# Technical Studies Reference

### MACD Bollinger Bands - Standard

This study calculates and displays 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 - Standard at Index $$t$$ for the given Inputs as $$TB^{(MBS)}_t(X,n_F,n_S,n_M,k)$$ (Top Band) and $$BB^{(MBS)}_t(X,n_F,n_S,n_M,k)$$ (Bottom Band), and we compute them for $$t \geq 2n_M + \max\{n_F,n_S\}$$ in terms of a Standard Deviation as follows.

$$TB^{(MBS)}_t(X,n_F,n_S,n_M,k) = \overline{MACD}_t(X,n_F,n_S,n_M) + k\cdot\sigma_t(MACD(X,n_F,n_S),n_M)$$

$$BB^{(MBS)}_t(X,n_F,n_S,n_M,k) = \overline{MACD}_t(X,n_F,n_S,n_M) - k\cdot\sigma_t(MACD(X,n_F,n_S),n_M)$$

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 an Exponential Moving Average as follows.

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

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