SMOOTHED HEIKIN-ASHI ALGORITHMS
OPTIMIZED FOR AUTOMATED TRADING SYSTEMS
Cristian Păuna, PhD student
Abstract: Heikin-Ashi is the Japanese term for "average bar". This methodology is well
known as one of the methods to identify and follow the trends using a price time series in
financial markets. Nowadays, in the first decades of the 21st century, in the electronic trading
environment, with very volatile price market conditions, using the Heikin-Ashi method gets
new and special connotations especially when it is about the high-frequency trading. It was
found that combining the classical Heikin-Ashi candlesticks with modern limit conditions
reliable trading algorithms can be generated in order to produce a good trading return with
automated trading systems. This paper will present several trading algorithms based on
Heikin-Ashi method for algorithmic trading especially adapted for high-frequency trading
systems. It will be revealed how the trading signals can be automatically built and used in
order to automate the trading decisions and orders. Exit signals will also be discussed.
Trading results obtained with the presented algorithms for Frankfurt Stock Exchange
Deutscher Aktienindex Market will be displayed in order to qualify the methods and to
compare them with any other trading strategies for high-frequency trading. As conclusions,
Heikin-Ashi combined with special limit conditions can generate reliable trading models for
Key words: algorithmic trading, automated trading systems, Heikin-Ashi
In the first decades of the 21st Century “the development of e-businesses represents an
important factor in boosting the growth and prosperity”  of the human society. In the new
electronic trading environment of the financial markets, automated trading systems (ATS)
have become an important part in any modern financial investment company. “The
development of the information and communication technology leads to the creation of new
business models and decision support systems” .
“In electronic financial markets, algorithmic trading (AT) refers to the use of computer
programs to automate one or more stages of the trading process” . The trading decisions
and orders are made partially or completely automatically nowadays by computers using
advanced mathematical algorithms. “High-frequency trading (HFT) is a type of algorithmic
trading characterized by high speeds, high turnover rates, and high order-to-trade ratios that
leverages high-frequency financial data and electronic trading tools” .
There is a considerable number of trading strategies and models in the literature, but not all of
them are adapted for algorithmic trading. Nowadays the algorithmic traders “represent 52% of
market order volume and 64% of nonmarketable limit order volume” . Different analytical
trading models that can be automated for the financial markets are presented by Larry
Connors in  and  with proved reliable results. Using the genetic based algorithms,
interesting reserches are presented by Yong Hu  and José Manuel Berutich . Hybrid
trading strategies are also developed in the last time, a hybrid system is presented by
Economic Informatics Doctoral School, Bucharest Academy of Economic Studies,
11th Tache Ionesc Str., Bucharest, Romania, email@example.com
This paper was co-financed by the Bucharest Academy of Economic Studies during the PhD program
Youngmin Kim . A significant number of the trading strategies that can be automated for
the stock exchanges are adapted from the currency market; some reliable strategies are
presented by Kathy Lien in  and . Considering the current academic literature related
with the trading strategies adapted for algorithmic trading, the subject about how the Heikin-
Ashi transformation can be used to detect the trend and to automate the trading signals is not
treated. This is the purposed filled by the current paper.
This paper will present some algorithms optimized especially for HFT. The models presented
here are based on the Heikin-Ashi (HA) methodology. HA is the Japanese term (平均足) for
the "average bar" and represents a transformation of the price time series into a new series
with the purpose to filter the noise and to obtain a graphic representation for the price trend.
The HA model is well known as a good method to identify and follow the trend in financial
markets. This paper will present how the HA methodology can be combined with modern
limit conditions (LC) in order to improve the trading efficiency and to automate the trading
decisions for inclusion in ATS.
It will be revealed the way how the trading signals based on HA can be automatically built
and used in order to automate the trading activity. Exit signals will also be discussed and built
using the same technique in order to automate the exit procedures. To qualify the presented
methods and to compare them with any other trading strategies for HFT, trading results will
be presented in the last part of the paper. These results were obtained with a HFT of the
Frankfurt Stock Exchange Deutscher Aktienindex DAX30 Market . The results will
qualify the signals obtained with HA as to be reliable trading signals for AT that can be
included and optimized for any ATS.
