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Study of Heiken Ashi Candlestick for Noise Reduction  

William Tchoudi 

LIGS University, USA 

Abstract 
In this study, we examined Heiken Ashi's ability to reduce the noise when the traditional 

candlestick bars are transformed into Heiken Ashi candlesticks. The transformed candlestick is 

done by a python program. The entropy is calculated at a given confidence level for both 

traditional candles and Heiken Ashi. By assumption, the noise is measured by the entropy. The 

higher the value of the entropy, the more pronounced the noise is. The hypothesis test for Heiken 

Ashi showed accepted results, and the Heiken Ashi candle entropy is lower than traditional 

candles. 

Keywords: Entropy, Heiken Ashi, Candlestick, Hypothesis Test, Noise, Prices 

 

1. Introduction 
The goal of this part is to propose to traders a new approach to technical analysis based on time 

series analysis. We have chosen a Heiken-Ashi (HA) base analysis to mix with the fundamental 

analysis. One big challenge for traders is to determine the right entry signal into the market. A lot 

of trading indicators exist out there, but none of them is absolute, so traders use different 

techniques in a single strategy. Also, high-frequency trading uses trading techniques 

programmed with algorithms that allow them to handle thousands of orders per second. High-

frequency trading is the most important cause of the market noise that makes today's financial 

markets noisier than they used to be before the era of algorithmic trading. So is Heiken Ashi 

value enough in that task to help technical analysis to perform robust trading strategy? 

In this study we handle the following points:  



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 Show visually the difference between Heiken-Ashi Candle stick and the normal candle 

stick in term of noise vision. 

 Evaluate Heiken-Ashi price entropy as a noise measurement and compare it to the real 

price 

 Perform hypothesis testing with a target probability of prediction of 0.7.  

 Build a simple trading strategy with Heiken-Ashion the basis and other technical 

indicator. 

The study is divided in many section, Part 2: key concept of using Heiken Ashi. Part 3: Noise 

modeling. 

 

2. Context of using Heiken Ashi 

2.1.Heiken-Ashi (HA) 

The Heikin-Ashi (HA) technique combines price data to create a Japanese candlestick chart, 

filtering out market noise and providing an immediate prediction of the trend on the market's 

next bar move. Heiken-Ashi charts share similar characteristics with traditional candlestick 

charts, but vary according to the values used to construct each candle. The HA technique uses a 

modified formula based on two-period averages instead of using the open, high, low, and close 

charts like traditional candlestick charts. It provides a cleaner look to the map, making 

identifying patterns and reversals easier. Modified Open, High, Low, and Close are defined as 

follows [2]: 

𝐻𝑎𝐶𝑙𝑜𝑠𝑒( ) =
𝑂𝑝𝑒𝑛( ) + 𝐻𝑖𝑔ℎ( ) + 𝐿𝑜𝑤( ) + 𝐶𝑙𝑜𝑠𝑒( )

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𝐻𝑎𝑂𝑝𝑒𝑛( ) =
𝐻𝑎𝑂𝑝𝑒𝑛( ) + 𝐻𝑎𝐶𝑙𝑜𝑠𝑒( )

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𝐻𝑎𝐻𝑖𝑔ℎ( ) = 𝑀𝑎𝑥(𝐻𝑖𝑔ℎ( ), 𝐻𝑎𝑂𝑝𝑒𝑛( ), 𝐻𝑎𝐶𝑙𝑜𝑠𝑒( )) 

𝐻𝑎𝐿𝑜𝑤( ) = 𝑀𝑖𝑛(𝐿𝑜𝑤( ), 𝐻𝑎𝑂𝑝𝑒𝑛( ), 𝐻𝑎𝐶𝑙𝑜𝑠𝑒( )) 



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2.2. Assumptions 

 We base our analysis on trend consideration because trend uses the history of the 

movement to give the evolution slope of the prices, which are all linked to volume. Some 

indicators can be used to validate some mathematical logic analysis; it is the case of the 

moving average, where it is not possible to have a bearish market with a bullish moving 

average. The trend can be used to predict the market's next move. 

 Handle noises: The market is full of noises that we should consider in our analysis. That 

is why we chose to use Heiken-Ashi Candlesticks instead of normal prices that carry all 

the noise. 

2.3. Why using Heiken Ashi method 

In this section, we perform the transformation of normal prices to Heiken-Ashi prices and then 

study the probability of a good prediction of the market movement. In this approach, we use time 

series comparison. The past data is divided into two parts: one is for modelling Heiken-Ashi 

prices, and the second is the benchmark real data to evaluate the prediction probability of the 

market move using Heiken-Ashi Bars. 

The next figure shows the candlestick bars for AAPL daily for the last 5 months. 

 

 

 

 

 

 
Figure 1: Candle stick Bars historic daily Stock price of AAPL 

The green bars represent the up-price movement and the red bars are the down-price movement. 

In this figure above, we can observe the noises which are represented by many little candles that 



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stick most of the time up in a bearish trend and down in a bullish trend. In a noisy market, the 

quasi-reversal of prices can mislead the trading based on the original price observation. That is 

why In our approach, we propose to first remove the noise while consolidating the trend. Thus, 

the Heiken-Ashi candlestick is an option to handle that situation, and we develop some analysis 

to evaluate how satisfying the method is. 

