# Technical Studies Reference

- Technical Studies Reference
- Common Study Inputs (Opens a new page)
- Using Studies (Opens a new page)

# Parabolic

This study calculates and displays the Welles Wilder Parabolic SAR (Stop and Reversal) study for the data specified by the **Input Data High** and **Input Data Low** Inputs.

Let \(X^{(High)}\) and \(X^{(Low)}\) be random variables denoting the **Input Data High** and **Input Data Low**, respectively, and let \(X_t^{(High)}\) and \(X_t^{(Low)}\) denote their respective values at Index \(t\). Let the **Start Acceleration Factor**, **Acceleration Increment**, and **Max Acceleration Factor** Inputs be denoted as \(\alpha_S\), \(\Delta\alpha\), and \(\alpha_{max}\), respectively.

We denote the Acceleration Factor, Extreme Point, and **Parabolic SAR** at Index \(t\) as \(EP_t\left(X^{(High)}, X^{(Low)}\right)\) and \(\alpha_t\left(X^{(High)}, X^{(Low)}, \alpha_S, \Delta\alpha, \alpha_{max}\right)\), \(SAR_t\left(X^{(High)}, X^{(Low)}, \alpha_S, \Delta\alpha, \alpha_{max}\right)\) respectively. Since this notation is cumbersome, we will suppress the Inputs and write these simply as \(EP_t\), \(\alpha_t\), and \(SAR_t\) going forward. We compute these quantities as follows.

The Extreme Point is the extreme High in an Uptrend or the extreme Low in a Downtrend.

Within an Uptrend, we use the following formula.

\(\displaystyle{EP_t = \left\{ \begin{matrix} X_t^{(High)} & X_t^{(High)} = \max_t\left(X^{(High)}\right) \\ EP_{t-1} & X_t^{(High)} \neq \max_t\left(X^{(High)}\right) \end{matrix}\right .}\)Within a Downtrend, we use the following formula.

\(\displaystyle{EP_t = \left\{ \begin{matrix} X_t^{(Low)} & X_t^{(Low)} = \min_t\left(X^{(Low)}\right) \\ EP_{t-1} & X_t^{(Low)} \neq \min_t\left(X^{(Low)}\right) \end{matrix}\right .}\)Within an Uptrend or a Downtrend, the Acceleration Factor starts with a value \(\alpha_S\) increases by an amount \(\Delta\alpha\) every time the Extreme Point changes, up to a maximum value of \(\alpha_{max}\). The formula is given as follows.

\(\displaystyle{\alpha_t = \left\{ \begin{matrix} \alpha_{t - 1} + \Delta\alpha & EP_t \neq EP_{t - 1} \\ \alpha_{t - 1} & EP_t = EP_{t - 1} \end{matrix}\right .}\)Within an Uptrend or a Downtrend, the **Parabolic SAR** is given by the following formula.

That is, the SAR of the next bar is calculated using information from the current bar.

These formulas are used with the following restrictions.

- If the chart starts in an Uptrend, then \(EP_1 = X_0^{(Low)}\), \(EP_2 = X_1^{(High)}\), and \(\alpha_1 = \alpha_2 = \alpha_S\).
- If the chart starts in a Downtrend, then \(EP_1 = X_0^{(High)}\), \(EP_2 = X_1^{(Low)}\), and \(\alpha_1 = \alpha_2 = \alpha_S\).
- When a Downtrend changes to an Uptrend at Index \(t\), \(EP_t = X_t^{(High)}\), \(\alpha_t = \alpha_S\), and \(SAR_t\) is set to the lowest value of \(X^{(Low)}\) of the previous Downtrend.
- When an Uptrend changes to a Downtrend at Index \(t\), \(EP_t = X_t^{(High)}\), \(\alpha_t = \alpha_S\), and \(SAR_t\) is set to the highest value of \(X^{(High)}\) of the previous Uptrend.
- The value of \(SAR_t\) may be adjusted depending on the setting of the
**Adjust for Gap**Input. The default setting for this is No.

#### Inputs

**Input Data High:**The default for the setting is High. The Parabolic study uses the High price of a bar in its calculations. This can be changed to any Subgraph value when basing the Parabolic study on another study rather than the main price graph.**Input Data Low:**The default for the setting is Low. The Parabolic study uses the Low price of a bar in its calculations. This can be changed to any Subgraph value when basing the Parabolic study on another study rather than the main price graph.**Start Acceleration Factor:**The parabolic study uses an Acceleration Factor in its calculations. This Inputs sets the starting value for this Acceleration Factor. The Acceleration Factor is incremented by the**Acceleration Increment**Input.**Acceleration Increment:**This Input sets the Acceleration Increment.**Max Acceleration Factor:**This Input sets the maximum amount the Acceleration Factor will be set to.**Adjust for Gap**: If set to 1 the parabolic will be adjusted up or down by the gap amount when a gap occurs at the opening of a new day.

#### 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, 28th September, 2022.