Financial and Statistical Formulas

Accumulation Distribution

The accumulation distribution formula is an improved On Balance Volume indicator. This indicator uses a relationship between volume and prices to estimate the strength of price movements. If the volume is increased, there is a high probability that prices will move up.

Average True Range

Average True Range is an indicator that measures commitmentcomparing the range between High, Low and Close prices. This indicator was developed by J. Welles Wilder.

Bollinger Bands

Bollinger Bands are indicators that are plotted at standard deviation levels above and below a simple moving average. Since standard deviation is a measure of volatility, a large standard deviation is a good indicator for a volatile market, while a smaller standard deviation is an indicator of a calmer market.

Bollinger Bands are a good way to compare volatility and relative price levels over a period of time.

Chaikin Oscillator

The Chaikin Oscillator indicator is the difference between a 3-day exponential moving average and a 10-day exponential moving average applied to Accumulation Distribution. Using the Chaikin Oscillator, it is possible to monitor volume flow on the market. The Chaikin Oscillator should be used together with the price envelope.

Commodity Channel Index

The Commodity Channel Index compares Prices with its moving averages. If the Commodity channel index is high, it means that the price is higher than its moving average, which is an indicator that the security is overbought. If the Commodity channel index is low, it means that the price is lower than its moving average which is an indicator that security is oversold.

Detrended Price Oscillator

The Detrended Price Oscillator is used to "remove" the trend from the price. Comparing Closing or any other price with it's moving average, the Detrende Price Oscillator eliminates cycles longer than moving average.

Ease of Movement

Ease of Movement deals with relationship between volume and price changes. This indicator uses volume to estimate how strong the price trend is. Ease of Movement was developed by Richard W Arms.

Envelopes

Envelopes are plotted above and below a moving average using a specified percentage. The Envelopes indicator is used to create signals for buying and selling. The percentage which will be used for calculating envelopes is specified by user and it depends on volatility of the market. If the market is more volatile the percentage is higher.

Exponential Moving Average

A Exponential Moving Average is an average of data calculated over a period of time where the most recent days have more weight. The exponential moving average can be used with any price: Hi, Low, Open, Close or it could be applied to other indicators. Exponential Moving average smoothes out data series, which is very important in a volatile market.

Dundas Chart has four types of moving averages: Simple, Exponential, Triangular, and Weighted. The most important difference between the various moving averages is how weights are applied.

Time Series and Forecasting

The Time Series analysis has two main goals: Identifying the nature of the sequence of observations and Predicting future values using historical observations (forecasting).

MACD

The MACD indicator compares two moving averages of prices. The MACD is used with its 9 day Exponential Moving average as signal. This signals indicate buying and selling moments. This indicator is developed by Gerald Appel.

Mass Index Formula

The Mass index is developed to predict trend reversal by comparing difference and range between High and Low prices. If the Mass index is going up, the range between High and low is bigger. If the Mass index is going down, the range between High and Low is smaller.

Median Price

Median price is the mid-point value of daily prices. Median price can be used as a filter for trend indicators. It is also used as the daily average price which is very useful if we want a simpler view of prices.

Money Flow

The money flow indicator compares upward changes and downward changes of the volume weighted typical prices. This indicator is similar to the relative strength index, with the difference being the volume weighted prices. This indicator could be used to identify market tops and bottoms.

Negative Volume Index

The Negative Volume Index should be used together with Positive Volume index. The negative volume index is changed only if the volume decreases from the previous day.

On Balance Volume

The On Balance Volume is one of the first volume indicators which measures positive and negative volume flows. Volume is added if the closing price moves up and subtracted if the closing price moves down. The On Balance Volume was developed by Joseph Granville.

Performance

The Performance indicator compares the current Close (or any other price) with the first Close value ( Close value from the first time period ). This indicator shows how much Close price was changed from the beginning.

Positive Volume Index

The Positive Volume Index should be used together with Negative Volume index. The Positive volume index is changed only if the volume decreases from the previous day.

Price Volume Trend

The Price Volume Trend is the cumulative volume total, which is calculated using relative changes of the Close price. The Price Volume trend is mostly used with other indicators.

Rate Of Change

Rate of Change indicator is very similar to the Performance indicator. Performance indicator compares the first price with current price while Rate of Change compares specified Close price with current price. This formula is used for prices and volume.

Relative Strength Index

The Relative Strength Index is a momentum oscillator which compares upward movements of the Close price with downward movements, resulting in a value which ranges between 0 and 100. The Relative Strength index was developed by J. Welles Wilder.

