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### 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 \(n_K\), \(n_{\overline{TR}}\), \(v_T\), \(v_B\), respectively. Then we denote the bands for the **Keltner Channel** at Index \(t\) for the given Inputs as \(TB^{(K)}_t(X,n_K,n_{\overline{TR}},v_T)\) (Top Band) and \(BB^{(K)}_t(X,n_K,n_{\overline{TR}},v_B)\) (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: \(TB^{(K)}_t(X,n_K,n_{\overline{TR}},v_T) = SMA_t(X,n_K) + v_T \cdot \overline{TR}_t(n_{\overline{TR}})\)

Bottom Band: \(BB^{(K)}_t(X,n_K,n_{\overline{TR}},v_B) = SMA_t(X,n_K) - v_B \cdot \overline{TR}_t(n_{\overline{TR}})\)

The band in the middle is the graph of \(SMA_t(X,n_K)\).

**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

#### 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 Thursday, 13th June, 2019.