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### Premier Stochastic Oscillator

This study calculates and displays both a Premier Stochastic Oscillator (PSO) the **Input Data for High**, **Input Data for Low**, and **Input Data for Last** Inputs.

The basis Stochastics used in the calculation are selected from Fast %K, Fast %D (aka Slow %K), and Slow %D. These Stochastics calculated as described in the studies KD - Fast and KD - Slow. We list these Stochastics below.

- Fast %K: \(Fast\% K_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK})\)
- Fast %D: \(Fast\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD})\)
- Slow %D: \(Slow\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD})\)

Refer to the documentation of these studies for an explanation of the symbols used in the above functions. Since these functions have long lists of parameters, we will suppress the parameters when referring to these functions going forward. For instance, we will simply write \(Fast\% K_t\) when referring to the value of Fast %K at Index \(t\).

We begin by normalizing the Stochastic as follows. The default Stochastic is Fast %K; either of the other two Stochastics may be substituted by appropriately setting the **Stochastic Type** Input.

Normalized Stochastic: \(0.1(Fast\% K_t - 50)\)

Let the **PSO Length** Input be denoted as \(n_{PSO}\). The Normalized Stochastic is then double-smoothed using Exponential Moving Averages as follows.

Double-Smoothed Normalized Stochastic: \(EMA_t(EMA(0.1(Fast\% K - 50), n_{PSO}), n_{PSO})\)

**Note**: Depending on the setting of the Input **PSO Moving Average Type**, the Exponential Moving Averages the above formula could be replaced with Linear Regression Moving Averages, Simple Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages.

We denote the value of the PSO at Index \(t\) for the given Inputs as \(PSO_t\left(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD},n_{PSO}\right)\), and we compute it as follows.

\(\displaystyle{PSO_t = \frac{\exp(EMA_t(EMA(0.1(Fast\% K - 50), n_{PSO}), n_{PSO})) - 1}{\exp(EMA_t(EMA(0.1(Fast\% K - 50), n_{PSO}), n_{PSO})) + 1}}\)For an explanation of the exponential function \(\exp\), see refer to our description here.

In addition to the PSO Subgraph, this study also displays four horizontal lines whose levels are determined by the Inputs **Line 1 Value**, **Line 2 Value**, **Line 3 Value**, and **Line 4 Value**. A fifth horizontal line is displayed at the zero level.

#### Inputs

- Input Data for High
- Input Data for Low
- Input Data for Last
**Stochastic Type**: A custom Input that determines whether Fast %K, Fast %D (Slow %K), or Slow %D is used as the basis for calculating the PSO- Fast %K Length
- Fast %D (Slow %K) Length
- Slow %D Length
- Fast/Slow %D Moving Average Type
- PSO Length
- PSO Moving Average Type
- Line 1 Value
- Line 2 Value
- Line 3 Value
- Line 4 Value

#### 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 Wednesday, 10th February, 2021.