# Laguerre RSI

This study calculates and displays a Laguerre RSI for the data given by the Input Data Input. This study is an ACSIL implementation of the Indicator given in Figures 14.8 and 14.9 of the book Cybernetic Analysis for Stocks and Futures by John Ehlers.

The Laguerre RSI can be loosely thought of as an RSI in which the Average Type is a Laguerre Moving Average, given by the components of the Laguerre Filter. See the documentation of that study for an explanation of the notation used here.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of $$X$$ at Index $$t$$. Let the Damping Factor Input be denoted as $$\gamma$$ (Greek letter gamma).

We begin by defining an Up Sum and a Down Sum, denoted as $$U_t(X,\gamma)$$ and $$D_t(X,\gamma)$$, respectively. We compute them as follows.

$$\displaystyle{U_t(X,\gamma) = \sum_{k = 0}^2 c^{(U)}_k\left(L^{(k)}_t(X,\gamma) - L^{(k + 1)}_t(X,\gamma)\right)}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.

In the above sum, $$c^{(U)}_k$$ is a coefficient defined for each $$k$$ as follows.

$$\displaystyle{c^{(U)}_k = \left\{ \begin{matrix} 1 & L^{(k)}_t(X,\gamma) - L^{(k + 1)}_t(X,\gamma) \geq 0 \\ 0 & L^{(k)}_t(X,\gamma) - L^{(k + 1)}_t(X,\gamma) < 0 \end{matrix}\right .}$$

$$\displaystyle{D_t(X,\gamma) = \sum_{k = 0}^2 c^{(D)}_k\left(L^{(k + 1)}_t(X,\gamma) - L^{(k)}_t(X,\gamma)\right)}$$

In the above sum, $$c^{(D)}_k$$ is a coefficient defined for each $$k$$ as follows.

$$\displaystyle{c^{(D)}_k = \left\{ \begin{matrix} 0 & L^{(k)}_t(X,\gamma) - L^{(k + 1)}_t(X,\gamma) \geq 0 \\ 1 & L^{(k)}_t(X,\gamma) - L^{(k + 1)}_t(X,\gamma) < 0 \end{matrix}\right .}$$

The Laguerre RSI at Index $$t$$ is denoted as $$RSI^{(L)}_t(X,\gamma)$$, and we compute it as follows.

$$\displaystyle{RSI^{(L)}_t(X,\gamma) = \left\{ \begin{matrix} \frac{U_t(X,\gamma)}{U_t(X,\gamma) + D_t(X,\gamma)} & U_t(X,\gamma) + D_t(X,\gamma) \neq 0 \\ 0 & U_t(X,\gamma) + D_t(X,\gamma) = 0 \end{matrix}\right .}$$

This study also displays horizontal lines at the levels specified by the Line 1 Value and Line 2 Value Inputs.