2. HEIKEN-ASHI TECHNIQUE
It is well known that a price time series in financial market is given by the four values Open,
High, Low and Close price levels for each time interval. The time interval can vary between
one second until one month or even one year. Having the values above, noted here with Oi,
Hi, Li respectively Ci for each i interval, the time price series can be easily recorded and used
further. For an easy view, the four price levels characteristic for each time periods are drawn
as candle sticks presented in Figure 1.
Figure 1: Bullish and bearish price time series candlesticks (source: )
Candlestick charts are thought to have been used and developed “in the 18th century by
Munehisa Homma (1724-1803), a Japanese rice trader” . The colors used for the
candlesticks are at the user disposal. The bullish and bearish differences are usually
highlighted using different colors. In the figure 2. it is represented a time price series of the
DAX30 index on daily timeframe using the candlesticks representation.
Figure 2: Time price series with candlesticks
The price trend is not obvious in the figure 2. Even the colors are different for bullish and
bearish candles the price tendency is not defined by this graph. The Heikin-Ashi technique
will highlight the bullish and bearish tendency of the graph. Reducing the noise and the
volatility a more accurate image will be obtained. A new price transformation will be made.
For each i time interval, the open level in the new space will be the average level between
open and close price of the last interval, the close level will be the average between the forth
price levels of the current interval and the low and high will be given by the minimum
respectively maximum of the price levels by:
This transformation will gives us a clearer image for the tendency of the price movement.
Using one color for the intervals with Ohai<Chai (usually green or blue) and other color for
the cases with Ohai>Chai (usual red) we will obtain a graphs like in figure 3.
Figure 3: Time price series with Heikin-Ashi candlesticks
The price time series in the Figure 3. is the same as in the Figure 2. In the figure 3. the
transform made by formula (1) is drawn.
3. SMOOTHED HEIKEN-ASHI
Even the image is clearer using HA candlesticks, trading in volatile price movements is still
difficult. As we can see in figure 3, between the two bullish intervals there are some red HA
candlesticks. The graph suggests the long trend is almost finished but a strong continuation
contradicts this conclusion after a small interval. To filter the false signals and to give a more
stable graph, remaining in strong correlation with the price behavior, a different smoothed HA
transform is proposed:
represent the averages values for the open, high, low respectively
close price levels for a specified M number of time intervals. Good results are obtained using
exponential moving averages . The smoothed HA technique obtained with formulas (2)
using exponential averaged of the price levels for M=6 time periods is presented in figure 4.
Figure 4: Time price series with smoothed Heikin-Ashi technique
Comparing the figure 3. and figure 4. it can be noticed that the indication given by the
candlesticks colors is clearer, a long trade being possible for the entire bullish period included
in the figure 4. In practice it is observed that using small period intervals for the moving
averages is proper to identify the secondary trends.
For the main trend higher values for the period of the smoothing moving averages must be
used. In the figure 5. is presented the same price time series with a modified smoothed HA
technique using M=40. It can be observed that the price trends are mode obvious. This
methodology is more adaptive to catch and follow the large trends. The graph forms the figure
5. was obtained using an exponential moving average for the smoothed HA. The timeframe
used in figure 3, figure 4. and figure 5. is the daily timeframe.
Figure 5: Time price series with smoothed Heikin-Ashi technique for longer intervals
Coding the smoothed HA technique in any multi query programming language is one usual
task. To exemplify, in the figure 6 it is presented a sample code for smoothed HA wrote in
Meta Quotes Language .
Figure 6: Meta Quotes code for smoothed HA
The problem that will be treated in the rest of the paper is how to use smoothed HA price
levels in order to build automated trading signals and how to include them into ATS.
4. TRADING SIGNALS
Once we have the methodology to obtain HA and smoothed HA candlesticks in order to
identify the price trends, in this chapter it will be presented the way to build automated trading
signals based on these techniques.
In order to automate the trading decisions and orders, the information regarding the price
evolution given by HA series must be transformed into a Boolean variable called trading
signal. When the BuySignal variable will have “true” value, a buy trade will be initiated by
the ATS. For those markets where sell trades can be considered, when the SellSignal variable
will have the “true” value, a short trade will be opened by the automated trading algorithm.
