2008issue C021
Heikin-Ashi OHLC construction and simplification
Heikin-Ashi replaces raw open, high, low, and close with a four-price average, a lagged reconstructed open, and a modified high and modified low. The four-price average cannot exceed the session high, so the modified high reduces to the larger of the session high and the reconstructed open.
- A Heikin-Ashi close is the four-price average of the current bar, and the reconstructed open is the midpoint of the previous reconstructed open and previous reconstructed close.
- The modified high is the largest of the session high, the reconstructed open, and the reconstructed close. The modified low is the smallest of the session low and those same reconstructed prices.
- The four-price average cannot exceed the session high, so dropping it from the high-selection step leaves a modified high equal to the larger of the session high and the reconstructed open. The modified low follows the same reduction.
- A nested extremum compares three candidate prices with two two-input steps and matches a single three-input comparison. Folding the open formula into the close formula on one line can produce a slightly different series if previous-value evaluation differs from a two-line sequence.
The reconstructed candlestick
Heikin-Ashi is a reconstructed candlestick that replaces raw open, high, low, and close with averaged and lagged values so consecutive bars share a smoother open-close path.
Close and reconstructed open
A Heikin-Ashi close is the four-price average of the current bar, the arithmetic mean of that bar's open, high, low, and close. A Heikin-Ashi open is the reconstructed open: the midpoint of the previous reconstructed open and the previous reconstructed close.
Modified high and modified low
A Heikin-Ashi high is the largest value among the session high, the reconstructed open, and the reconstructed close. That selection is the modified high.
A Heikin-Ashi low is the smallest value among the session low, the reconstructed open, and the reconstructed close. That selection is the modified low.
A term that never binds
The four-price average cannot exceed the session high, so including that average inside the high-selection step does not change the reconstructed high. After that redundant term is removed, the modified high reduces to the larger of the session high and the reconstructed open, and the modified low follows the same reduction.
Nested extremum and evaluation order
When a platform maximum or minimum accepts only two inputs, three candidate prices must be compared by nesting two two-input steps. The nested form matches a single three-input comparison. A nested extremum is that pair of two-input steps.
Folding the open formula into the close formula on one line can produce a slightly different series if the platform evaluates its previous-value function differently than a two-line sequence.
All readings on this track · 16 readings
- 2004Reconstructing Heikin-Ashi bars from smoothed OHLC
- 2004Heikin-Ashi candle construction as an OHLC transform
- 2004Stacking heikin-ashi, swing charts, and a moving average in strong trends
- 2007Constructing a Heikin-Ashi volume-price oscillator
- 2007A volume-price oscillator is a timing trigger, not a standalone entry
- 2008Heikin-Ashi OHLC construction and simplification
- 2008How a Heikin-Ashi candlestick oscillator is built from color, lag, and hold rules
- 2008Heikin-Ashi color-coded candles and smoothed trend filters
- 2010Heikin-Ashi smoothed percent b for divergence timing
- 2011Constructing Heikin-Ashi, moving-average, and MACD filters
- 2011Constructing candlestick, Elliott-wave, and Heikin-Ashi hypotheses
- 2012Constructing a three-state Heikin-Ashi trend filter
- 2012Heikin-ashi as a trend-state signal without candlestick-patterns
- 2013Heikin-Ashi volume gates, smoothing, and denominator floors
- 2013How Heikin-Ashi close and typical-price form a two-average crossover
- 2013Walk-forward tests for color-coded Heikin-Ashi crosses