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SuperTrend
This study calculates and displays the SuperTrend Indicator.
Let \(X\) and \(C\) be random variables denoting the Input Data and Close Price, respectively, and let \(X_t\) and \(C_t\) be their values at Index \(t\). Let the Inputs ATR Period and ATR Multiplier be denoted as \(n\) and \(k\), respectively.
We begin by computing Top Band - Basic and Bottom Band - Basic, whose values at Index \(t\) are denoted as \(TBB_t^{(ST)}(X,n,k)\) and \(BBB_t^{(ST)}(X,n,k)\), respectively. We compute them in terms of the Average True Range as follows.
\(TBB_t^{(ST)}(X,n,k) = X_t + k \cdot ATR(n)\)\(BBB_t^{(ST)}(X,n,k) = X_t - k \cdot ATR(n)\)
The moving average type is determined by the ATR Moving Average Type Input.
We then calculate the Top Band, \(TB_t^{(ST)}(X,n,k)\) and Bottom Band, \(BB_t^{(ST)}(X,n,k)\), as follows.
\(TB_t^{(ST)}(X,n,k) = \left\{ \begin{matrix} TBB_t^{(ST)}(X,n,k) & TBB_t^{(ST)}(X,n,k) < TB_{t - 1}^{(ST)}(X,n,k) \space or \space C_{t - 1} > TB_{t - 1}^{(ST)}(X,n,k) \\ TB_{t - 1}^{(ST)}(X,n,k) & TBB_t^{(ST)}(X,n,k) \geq TB_{t - 1}^{(ST)}(X,n,k) \space or \space C_{t - 1} \leq TB_{t - 1}^{(ST)}(X,n,k) \end{matrix}\right .\)Finally, we denote the SuperTrend at Index \(t\) as \(ST_t(X,n,k)\), and we compute it as follows.
For \(t = 0\), \(ST_0(X,n,k) = TB_0^{(ST)}(X,n,k)\). For \(t > 0\), we have the following. \(ST_t(X,n,k) = \left\{ \begin{matrix} TB_t^{(ST)}(X,n,k) & (ST_{t - 1}(X,n,k) = TB_{t - 1}^{(ST)}(X,n,k) \space and \space C_t < TB_t^{(ST)}(X,n,k)) \space or \space (ST_{t - 1}(X,n,k) = BB_{t - 1}^{(ST)}(X,n,k) \space and \space C_t < BB_t^{(ST)}(X,n,k)) \\ BB_{t - 1}^{(ST)}(X,n,k) & (ST_{t - 1}(X,n,k) = TB_{t - 1}^{(ST)}(X,n,k) \space and \space C_t > TB_t^{(ST)}(X,n,k)) \space or \space (ST_{t - 1}(X,n,k) = BB_{t - 1}^{(ST)}(X,n,k) \space and \space C_t > BB_t^{(ST)}(X,n,k)) \\ ST_{t - 1}(X,n,k) & Otherwise \end{matrix}\right .\)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, 09th January, 2023.