For this purpose, the price behavior must be included in these signal variables. The way to
build the trading signals based on smoothed HA technique is:
Using smoothed HA technique exit signals can be also considered when the HA changes the
color of the candlesticks:
The exit signals given by formula (4) can be optimized finding the best value for the M
number of time intervals used in the smoothed HA series. The relations (4) are used for AT,
especially when trades are kept longer to catch longer trends.
The formula (4) is not proper for HFT where the profit target is very small. For HFT
additional conditions must to be imposed in order to avoid opening trades in the overbought
and oversold intervals. These conditions will be presented in the next chapter.
Looking to the figure 5. it can be seen a direct relation between the price tendency and the
distance between the Open and the Close of the smoothed HA price levels. When the distance
between Ohai and Chai is increasing, the price has a strong movement tendency, when the
distance between the open and close of the HA smoothed levels is decreasing, the price is
slowing down and it is approaching to change its behavior or trend. This considerations will
generate the second type of trading signals based on HA technique. A buy signal can be
considered when the open of the smoothed HA is lower than the close and the distance
between the two levels is increasing. The sell signal can be made in the same idea for those
periods with close less than open of the smoothed HA:
The relations (5) will generate trades only on the intervals when the price makes significant
movements in the direction of the trend. All the rest intervals will be ignored or used in order
to close the already opened trades. Decreasing the distance between the open and close of the
smoothed HA can be also a good exit signal:
The signals (3), (4), (5) and (6) can be applied for different timeframes. These signals can be
used for both AT and HFT. For HFT the profit target is small. A significant larger number of
trades will be made for HFT. For this case additional conditions must to be imposed in order
to avoid opening trades on overbought and oversold intervals.
5. LIMIT CONDITIONS
Good results were obtained combining the trading signals presented in the last chapter with
limit conditions imposed in the “Price Cyclicality function”  values. Noting with PCYi
the value of the price cyclicality function, the limit conditions for the long signals can be
automated using the next formulas:
where ρ and ξ are two functional parameters that will be optimized for each traded market.
The computational way to build the PCY function can be found in the author paper . The
parameter ρ assure that the trading signal is not initiated too earlier while the parameter ξ will
filter the trades in order not to be opened in overbought intervals. The sell signals using the
limit conditions with the PCY function can be built similarly.
It was found that the trading signals (7) can open trades even the price trend is not strong
enough. In order to filter these cases, a limit condition can be imposed for the gradient of the
PCY function. Especially for HFT this filter will ensure good and positive profit expectancy.
New trades will be opened by (7) only if the gradient of the PCY function will be higher a
specified δ value:
The measure of the functional parameters ρ, ξ and δ will be found by an optimization process
using the time price series for a historical interval. Using an iterative process, the optimal
values for each functional parameter will be found checking the trading signals for each time
interval in the historical price series. Trading results obtained with (8) will be presented in the
6. TRADING RESULTS
In this section we will present trading results obtained with the signals detailed above. These
results were obtained using TheDaxTrader , an automated trading system that uses
smoothed HA trading signals in order to generate buy trades for DAX30.
The results presented in table 1. were obtained for HFT of contract for difference (CFD) of
DAX30 the period 01.06.2015 – 30.06.2018 with a spread of 1 point using a fixed target of 10
points for each trade. The risk and exposed capital management were made using the “Global
Stop Loss Method” presented in the author paper .
The smoothed HA trading signals (8) were built for a four hours timeframe interval. An
additional condition was imposed regarding the hourly intervals of the executed trades
between 8:00 and 16:00 coordinated universal time (UTC) in order to ensure the liquidity on
Trading signals (8)
Number of trades
Table. 1. Trading results obtained with smoothed HA trading signals
The results presented were obtained with the next functional parameters included in the
formula (8): M=40, ρ=5, ξ=95 and δ=8. The capital evolution due to the smoothed HA signals
is presented in figure 7. In the case presented no losing trade were recorded.