Simple Moving Average

A Simple Moving Average is an average of data calculated over a period of time. The moving average is the most popular price indicator used in technical analyses, and can be used with any price: Hi, Low, Open, Close or it could be applied to other indicators. Moving average smoothes a data series which is very important in a volatile market. With a moving average it is much easier to spot a trend.

Standard Deviation

Standard deviation is used to indicate volatility. It measures the difference between values (Closing Price) and average. If the difference is larger, the standard deviation and volatility are higher. If the value (Closing price) is closer to the average price, the standard deviation and volatility are lower.

Stochastic Indicator

When a trend is upward, there is a tendency that close price will be very close to that day's high. During a downward trending market there is a tendency that close price is close to low price. The Stochastic Indicator helps to find trend reversal searching for a period when close prices is close to low price in up trending market or close prices is close to high price in down trending market. This formula has two output values: %K - Simple Stochastic Indicator and %D - Smoothed Stochastic Indicator (Moving Average of %K).

Triangular Moving Average

A Triangular Moving Average is an average of data calculated over a period of time where the middle portion of the data has more weight. The Triangular Moving Average can be used with any price: Hi, Low, Open, Close or it could be applied to other indicators. Triangular Moving Average smoothes a data series which is very important in volatile market.

TRIX

The TRIX is based on triple moving average of Closing Price and its purpose is to eliminate shorter cycles. This indicator keeps the Close price in trends that are shorter than the specified period.

Typical Price

Typical price is the average value of daily prices. Typical price can be used as a filter for trend indicators as well as the daily average price which is very useful if we want a simpler view of prices.

Volatility Chaikins

The Volatility Chaikins indicator measures the difference between High and Low prices. This formula is used to indicate the top or bottom of the market. This formula was developed by Marc Chaikin.

Volume Oscillator

The Volume oscillator tries to identify any trends in volume, comparing two moving averages; one with a short period and the second with a longer period.

Weighted Close

Weighted Close formula calculates the average value of daily prices. The only difference between Typical Price and Weighted Close is that the closing price has extra weight as the most important price. Weighted Close could be used as a filter for trend indicators, as well as being used as the daily average price which is very useful if we want a simpler view of prices.

Weighted Moving Average

A Weighted Moving Average is the average of the data calculated over a period of time where the greater weights are attached to the most recent data. The weighting is calculated from the sum of days. The Weighted Moving Average can be used with any price: Hi, Low, Open, Close or it could be applied to other indicators. Weighted Moving Average smoothes a data series which is very important in a volatile market.

William's %R

William's %R is a momentum indicator. This indicator is used to measure overbought and oversold levels. This indicator is very similar to Stochastic %K indicator, except that Williams %R is always negative value between 0 and -100. This indicator is developed by Larry Williams.

Anova

An ANOVA test is used to determine the existence (or non-existence) of a statistically significant difference between the means of two or more groups of data.

Correlation Formula

The Correlation formula shows how strong the relation is between two random variables.

Covariance Formula

The Covariance formula measures the degree of dependence between two random variables

F-distribution Formula

This formula returns the probability for the F-distribution.

F-Test Formula

This formula performs an F Test using F distribution, and is used to see if two samples have different variances

Gamma Function

The GammaFunction method returns the gamma function for a given value

Inverse F cumulative distribution

Returns the inverse of the F cumulative distribution.

Inverse normal distribution formula

Returns the inverse of the standard normal cumulative distribution. The distribution has a mean of 0 (zero) and a standard deviation of one.

Inverse T Distribution formula

Returns the inverse of the T cumulative distribution.

Mean Formula

This formula returns the average, or mean, of data stored in a data series.

Median Formula

This formula returns the median for data stored in a data series.

Normal Distribution Formula

Returns the value of the standard normal cumulative distribution. The distribution has a mean of 0 (zero) and a standard deviation of one.

T Distribution Formula

Returns the probability for the T distribution (student's distribution).

T Test with Equal Variances Formula

Perform a T Test using Student's distribution (T distribution) with equal variances

T Test Paired Formula

Performs a T Test using Student's distribution (T distribution) with paired samples. This is useful when there is a natural pairing of observations in samples (i.e. when a sample group is tested twice).

T Test with unequal variances Formula

Perform a T Test using Student's distribution (T distribution) with unequal variances.

Variance Formula

This formula returns the variance within a group of data.

Z Test Formula

This formula performs a Z Test using Normal distribution