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# Technical Studies Reference

### 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.

$$\displaystyle{\overline{RVI}_t(n) = \frac{SMA_t\left(\overline{P}^{(CO)},n\right)}{SMA_t\left(\overline{P}^{(HL)},n\right)}}$$

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 $$Trig^{(RVI)}_t(n) + \frac{k}{100}Trig^{(RVI)}_t(n)$$.