Figure 7: Capital evolution due to HA trading signals
The trading results above were obtained considering only one trade opened in a moment of
time. If a trade is opened and a new trading signal appears, no additional trade will be
considered until the initial trade is closed. The maximal time interval of the longest trade was
In order to reveal the advantages of the Smoothed Heikin-ashi methodology we present a
comparison with other known trading methods. The results presented in table 2. were
obtained using algorithmic trading in the same period of time (01.06.2015 – 30.06.2018), on
the same financial market (DAX30) with the same ten points target.
Smoothed Heikin-Ashi signals
Moving averages perfect order signals
Parabolic stop and reverse signals
Relative Strength Index signals
Table 2. Comparison between trigonometric interpolation and other known trading methodologies
The known trading methods used were the “Moving averages perfect order methodology”
, “Parabolic stop and reverse methodology”  and “Relative strength index
methodology” . Each method was optimized to obtain the best trading efficiency for the
financial market used. In table 2 it can be seen that the SHA methodology makes a significant
larger number of trades with a very good value for the risk and reward ratio (RRR). These
results are an additional confirmation that the method is a reliable trading methodology for
The author uses the HSA trading signals presented in this paper since 2013 year. This
methodology was included in TheDaxTrader automated trading software. With a proper
optimization parameters set, the HSA trading signals generate only profitable trades in the
stock markets. This methodology was tested, implemented and used with the same good
results for a representative number of financial markets: Deutscher Aktienindex (DAX30),
Dow Jones Industrial Average (DJIA30), Financial Times London Stock Exchange
(FTSE100), Cotation Assistée en Continue Paris (CAC40), Swiss Stock Exchange Market
Index (SMI20), Australian Securities Exchange Sydney Index (ASX200), Tokyo stock
Exchange Nikkei Index (Nikkei225), NASDAQ100 Index, Standard & Poor’s Index
(S&P500) and Small Capitalization US Index (Russell2000). Also with good and stable
results the trigonometric interpolation methodology presented in this paper was applied for
Gold and Bent Crude Oil financial markets starting with 2015 year.
The Heikin-Ashi trading technique can be improved using smoothed methods with different
types of moving averages. The smoothed Heikin-Ashi model can be adapted for algorithmic
trading and high-frequency trading in the electronic trading today’s market conditions. The
presented model permits to identify the up and down trends for different timeframes in any
financial market. When an up trend is detected, a buy signal will be generated by the trading
software. Similarly, for those markets with profitable sell conditions, when a down trend is
detected, sell trades can be considered.
Automated trading signals can be built using the smoothed Heikin-Ashi time series. Both buy
and sell trading signals can be automated together with the exit signals using Boolean
variables. In order to avoid opening trades in the overbought and oversold price intervals,
additional limit conditions must to be imposed for the Smoothed Heikin-Ashi trading model.
Using the price cyclicality model these conditions can be included in the trading signals
variables in order to automate the trade decisions. In order to avoid opening trade in the
intervals when the price is not making significant movements additional limit conditions can
be imposed with the gradient of the price cyclicality function in order to consider only the
strong trends. With all these conditions, the smoothed Heikin-Ashi trading signals can
produce a significant number of trades with positive profit expectancy.
The presented trading methodology can be optimized based on the functional parameters in
order to be traded on different timeframe intervals and different markets. The functional
parameters included in the trading signals formulas will be optimized using repetitive
algorithms in order to maximize the profit and to reduce the exposure and capital risk. The
proper parameter set will be obtained for each traded market.
The presented trading signals can be named reliable, once a period of 36 months produced
trading results with 1:4.27 RRR and 1:10.55 absolute RRR. The optimization process of the
functional parameters for the trading signals presented can be made using a time price series
of the historical price for any market with good liquidity. These signals can be also optimized
for algorithmic trading with longer profit target for automated trading or automated
Looking at the compared results included in table 2. we can say that the signals obtained
using the smoothed Heikin-Ashi methodology are reliable trading signals. The values for the
RRR and the number of trades and profit obtained with the presented methodology are a good
confirmation for this assumption.
All trading and the exit conditions included in the presented methodology are based on the
Heikin-Ashi price transformation and can constitute a stand-alone trading model for
automated trading systems. Being exclusively a mathematical model, the methodology
presented in this paper can be applied with good results for algorithmic trading and high-
frequency trading. This model can also be used for manual trading.
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