# Technical Studies Reference

### 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.

$$\displaystyle{SAR_{t + 1} = SAR_t + \alpha_t(EP_t - SAR_t)}$$

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.