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This study calculates and displays a divergence in slope between the regression line of the Main Price Graph of a chart and that of a Study Subgraph (which corresponds to the Study Subgraph Reference Input) on the same chart.

A divergence occurs when there is a significant difference in slope. The conditions for a divergence are discussed below.

Let \(X\) and \(S\) be random variables denoting the Input Data and the data from the Study Subgraph, respectively, and let \(X_t\) and \(S_t\) be their respective values at Index \(t\).

Let the Divergence Length, Divergence Threshold in Degrees, Opposite Slope Divergence Threshold in Degrees, and Value Per Point for Study Reference be denoted as \(n\), \(\phi_D\), \(\phi_O\), and \(v_1\), respectively.

There are two other parameters that are used in the calculation but are not listed in the Inputs. These are the Tick Size \(s\) and the Value Increment Per Bar in Ticks \(v_2\). \(s\) can be set through Chart >> Chart Settings >> Main Settings, and \(v_2\) can be set through Chart >> Chart Settings >> Chart Drawings.

We begin by computing the Linear Regression statistics for both the Main Price Graph and the Study Subgraph, from which we take the following slopes.

These Angles are in the interval \((-90^{\circ},90^{\circ})\).

A Divergence exists if any of the following conditions is satisfied.

• \(\left|\theta_t(X, s\cdot v_2, n) - \theta_t(S, v_1, n)\right| \geq \phi_D\)
• \(\theta_t(X, s\cdot v_2, n) > 0\) and \(\theta_t(S, v_1, n) < 0\) and \(\left|\theta_t(X, s\cdot v_2, n) - \theta_t(S, v_1, n)\right| \geq \phi_O\)
• \(\theta_t(X, s\cdot v_2, n) < 0\) and \(\theta_t(S, v_1, n) > 0\) and \(\left|\theta_t(X, s\cdot v_2, n) - \theta_t(S, v_1, n)\right| \geq \phi_O\)

If a Divergence exists at Index \(t\), then the Divergence is either Positive or Negative. Positive and Negative Divergences are denoted as \(PD_t(X,S,n,s,v_1,v_2,\phi_D,\phi_O)\) and \(ND_t(X,S,n,s,v_1,v_2,\phi_D,\phi_O)\), respectively. Since this notation is cumbersome, we will omit the function parameters going forward. These Divergences are computed as follows.

In the above formulas, \(H_t\) and \(L_t\) denote the High Price and Low Price, respectively, at Index \(t\).

Positive Divergences are indicated with an Up Arrow below a chart bar where they occur. Negative Divergences are indicated with a Down Arrow above the bar where they occur. This behavior as documented here is effective with version 1576 and higher.

The Tool Values Window displays the calculated angles by the Divergence Detector study and those angles can be viewed for any chart bar by using the Chart Values Tool. This is very helpful in order to determine the proper Divergence Threshold in Degrees Input settings.

The Subgraph >> Draw Style setting for the Positive Divergence and Negative Divergence Subgraphs in the Study Settings window can be changed from the default arrows to any other Draw Style that you require. Refer to Draw Style.

When there is a positive divergence, this generally would indicate that based upon the Study Subgraph being referenced by the Divergence Detector study that the main price graph may change direction from its downward trend if there has been a downward trend. When there is a negative divergence, this generally would indicate that based upon the Study Subgraph being referenced by the Divergence Detector study that the main price graph may change direction from its upward trend if there has been a upward trend.