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.