# Technical Studies Reference

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# 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.

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

#### Inputs

- Input Data
**Damping Factor**: A custom Input that determines the weighting factor given to both current and previous values of the Input Data.- Line 1 Value
- Line 2 Value

#### 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 Monday, 26th September, 2022.