# Technical Studies Reference

### Repulse

This study calculates and displays a Repulse indicator of the price data.

Let $$O$$, $$H$$, $$L$$, and $$C$$ be random variables denoting the Open, High, Low, and Close Prices, respectively, and let their respective values at Index $$t$$ be $$O_t$$, $$H_t$$, $$L_t$$, and $$C_t$$.

We denote the Highest High and Lowest Low at Index $$t$$ over $$n$$ periods as $$\max_t(H,n)$$ and $$\min_t(L,n)$$, respectively, and we compute them for $$t \geq 0$$ as follows.

$$\max_t(H,n) = \displaystyle{ \left\{ \begin{matrix} \max\{H_0,...,H_t\} & t < n - 1 \\ \max\{H_{t - n + 1},...,H_t\} & t \geq n - 1 \end{matrix}\right .}$$

$$\min_t(L,n) = \displaystyle{ \left\{ \begin{matrix} \min\{L_0,...,L_t\} & t < n - 1 \\ \min\{L_{t - n + 1},...,L_t\} & t \geq n - 1 \end{matrix}\right .}$$

Let the Length Input be denoted as $$n$$. Then we denote the Bullish Weighting and the Bearish Weighting for the given Input as $$W^{(Bull)}_t(n)$$ and $$W^{(Bear)}_t(n)$$, respectively, and we compute them for $$t \geq 0$$ as follows.

$$W^{(Bull)}_t(n) = \displaystyle{\left\{ \begin{matrix} 100\cdot\frac{3C_t - 2\min_t(L,n) - O_0}{C_t} & t < n - 1 \\ 100\cdot\frac{3C_t - 2\min_t(L,n) - O_{t - n + 1}}{C_t} & t \geq n - 1 \end{matrix}\right .}$$

$$W^{(Bear)}_t(n) = \displaystyle{\left\{ \begin{matrix} 100\cdot\frac{O_0 + 2\max_t(H,n) - 3C_t}{C_t} & t < n - 1 \\ 100\cdot\frac{O_{t - n + 1} + 2\max_t(H,n) - 3C_t}{C_t} & t \geq n - 1 \end{matrix}\right .}$$

Finally, we denote Repulse at Index $$t$$ for the given Input as $$Repulse_t(n)$$, and we compute it in terms of Exponential Moving Averages of the Bullish and Bearish Weightings for $$t \geq 0$$ as follows.

$$Repulse_t(n) = EMA_t\left(W^{(Bull)}(n),5n\right) - EMA_t\left(W^{(Bear)}(n),5n\right)$$