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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 \(VR_t(n_{VPN},n_S)\).

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.

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.