# Technical Studies Reference

### Keltner Channel

This study calculates and displays the Keltner Channel, which consists of three bands calculated for the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let the Keltner Mov Avg Length, True Range Avg Length, Top Band Multiplier, Bottom Band Multiplier Inputs be denoted as $$n_K$$, $$n_{TR}$$, $$v_T$$, $$v_B$$, respectively. Then we denote the bands for the Keltner Channel at Index $$t$$ for the given Inputs as $$TB_t(X,n_K,n_{TR},v_T)$$ (Top Band) and $$BB_t(X,n_K,n_{TR},v_B)$$ (Bottom Band), and we compute them for $$t \geq \max\{n_K,n_{TR}\}$$ in terms of a Simple Moving Average and an Average True Range as follows.

Top Band: $$TB_t(X,n_K,n_{TR},v_T) = MA_t(X,n_K) + v_T \cdot \overline{TR}_t(n_{TR})$$

Bottom Band: $$BB_t(X,n_K,n_{TR},v_B) = MA_t(X,n_K) - v_B \cdot \overline{TR}_t(n_{TR})$$

The band in the middle is the graph of $$MA_t(X,n_K)$$.

Note: Depending on the setting of the Input Keltner Mov Avg Type (Center Line), the Simple Moving Average in each of the above formulas could be replaced with an Exponential Moving Average, a Linear Regression Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

Note: The ATR Mov Avg Type Input determines the Moving Average Type of the Average True Range.

#### Inputs

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.