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This study calculates and displays the Negative Volume Index (NVI) for the Volume data and the data specified by the Input Data Input. This study uses the version of the NVI created by Norman G. Fosback.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of the Input Data at Index \(t\). Let the Input Initial Value be denoted as \(NVI_0\). Then we denote the Negative Volume Index for the given Inputs at Index \(t\) as \(NVI_t(X,NVI_0)\), and we compute it for \(t \geq 0\) as follows.

For \(t = 0\): \(NVI_0(X,NVI_0) = NVI_0\)

For \(t > 0\): \(\displaystyle{NVI_t(X,NVI_0) = \left\{ \begin{matrix} NVI_{t - 1}(X,NVI_0) + \frac{X_t - X_{t - 1}}{X_{t - 1}}\cdot NVI_{t - 1}(X,NVI_0) & V_t < V_{t - 1} \\ NVI_{t - 1}(X,NVI_0) & V_t \geq V_{t - 1} \end{matrix}\right .}\)