Learn Heiken Ashi
"Heikin" in Japanese means 'average' and "Ashi" means 'bar'. So a literal translation would be 'average bar'. Indeed, the method employs an averaging technique as follows:
* haClose = (Open + High + Low + Close) / 4
* haOpen = (haOpen(previous bar) + haClose(previous bar))/2
* haHigh = Maximum(High, haOpen)
* haLow = Minimum(Low, haOpen)

It is mathematically impossible for the haClose to be higher than the bar High, or lower than the bar Low. haClose is an average of the bar's open, high, low and close. The open must be in the high-low range. The close must be in the high-low range. The low must be equal to or lower than the high. Therefore, the haClose can never be higher than the High, nor lower than the Low.
Because the haClose can never be higher than the High, the Heikin-Ashi High does not need to test for the haClose as a possible price that would set haHigh. Choosing the higher of High and haOpen is sufficient. The same reasoning applies to picking a price for the Heikin-Ashi Low. Choosing the lower of Low and haOpen is sufficient. haLow does not need to consider haClose because haClose will never be lower than the Low.
haClose
The Heikin-Ashi Close is the average of four bar prices: open, high, low and close. This creates an interesting effect in strongly trending markets. Let we illustrate the effect with the following example.

The example shows the original bar data in the top half of the chart, and the Heikin-Ashi method in the bottom half. Ensign Windows was used to prepare the examples. Bars 1 through 4 are strongly trending up, and bars 5 through 8 are strongly trending down.
In an Up candle the haClose will always be below the actual close, and in a Down candle, the haClose will always be above the actual close. These two principles are illustrated by comparing the position of the close red dots to the bar closes in the Original chart image
Mathematically the haClose can never exceed 75% of the original bar's range. 75% would be achieved when the Open and the Close occur at the extreme of the bar's High. In that case, haClose = (H+H+H+L)/4. Simple example: O=4, H=4, C=4, L=0, so haClose = 12 / 4 = 3 So the maximum haClose value is 3/4th of the range because the range was 4. Thus the high wick size in an Up candle will be 25% of the original bar range or greater. The low wick size in a Down candle will be 25% of the original bar range or more.
haOpen
The haOpen formula can be stated more simply as the midpoint of the prior Heikin-Ashi bar's candle body. See the graphical illustration of this where the cyan lines from the prior bar's candle body range point to the candle body midpoint. This midpoint is used as the open of the following Heikin-Ashi bar.

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