed %K.

%D Always refers to a smoothed %K (whether or not the %K itself is smoothed).

**Stochastic RSI**

Stochastic RSI (StochRSI) is an indicator of an indicator. It calculates the Relative Strength Indicator (RSI) relative to its range in order to increase the sensitivity of the standard RSI. The values of the StochRSI are from zero to one.

The Stochastic RSI can be interpreted several ways. Overbought/oversold conditions are indicated when the StochRSI crosses above .80 / below .20. A buy signal is generated when the StochRSI moves from oversold to above the midpoint (.50). A sell signal is generated when the StochRSI moves from overbought to below the midpoint. Also look for divergence with the price to indicate the end of a trend.

**SUM (summation) 30 days**

Sum of the Close price over 30 day timeframe.

**Swing Index**

The Swing Index attempts to determine the real price. The numbers range from -100 to +100. It is difficult to interpret in its raw form, and is usually summed to form the Accumulation Swing Index. It is important to use the correct limit move for the commodity you are analyzing (e.g. $3.00 for T-Bonds, $0.04 for Heating Oil, etc.). For a stock, limit move should be a large number, such as $10,000.

**T3**

The T3 is a type of moving average, or smoothing function. It is based on the DEMA. The T3 takes the DEMA calculation and adds a vfactor which is between zero and 1. The resultant function is called the GD, or Generalized DEMA. A GD with vfactor of 1 is the same as the DEMA. A GD with a vfactor of zero is the same as an Exponential Moving Average. The T3 typically uses a vfactor of 0.7. The T3 triple-smoothes the data series by calling the GD three times. You can pass any value for tcount to the T3 function. For instance, a tcount of 4 would be quadruple-smoothed, in effect a T4. A tcount of 1 would be a single-smoothed GD. Any data series can be smoothed with the T3, including price or the output of another indicator.

See also Exponential Moving Average, DEMA, and TEMA.

**T4**

A quadruple-smoothed GD (Generalized DEMA). See T3 above.

**TEMA**

The TEMA is a smoothing indicator with less lag than a straight exponential moving average. TEMA is an acronym for Triple Exponential Moving Average, but the calculation is more complex than that.

**Trend Score**

The Trend Score is a simple indicator that attempts to show when price is trending by looking at up and down days. The trend is equal to one when the price is greater than or equal to the previous price, and as a negative one when the price is less than the previous price. The Trend Score is the moving summation of those ones and negative ones over the past n periods.

**Triangular Moving Average**

TMA 10, 14, 20, 50, 100, 200

The Triangular Moving Average is a form of Weighted Moving Average wherein the weights are assigned in a triangular pattern. For example, the weights for a 7 period Triangular Moving Average would be 1, 2, 3, 4, 3, 2, 1. This gives more weight to the middle of the time series and less weight to the oldest and newest data. The Triangular Moving Average is mathematically equivalent to a Simple Moving Average of a Simple Moving Average. The default time period is 14 days.

See also Exponential MA, Least Squares MA, Simple MA, Weighted MA, Welles MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3.

**TRIX**

The TRIX indicator calculates the rate of change of a triple exponential moving average. The values oscillate around zero. Buy/sell signals are generated when the TRIX crosses above/below zero. A (typically) nine period exponential moving average of the TRIX can be used as a signal line. Buy/sell signals are generated when the TRIX crosses above/below the signal line or above/below zero.

**True Range**

The True Range function is used in the calculation of many indicators, most notably, the Welles Wilder DX. It is a base calculation that is used to determine the normal trading range of a stock or commodity.

**True Strength Index (TSI)**

The True Strength Index (TSI) is a variation of the Relative Strength Index (RSI). The TSI uses a double smoothed exponential moving average of price momentum to eliminate choppy price changes and spot trend changes. This indicator has a little or no time lag.

**Time Series Forecast (TSF)**

The Time Series Forecast (TSF) is a linear regression calculation that plots each bar’s current regression value using the least square fit method. This indicator is sometimes referred to as a moving linear regression similar to a moving average. For example, the TSF value that covers 10 days will have the same value as a 10-day Time Series Forecast. This differs slightly from the Linear Regression indicator in that the Linear Regression indicator does not add the slope to the ending value of the regression line. The TSF is the same as the Least Squares Moving Average, assuming the time periods for the calculations are the same.

**Typical Price**

The Typical Price is the average of the high + low + close of a bar. It is used in the calculation of several indicators. It can be used to smooth an indicator that normally takes just the closing price as input.

**Ultimate Oscillator**

The Ultimate Oscillator is the weighted sum of three oscillators of different time periods. The typical time periods are 7, 14, and 28. The values of the Ultimate Oscillator range from zero to 100. Values over 70 indicate overbought conditions, and values under 30 indicate oversold conditions. Also look for agreement/divergence with the price to confirm a trend or signal the end of a trend.

**Up Average**

The Up Average is a Welles Wilder style moving average of the increases between consecutive prices. Used in the calculation of the RSI.

**Variable Moving Average**

A Variable Moving Average is an exponential moving average that automatically adjusts the smoothing weight based on the volatility of the data series. The more volatile the data is, the more weight is given to the more recent values. The Variable Moving Average solves a problem with most moving averages. In times of low volatility, such as when the price is trending, the moving average time period should be shorter to be sensitive to the inevitable break in the trend. Whereas in more volatile non-trending times, the moving average time period should be longer to filter out the choppiness. Almost any measure of volatility can be used in calculating the Variable Moving Average, however, most implementations use a 9 period Chande Momentum Oscillator (CMO).

The default time period is 14 days.

**Variance**

Variance in statistics is a measurement of the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean and therefore from every other number in the set.

