# Technical Studies Reference

- Technical Studies Reference
- Common Study Inputs (Opens a new page)
- Using Studies (Opens a new page)

# MACD

The Moving Average Convergence/Divergence (MACD) is a trend-following momentum indicator that shows the relationship between two moving averages of prices. The MACD was developed by Gerald Appel. In Sierra Chart you have a choice of the Moving Average type to use in the calculations. We describe the calculation below.

Let \(X\) be a random variable denoting the **Input Data** Input. Let the Inputs **Fast Moving Average Length**, **Slow Moving Average Length**, and **MACD Moving Average Length** be denoted as \(n_F\), \(n_S\), and \(n_M\), respectively. This study calculates and displays three indicators: the MACD, the Moving Average of the MACD, and the MACD Difference. We denote the values of these indicators for the given Inputs at Index \(t\) as \(MACD_t\left(X,n_F,n_S\right)\), \(\overline{MACD}_t\left(X,n_F,n_S,n_M\right)\), and \(\Delta MACD_t\left(X,n_F,n_S,n_M\right)\), respectively. We describe the methods of calculation of these indicators below.

The MACD is calculated for \(t \geq 0\) in terms of Exponential Moving Averages as follows.

\(MACD_t\left(X,n_F,n_S\right) = EMA_t\left(X,n_F\right) - EMA_t\left(X,n_S\right)\)The Moving Average of the MACD is calculated for \(t \geq \max\{n_S,n_F\} + n_M\) in terms of an Exponential Moving Average as follows.

\(\overline{MACD}_t\left(X,n_F,n_S,n_M\right) = EMA_t\left(MACD\left(X,n_F,n_S\right),n_M\right)\)

In the above formula, \(MACD\left(X,n_F,n_S\right)\) is a random variable denoting the MACD with Inputs as listed in the parentheses.

**Note**: Depending on the setting of the Input **Moving Average Type**, the Exponential Moving Averages in each of the above formulas could be replaced with Linear Regression Moving Averages, Simple Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.

The MACD Difference is calculated for \(t \geq \max\{n_S,n_F\} + n_M\) in terms of the MACD and the Moving Average of the MACD as follows.

\(\Delta MACD_t\left(X,n_F,n_S,n_M\right) = MACD_t\left(X,n_F,n_S\right) - \overline{MACD}_t\left(X,n_F,n_S,n_M\right)\)#### Inputs

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Monday, 26th September, 2022.