# Technical Studies Reference

### 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.

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

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

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.