# Technical Studies Reference

### On Balance Volume - Short Term

This study calculates and displays the On Balance Volume over a specific length of bars.

Let $$C_t$$ be the value of the Close Price at Index $$t$$. We denote the Signed Volume at Index $$t$$ as $$V^{(\pm)}_t$$, and we initialize this quantity to zero (that is, $$V^{(\pm)}_0 = 0$$). We compute the Signed Volume for $$t > 0$$ in terms of the Volume as follows.

$$\displaystyle{V^{(\pm)}_t = \left\{ \begin{matrix} V_t & C_t > C_{t - 1} \\ 0 & C_t = C_{t - 1} \\ -V_t & C_t < C_{t - 1} \end{matrix}\right .}$$

Let the Length Input be denoted as $$n$$. We denote the On Balance Volume - Short Term for this Input at Index $$t$$ as $$V^{(OB)}_t(n)$$, and we describe the calculation of this quantity below.

For $$0 \leq t < n$$, $$V^{(OB)}_t(n)$$ is calculated internally as follows. These values are not displayed as output.

$$\displaystyle{V^{(OB)}_t(n) = \left\{ \begin{matrix} 0 & t = 0 \\ V^{(OB)}_{t - 1}(n) + V^{(\pm)}_t & 0 < t < n \end{matrix}\right .}$$

The above formula is equivalent to $$V^{(OB)}_t(n) = V^{(OB)}_t$$, where $$V^{(OB)}_t$$ is the On Balance Volume. That is, for $$0 \leq t < n$$, the On Balance Open Volume - Short Term is equivalent to the ordinary On Balance Volume.

For $$t \geq n$$, $$V^{(OB)}_t(n)$$ is calculated as follows. These values are displayed as output.

$$V^{(OB)}_t(n) = V^{(OB)}_{t - 1}(n) + V^{(\pm)}_t - V^{(\pm)}_{t - n}$$