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### MACD Bollinger Bands - Improved

This study calculates and displays an improved version of MACD Bollinger Bands for the data specified by the **Input Data** Input, as well as a moving average of the MACD. Refer to the documentation of the MACD study for an explanation of the notation used here.

Let the **Number of Standard Deviations** Input be denoted as \(k\). Then we denote the **MACD Bollinger Bands - Improved** at Index \(t\) for the given Inputs as \(TB^{(MBI)}_t(X,n_F,n_S,n_M,k)\) (Top Band) and \(BB^{(MBI)}_t(X,n_F,n_S,n_M,k)\) (Bottom Band), and we compute them for \(t \geq 2n_M + \max\{n_F,n_S\}\) in terms of a Standard Deviation as follows.

\(BB^{(MBI)}_t(X,n_F,n_S,n_M,k) = \overline{MACD}_t(X,n_F,n_S,n_M) - SMA_t(|\Delta MACD(X,n_F,n_S,n_M)|,n_M) - k\cdot\sigma_t(MACD(X,n_F,n_S),n_M)\)

The band in the middle is the graph of \(\overline{MACD}_t(X,n_F,n_S,n_M)\), which by default is computed in terms of a Simple Moving Average as follows.

\(\overline{MACD}_t(X,n_F,n_S,n_M) = SMA_t(MACD(X,n_F,n_S),n_M)\)**Note**: Depending on the setting of the **Moving Average Type** Input, the Simple Moving Average in the above formula could be replaced with an Exponential Moving Average, a Linear Regression Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

#### 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 Friday, 14th June, 2019.