In investing, the variance of the returns among assets in a portfolio is analyzed as a means of achieving the best asset allocation. The variance equation, in financial terms, is a formula for comparing the performance of the elements of a portfolio against each other and against the mean.

Variance is calculated by taking the differences between each number in the data set and the mean, then squaring the differences to make them positive, and finally dividing the sum of the squares by the number of values in the data set. We compare the current price of an asset with the prior prices. We do this for different time frames – 5,10,14,20,50,100, and 200 days.

**Vertical Horizontal Filter (VHF)**

The Vertical Horizontal Filter (VHF) determines whether prices are trending. When the VHF is rising, it indicates the formation of a trend. Higher VHF values indicate a stronger trend. When the VHF is falling, it indicates the trend is ending and price is becoming congested. Very low VHF values indicate a trend may follow.

**VIDYA**

VIDYA is an acronym of Variable Index Dynamic Average. The VIDYA is an exponential moving average that automatically adjusts the smoothing weight based on the volatility of the data series. The more volatile the data is the more weight is given to the more recent values. The VIDYA solves a problem with most moving averages. In times of low volatility, such as when the price is trending, the moving average time period should be shorter to be sensitive to the inevitable break in the trend. Whereas, in more volatile non-trending times, the moving average time period should be longer to filter out the choppiness.

**Volume Adjusted Moving Average**

VAMA 10, 14, 20, 50, 100, 200

The Volume Weighted Moving Average is a weighted moving average that uses the volume as the weighting factor, so that higher volume days have more weight. It is a non-cumulative moving average in that only data within the time period is used in the calculation.

See also Exponential MA, Least Squares MA, Simple MA, Triangular MA, Weighted MA, Welles MA, Variable MA, Zero Lag Exponential MA, DEMA, KAMA, TEMA, and T3. The default time period is 14 days.

**Weighted Close**

The Weighted Close is the average of the high, low and close of a bar, but the close is weighted, actually counted twice. It is used in the calculation of several indicators. It can be used to smooth an indicator that normally takes just the closing price as input.

**Weighted Moving Average**

WMA 10, 14, 20, 50, 100, 200

The Weighted Moving Average calculates a weight for each value in the series. The more recent values are assigned greater weights. The Weighted Moving Average is similar to a Simple Moving average in that it is not cumulative, that is, it only includes values in the time period (unlike an Exponential Moving Average). The Weighted Moving Average is similar to an Exponential Moving Average in that more recent data has a greater contribution to the average.

See also Exponential MA, Least Squares MA, Simple MA, Triangular MA, Welles MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3. The default time period is 14 days.

**Welles Wilder Moving Average**

WWMA 10, 14, 20, 50, 100, 200

The Welles Wilder method of calculating moving averages is very similar to a Simple Moving Average. Both calculations provide similar results. Welles designed his formula to be easily computed by hand or with a simple calculator. For the sake of consistency Welles’ Moving Averages are used in all Welles indicator formulas (ADX, ADXR, and ATR). The default time period is 14 days.

See also Exponential MA, Least Squares MA, Simple MA, Triangular MA, Weighted MA, Variable MA, Volume Adjusted MA, Zero Lag Exponential MA, DEMA, TEMA, and T3.

**Welles Wilder Summation**

The Welles Sum is the Welles Wilder method of creating the moving sum of a data series. Each value is the sum of the last n periods. Welles designed his formula to be easily computed by hand or with a simple calculator. The numbers will vary slightly from a simple (arithmetic) sum. For consistency with the original formulas, the Welles Sum is used in the calculation of Welles Wilder’s indicators (the +/-DI and by extension the DX, ADX, ADXR).

**Welles Wilder Volatility System**

This function calculates the components of the Welles Wilder Volatility System. The components are as follows:

**ARC**– the Average True Range (ATR) times a constant.

**SIC**– Significant Close, the extreme favorable close price reached while in the trade.

**SAR**– Stop And Reverse point, a point defined by the distance between the ARC and SIC. The point at which a trade should be made to close the current position and open a new position in the opposite direction. This occurs when the price breaks above/below the SAR.

The Volatility System was developed by J. Welles Wilder and is described in his 1978 book New Concepts in Technical Trading Systems.

**Williams %R**

The Williams %R is similar to an unsmoothed stochastic %K. The values range from zero to 100, and are charted on an inverted scale, that is, with 0 at the top and 100 at the bottom. Values below 20 indicate an overbought condition and a sell signal is generated when it crosses the 20 line. Values over 80 indicate an oversold condition and a buy signal is generated when it crosses the 80 line.

**Williams Accumulation/Distribution**

Williams Accumulation/Distribution indicator measures market pressure. Look for divergence with price. When the price makes a new low, but the AD does not, look for the price to turn up, and vice versa. The Williams Accumulation/Distribution Indicator is also known as the Williams AD. It was developed by Larry Williams.

**Zero Lag Exponential Moving Average**

ZLMA 10, 14, 20, 50, 100, 200

The Zero-Lag Exponential Moving Average is a variation on the Exponential Moving Average. The Zero-Lag keeps the benefit of the heavier weighting of recent values but attempts to remove lag by subtracting older data to minimize the cumulative effect. See also Exponential MA, Least Squares MA, Simple MA, Triangular MA, Weighted MA, Welles MA, Variable MA, Volume Adjusted MA, DEMA, TEMA, and T3. The default time period is 14 days.

**Zig Zag**

The Zig Zag filters out small movements in price to highlight trends. It looks for price moves greater than the threshold level and plots straight lines between those points. The Zig Zag is more of a visual tool than an indicator. It is non-predictive; in fact, the formula looks forward in time to find the zig zag points. The purpose of the Zig Zag is to make chart patterns clear.