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# Volume Positive Negative Indicator

This study calculates and displays a Volume Positive Negative Indicator of the data specified by the **Input Data** Input.

Let \(X_t\) and \(V_t\) be the values of the **Input Data** and Volume, respectively, at Index \(t\). Let the Inputs **ATR Coefficient**, **VPN Length**, **VPN Smoothing Length**, and **Avg VPN Length** be denoted as \(k\), \(n_{VPN}\), \(n_S\), and \(n_{\overline{VPN}}\), respectively.

We denote the Volume Up and Volume Down at Index \(t\) as \(V^{(+)}_t(k,n_{VPN})\) and \(V^{(-)}_t(k,n_{VPN})\), respectively, and we compute in terms of the Average True Range them as follows.

\(\displaystyle{V^{(+)}_t(k,n_{VPN}) = \left\{ \begin{matrix} V_t & X_t \geq X_{t - 1} + k \cdot ATR_t(n_{VPN}) \\ 0 & X_t < X_{t - 1} + k \cdot ATR_t(n_{VPN}) \end{matrix}\right .}\)

\(\displaystyle{V^{(-)}_t(k,n_{VPN}) = \left\{ \begin{matrix} V_t & X_t \leq X_{t - 1} - k \cdot ATR_t(n_{VPN}) \\ V_t & X_t < X_{t - 1} - k \cdot ATR_t(n_{VPN}) \end{matrix}\right .}\)

Note: In the above formulas, \(ATR_t(n_{VPN})\) is computed using the Welles Wilder Moving Average by default. This average type can be changed via the **ATR Avg Type** Input.

Next we compute the following Volume Ratio, denoted as \(VR_t(n_{VPN},n_S)\).

\(\displaystyle{VR_t(k,n_{VPN}) = \frac{\sum_{i = t - n_{VPN} + 1}^t (V^{(+)}_t(k,n_{VPN}) - V^{(-)}_t(k,n_{VPN}))}{\sum_{i = t - n_{VPN} + 1}^t V_t}}\)If the sum in the denominator of the Volume Ratio is zero, then \(VR_t(k,n_{VPN}) = 0\).

We denote the **Volume Positive Negative Indicator** at Index \(t\) as \(VPN_t(k,n_{VPN},n_S)\), and we compute it by smoothing the Volume Ratio with an Exponential Moving Average as follows.

Note: In the above formula, the moving average type can be changed via the **VPN Smoothing Avg Type** Input.

A second Subgraph that is displayed is the Average VPN, denoted as \(\overline{VPN}(k,n_{VPN},n_S,n_{\overline{VPN}})\). We compute it using a Simple Moving Average as follows.

\(\overline{VPN}(k,n_{VPN},n_S,n_{\overline{VPN}}) = SMA_t(VPN_t(k,n_{VPN},n_S),n_{\overline{VPN}})\)A third Subgraph that is displayed is a horizontal line at the level of the **Critical Value** Input.

Finally, a fourth Subgraph that is displayed is a Center Line.

#### Inputs

#### Spreadsheet

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

Open it through **File >> Open Spreadsheet**.

*Last modified Monday, 03rd October, 2022.