# Technical Studies Reference

### Heikin-Ashi

The Heikin-Ashi study calculates and displays Heikin-Ashi bars. These are average price bars. By default these bars are displayed in the Chart Region below the main price graph.

If you want to view the Heikin-Ashi study as the main price graph and replace the existing chart bars, open the Study Settings window for the Heikin-Ashi study and enable the Display As Main Price Graph option.

Let $$O$$, $$H$$, $$L$$, and $$C$$ be random variables denoting the Opening, High, Low, and Closing Prices, respectively, and let $$O_t$$, $$H_t$$, $$L_t$$, and $$C_t$$ be their respective values at Index $$t$$. Then we denote the Heikin-Ashi Opening, High, Low, and Closing Prices at Index $$t$$ as $$O_t^{(HA)}$$, $$H_t^{(HA)}$$, $$L_t^{(HA)}$$, and $$C_t^{(HA)}$$, respectively. These are the Prices that determine the Heikin-Ashi bars, and we compute them for $$t \geq 0$$ as follows.

$$O_t^{(HA)} = \displaystyle{\left\{ \begin{matrix} O_t & t = 0 \\ \frac{O_{t - 1}^{(HA)} + C_{t - 1}^{(HA)}}{2} & t > 0 \end{matrix}\right .}$$

$$H_t^{(HA)} = \max\left\{H_t,O_t^{(HA)}\right\}$$

$$L_t^{(HA)} = \min\left\{L_t,O_t^{(HA)}\right\}$$

$$C_t^{(HA)} = \displaystyle{\frac{O_t + H_t + L_t + C_t}{4}}$$

Note: If the Set Close to Current Price for Last Bar Input is set to Yes, then $$C_t^{(HA)}$$ at the last bar in the chart is set equal to the current Price.

Understand that because all values of a chart bar are modified by the Heikin-Ashi study that the chart bars no longer display real values. You cannot make comparisons of these type of chart bars to another chart which does not have the Heikin-Ashi study. This will also mean that depending upon the chart bar timeframe, that the Close/Last price of the last bar in the chart will be different among charts for the same symbol using this study.

#### Inputs

• Set Close to Current Price for Last Bar: When this input is set to Yes, the default, then the Close/Last price of the last bar in the chart is set to the actual current price.