Technical Studies Reference

Stochastic - Percentile

This study calculates and displays the percentile rank of the data specified by the Input Data Input. The ranking is done over a moving window whose size is specified by the Length Input. This study also calculates and displays a moving average of the percentile rank. This indicator was developed by Peter Worden, and is sometimes referred to as a Worden Stochastic.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of the Input Data at Index \(t\). Let the Input Length be denoted as \(n\).

At Index \(t\), the \(n\) values \(X_{t - n + 1},...,X_t\) of the Input Data are arranged in ascending order and ranked from lowest to highest, starting with a Rank of \(0\) and going up to a Rank of \(n - 1\). The Rank of the most recent value of \(X\) at Index \(t\) for the given Length is denoted as \(R_t(X,n)\).

We denote the value of the Stochastic - Percentile at Index \(t\) for the given Inputs as \(SP_t(X,n)\), and we compute it for \(t \geq n - 1\) as follows.

\(SP_t(X,n) = 100\cdot\displaystyle{\frac{R_t(X,n)}{n - 1}}\)

Note: We perform the following internal calculations for \(0 \leq t < n - 1\). These values are not displayed as output.

\(\displaystyle{SP_t(X,n) = \left\{\begin{matrix} 0 & t = 0 \\ 100\cdot\frac{R_t(X,t)}{t} & 0 < t < n - 1 \end{matrix}\right .}\)

Let the Moving Average Length Input be denoted as \(n_{MA}\). Then we denote the Moving Average of Stochastic - Percentile at Index \(t\) for the given Inputs as \(\overline{SP}_t(X,n,n_{MA})\), and we compute it in terms of a Simple Moving Average for \(t \geq n - 1\) as follows.

\(\overline{SP}_t(X,n,n_{MA}) = MA_t(SP(X,n),n_{MA})\)

In the above formula, \(SP(X,n)\) is a random variable denoting the Stochastic - Percentile of Length \(n\) for the Input Data \(X\).

In addition to the graphs of \(SP_t(X,n)\) and \(\overline{SP}_t(X,n,n_{MA})\), this study also displays two horizontal lines whose levels are determined by the Inputs Line 1 Value and Line 2 Value.



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 Wednesday, 03rd January, 2018.