# Technical Studies Reference

### MACD - Volume Weighted

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 Volume Weighted MACD, the Moving Average of the Volume Weighted MACD, and the Volume Weighted MACD Difference. These indicators are the same as those in the MACD study, but with the Volume Weighted Moving Average used in place of the Exponential Moving Average. We describe the methods of calculation of these indicators below.

The Volume Weighted MACD is calcuated $$t \geq \max\{n_S,n_F\} + n_M$$ in terms of Volume Weighted Moving Averages as follows.

$$MACD_t\left(X,n_F,n_S\right) = VWMA_t\left(X,n_F\right) - VWMA_t\left(X,n_S\right)$$

Note: $$MACD_t\left(X,n_F,n_S\right)$$ is calculated internally for $$n_S \leq t < \max\{n_S,n_F\} + n_M$$, but these values are not displayed as output. However, the value at $$t = \max\{n_S,n_F\} + n_M - 1$$ is used to calculate the Exponential Moving Average in the next step.

The Moving Average of the Volume Weighted MACD is then calculated using 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 th Volume Weighted MACD with Inputs as listed in parentheses.

Finally, the Volume Weighted Moving Average Difference is calculated as follows.

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