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# Detrended Oscillator

This study calculates and displays a Detrended Oscillator for the Price Data.

Let \(C_t\) be the value of the Close Price at Index \(t\), and let \(n\) be the **Length** Input. We define two quantities \(N^{(1)}(n)\) and \(N^{(2)}(n)\) and compute them as follows.

\(N^{(2)}(n) = \left\lfloor{\frac{N^{(1)}(n)}{2}} + 1\right\rfloor\)

For an explanation of the floor function (\(\left\lfloor{\space\space}\right\rfloor\)), refer to our description here.

The **Detrended Oscillator** at Index \(t\) is denoted as \(DO_t(n)\), and it is computed in terms of a Simple Moving Average for \(t \geq n\) as follows.

**Note**: Depending on the setting of the **Moving Average Type** Input, the Simple Moving Average in the above formula 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.

This study also displays horizontal lines at levels determined by the **Overbought Level** and **Oversold Level** Inputs.

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