# Relative Vigor Index 1

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 1 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 1 that are used to generate Buy and Sell signals: the Smoothed RVI and the Signal Line.

Let $$n$$ and $$n_T$$ denote the Smoothed RVI Length and Signal Length Inputs, respectively. We denote the Smoothed RVI and the Signal (Trigger) Line for the given Inputs at Index $$t$$ as $$\overline{RVI}_t(n)$$ and $$Trig^{(RVI)}_t(n_T)$$, respectively, and we compute them for $$t \geq \max\{n,n_T\} - 1$$ in terms of Simple Moving Averages as follows.

$$\overline{RVI}_t(n) = SMA_t\left(RVI,n\right)$$

$$Trig^{(RVI)}_t(n_T) = SMA_t\left(RVI,n_T\right)$$

Note: Depending on the setting of the Inputs Smoothed RVI Average Type and Signal Average Type, the Simple Moving Averages in the calculations of the Smoothed RVI and the Signal Line 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.

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 $$\overline{RVI}_{t - 1}(n) < Trig^{(RVI)}_{t - 1}(n_T)$$ and $$\overline{RVI}_t(n) > Trig^{(RVI)}_t(n_T)$$. The vertical coordinate of the tip of the arrow is given by $$Trig^{(RVI)}_t(n_T) - \frac{k}{100}Trig^{(RVI)}_t(n_T)$$.

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 $$\overline{RVI}_{t - 1}(n) > Trig^{(RVI)}_{t - 1}(n_T)$$ and $$\overline{RVI}_t(n) < Trig^{(RVI)}_t(n_T)$$. The vertical coordinate of the tip of the arrow is given by $$Trig^{(RVI)}_t(n_T) + \frac{k}{100}Trig^{(RVI)}_t(n_T)$$.