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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.
\(N^{(1)}(n) = \left\lfloor{\frac{n}{2}}\right\rfloor\)\(N^{(2)}(n) = \left\lfloor{\frac{N^{(1)}(n)}{2}} + 1\right\rfloor\)
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.
\(DO_t(n) = C_t - SMA_{t - N^{(2)}(n)}\left(C,N^{(1)}(n)\right)\)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 Thursday, 13th June, 2019.