# Technical Studies Reference

### Bands/Envelope

This study calculates and displays Bands based on the Input Data. The Bands are referred to as the Top Band and Bottom Band, and they are drawn, respectively, above and below the Main Price Graph.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Input Percentage/Fixed Value/Ticks be denoted as $$v$$. Then we denote the values of the Top Band and Bottom Band at Index $$t$$ for the given Inputs as $$TB^{(E)}_t(X,v)$$ and $$BB^{(E)}_t(X,v)$$, respectively. The methods of calculating these values depends on the value of the Bands Type Input. We describe each method below.

Bands Type = Percentage:
The Bands are drawn above and below the Main Price Graph by a Percentage of the Input Data. If the Percentage is to be 5%, then a value of $$v = 0.05$$ should be entered.

$$TB^{(E)}_t(X,v) = X_t + X_t \cdot v$$
$$BB^{(E)}_t(X,v) = X_t - X_t \cdot v$$

Bands Type = Fixed Value:
The Bands are drawn above and below the Main Price Graph by a Fixed Value $$v$$.

$$TB^{(E)}_t(X,v) = X_t + v$$
$$BB^{(E)}_t(X,v) = X_t - v$$

Bands Type = Number of Ticks:
We denote the Tick Size as $$s$$, and it appears as a third argument of the Band functions. This value is set through Chart >> Chart Settings >> Main Settings. The Bands are drawn above and below the Main Price Graph by a Fixed Value $$v \cdot s$$. With this Band Type, the band functions have an extra parameter, $$s$$.

$$TB^{(E)}_t(X,v,s) = X_t + v \cdot s$$
$$BB^{(E)}_t(X,v,s) = X_t - v \cdot s$$

#### Inputs

• Input Data
• Percentage/Fixed Value/Ticks: This Input sets the Percentage, where 1 percent is .01, to multiply the Input Data by. Or sets the Fixed Value to add or subtract from the Input Data.
• Bands Type: Sets the bands type to either a Percentage, Fixed Value, or Number of Ticks.