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### Relative Vigor Index 2

This study calculates and displays three indicators: the Relative Vigor Index (RVI), a Smoothed RVI, and a Signal Line (aka a Trigger Line) for the Price Data.

Let \(O_t\), \(H_t\), \(L_t\), and \(C_t\) denote, respectively, the values of the Open, High, Low, and Close Prices at Index \(t\). The Relative Vigor Index at Index \(t\) is denoted as \(RVI_t\), and we compute it for \(t \geq 0\) as follows.

\(\displaystyle{RVI_t = \frac{C_t - O_t}{H_t - L_t}}\)It is the other two Subgraphs of **Relative Vigor Index 2** that are used to generate Buy and Sell signals: the Smoothed RVI and the Signal Line.

We first compute two Average Prices at Index \(t\): The Close-Open Average Price and the High-Low Average Price, denoted as \(\overline{P}^{(CO)}_t\) and \(\overline{P}^{(HL)}_t\), respectively. These are symmetric weighted averages computed over \(4\) periods for \(t \geq 3\) as follows.

\(\displaystyle{\overline{P}^{(CO)}_t = \frac{(C_{t - 3} - O_{t - 3}) + 2(C_{t - 2} - O_{t - 2}) + 2(C_{t - 1} - O_{t - 1}) + (C_t - O_t)}{6}}\)\(\displaystyle{\overline{P}^{(HL)}_t = \frac{(H_{t - 3} - L_{t - 3}) + 2(H_{t - 2} - L_{t - 2}) + 2(H_{t - 1} - L_{t - 1}) + (H_t - L_t)}{6}}\)

Let \(n\) denote the **Smoothed RVI Length** Input. We denote the Smoothed RVI for the given Input at Index \(t\) as \(\overline{RVI}_t(n)\) and we compute it in terms of Simple Moving Averages for \(t \geq n + 5\) as follows.

**Note**: Depending on the setting of the Input **Smoothed RVI Average Type**, the Simple Moving Averages in the above formula could be replaced with Exponential Moving Averages, Linear Regression Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.

We denote the Signal Line for the given Inputs at Index \(t\) as \(Sig_t(n)\). We compute it for \(t \geq n + 5\) as a symmetric weighted average over \(4\) periods as follows.

\(\displaystyle{Trig^{(RVI)}_t(n) = \frac{\overline{RVI}_{t - 3}(n) + 2\overline{RVI}_{t - 2}(n) + 2\overline{RVI}_{t - 1}(n) + \overline{RVI}_t(n)}{6}}\)Let the **Arrow Offset Percentage** Input be denoted as \(k\).

A Buy Signal is indicated by an Up Arrow at Index \(t\) if the Subgraph of the Smoothed RVI crosses the Subgraph of the Signal Line from below. That is, a Buy Signal at \(t\) satisfies the conditions \(\overline{RVI}_{t - 1}(n) < Trig^{(RVI)}_{t - 1}(n)\) and \(\overline{RVI}_t(n) > Trig^{(RVI)}_t(n)\). The vertical coordinate of the tip of the arrow is given by \(Trig^{(RVI)}_t(n) - \frac{k}{100}Trig^{(RVI)}_t(n)\).

A Sell Signal is indicated by a Down Arrow at Index \(t\) if the Subgraph of the Smoothed RVI crosses the Subgraph of the Signal Line from above. That is, a Sell Signal at \(t\) satisfies the conditions \(\overline{RVI}_{t - 1}(n) > Trig^{(RVI)}_{t - 1}(n)\) and \(\overline{RVI}_t(n) < Trig^{(RVI)}_t(n)\). The vertical coordinate of the tip of the arrow is given by \(Trig^{(RVI)}_t(n) + \frac{k}{100}Trig^{(RVI)}_t(n)\).

#### 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 Sunday, 21st November, 2021.