# Technical Studies Reference

### Moving Average - Elastic Volume Weighted

This study calculates and displays an Elastic Volume Weighted Moving Average of the data specified by the Input Data Close Input. It also displays Top and Bottom Bands based on the Input Data High and Input Data Low Inputs, respectively.

Let $$X^{(C)}$$, $$X^{(H)}$$, and $$X^{(L)}$$ be random variables denoting the Input Data Close, Input Data High, and Input Data Low, respectively, and let $$X_t^{(C)}$$, $$X_t^{(H)}$$, $$X_t^{(L)}$$ be their respective values at Index $$t$$. Let the Input Length be denoted as $$n$$. Let $$V_t$$ denote the Volume at Index $$t$$.

We denote the Number of Floating Shares at Index $$t$$ as $$N_t(n)$$. If the Use Cumulative Volume Input is set to Yes, then we compute $$N_t(n)$$ as follows.

$$\displaystyle{N_t(n) = \sum_{i = 0}^t V_i}$$

If Use Cumulative Volume is set to No (the default setting), then we compute $$N_t(n)$$ as follows.

$$\displaystyle{N_t(n) = \left\{ \begin{matrix} (n - t)*V_0 + \sum_{i = 1}^t V_i & 0 < t < n \\ \sum_{i = t - n + 1}^t V_i & t \geq n \end{matrix}\right .}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.

We denote the Moving Average - Elastic Volume Weighted at Index $$t$$ for the given Inputs as $$EVWMA_t\left(X^{(C)},n\right)$$, and we compute it as follows.

For $$t = 0$$: $$EVWMA_t\left(X^{(C)},n\right)= X^{(C)}_0$$

For $$t > 0$$:

$$\displaystyle{EVWMA_t\left(X^{(C)},n\right) =\left\{ \begin{matrix} 0 & N_t(n) = 0 \\ \left(1 - \frac{V_t}{N_t(n)}\right)EVWMA_{t - 1}\left(X^{(C)},n\right) + \frac{V_tX_t^{(C)}}{N_t(n)} & N_t(n) \neq 0 \end{matrix}\right .}$$

The values of the Top and Bottom Bands at Index $$t$$ are denoted as $$TB_t^{(EVW)}$$ and $$BB_t^{(EVW)}$$, respectively, and we compute them as follows.

For $$t = 0$$:

$$TB_0^{(EVW)}\left(X^{(H)},n\right) = X^{(H)}_0$$

$$BB_0^{(EVW)}\left(X^{(L)},n\right) = X^{(L)}_0$$

For $$t > 0$$:

$$\displaystyle{TB_t^{(EVW)}\left(X^{(H)},n\right) = \left\{ \begin{matrix} 0 & N_t(n) = 0 \\ \left(1 - \frac{V_t}{N_t(n)}\right)TB_{t - 1}^{(EVW)}\left(X^{(H)},n\right) + \frac{V_tX_t^{(H)}}{N_t(n)} & N_t(n) \neq 0 \end{matrix}\right .}$$

$$\displaystyle{BB_t^{(EVW)}\left(X^{(L)},n\right) = \left\{ \begin{matrix} 0 & N_t(n) = 0 \\ \left(1 - \frac{V_t}{N_t(n)}\right)BB_{t - 1}^{(EVW)}\left(X^{(L)},n\right) + \frac{V_tX_t^{(L)}}{N_t(n)} & N_t(n) \neq 0 \end{matrix}\right .}$$