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### On Balance Open Interest - Short Term

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

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

\(\displaystyle{OI^{(\pm)}_t = \left\{ \begin{matrix} OI_t & C_t > C_{t - 1} \\ 0 & C_t = C_{t - 1} \\ -OI_t & C_t < C_{t - 1} \end{matrix}\right .}\)Let the **Length** Input be denoted as \(n\). We denote the **On Balance Open Interest - Short Term** for this Input at Index \(t\) as \(OI^{(OB)}_t(n)\), and we describe the calculation of this quantity below.

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

\(\displaystyle{OI^{(OB)}_t(n) = \left\{ \begin{matrix} 0 & t = 0 \\ OI^{(OB)}_{t - 1}(n) + OI^{(\pm)}_t & 0 < t < n \end{matrix}\right .}\)The above formula is equivalent to \(OI^{(OB)}_t(n) = OI^{(OB)}_t\), where \(OI^{(OB)}_t\) is the On Balance Open Interest. That is, for \(0 \leq t < n\), the **On Balance Open Interest - Short Term** is equivalent to the ordinary **On Balance Open Interest**.

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

\(OI^{(OB)}_t(n) = OI^{(OB)}_{t - 1}(n) + OI^{(\pm)}_t - OI^{(\pm)}_{t - n}\)#### Inputs

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

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*Last modified Friday, 23rd February, 2018.