The figure below shows the same graph with Heiken-Ashi candlesticks. 

 

 

 

 

 

 

 

Figure 2: Heiken-Ashi Candlestick Bars historic daily Stock price of AAPL 
 

The blue bars represent the up-modified price movement, and the red bars represent the down-

modified price movement. We can observe the trend now because the noise is reduced and it is 

better for traders to identify bullish and bearish trends with many consecutive bars of the same 

colour and a pronounced slope. When Heiken-Ashi candlestick bars appear, a colour indicates 

the trend, thus indicating the prediction of the next bar. So in this study, we are going to 

determine the statistics of good predictions and validate the accuracy of the method. 

The study was conducted over one year of historical prices of 10 different stocks. 

The goal of the analysis is to determine the accuracy of the next day's prediction with Heiken-

Ashi. In each graph, we determine the probability of a good prediction. A good prediction is 

made when the same colour bar is maintained. When it changes, the prediction is false. 



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So we handle this problem by introducing the entropy measure in order to quantify the noise and 

make a comparison between the raw data market and the Heiken-Ashi data, and then calculate 

the cumulated percentage of the good trend prediction. 

3. Noise Modeling   

3.1.Entropy Approach to Evaluate Noise 

In this section, we choose to use entropy to evaluate the noise. The base hypothesis is to consider 

that if during a certain time series period the market establishes a trend, for example, with all 

bars only bullish or only bearish, that means there is no noise, therefore the entropy is zero for 

that period. So, the uncertainty can be modelled with the reversal of the bar. It is done by a 

bearish bar that turns bullish or a bullish bar that turns bearish, so this is the origin of the 

volatility. The reversal market is indeed uncertain, thus a measure of the uncertainty of the trend 

can be applied. 

a) Notion of Entropy 

Entropy is the measure of the uncertainty. 

The entropy of a discrete random variable is calculated by the following formula [1]: 

𝐻(𝑋) = − ∑ 𝑃(𝑥 ) 𝐿𝑜𝑔(𝑃(𝑥 ))       (1) 

From this formula above, X is the discrete random variable with values by the set of xk 

𝑋 = {𝑥 , 𝑥 … … 𝑥 }, 𝑃(𝑥 )is the probability of the event xk.  

b) Calculation of the probability 

We modelling this problem as a space Ω which is time series over the studied period of time with 

N days typically for a year N=251. There is two trend direction the up direction (bullish)and the 

down direction (bearish) and during a period of time the two movements alternate. 

 Assumptions 

o Successive bars in same directions are considered as a partition each partition and 

the total number on bar for all partitions is Np 

o The reversal bar is a transition and the total number of transitions is Nr 



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o The total bars studied day period N is the sum of the total partitions and the total 

transition 

𝑁 =  𝑁 ( ) + 𝑁( )    (2) 

o The discrete random variableX is a set of xkpartitions and transitions each 

partition is made by npnumber of bar and transition is only one bar each time 

𝑁 ( ) =  ∑ 𝑛      (3) 

𝑁 ( ) =  ∑ 𝑛        𝑤𝑖𝑡ℎ  𝑛 = 1   (4) 

 

 

 

 

 

 

Figure 3: Consideration of trend number of bars 

The probability for either a partition or a transition is then calculated by: 

𝑃(𝑥 ) =   𝑤𝑖𝑡ℎ 𝑘 ∈ {𝑝, 𝑟}    (5) 

The uncertainty in this scope comes from the difficulty of predicting the next day and the risk of 

losing money. Thus, a certain trend during a period is good for investors and increases the 

probability of making money. However, the noise misleads the prediction and for day traders it is 

a real puzzle. That is why we propose to study an analytic method that focuses on the trend and 

hides the noise. 

The cumulative probability of a good prediction is done by: 

𝑃 𝑋 = 𝑥 =
∑

     (6) 



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3.2. Analysis of the results for Heiken-Ashi Analysis and trend cumulative 
probability 

For the study, we computed 20 companies’ data from all sectors. Then we computed the entropy 

from raw data provided by the market and the calculated Heiken-Ashi (HA). The tab below 

shows the computed results. 

Tab 1: Computed data of entropy and cumulative prediction probability 

ticker Raw Entropy Raw Prediction 
Probability  

HA entropy HA Prediction 
Probability  

FB 5.14 0.47 4.37 0.72 
AAPL 5.12 0.49 4.07 0.68 
AMG 5.13 0.47 4.3 0.7 
AMZN 5.13 0.47 4.15 0.69 
MSFT 5.04 0.51 4.41 0.71 
AOS 4.86 0.49 4.2 0.75 
MMM 5.05 0.52 4.18 0.74 
AFL 5.1 0.45 4.41 0.69 
ABT 5.0 0.5 4.47 0.7 
CTL 4.98 0.47 4.35 0.74 
AES 4.89 0.5 4.16 0.72 
LNT 5.05 0.52 4.41 0.75 
ABBV 4.97 0.49 4.39 0.73 
ALB 5.06 0.47 4.09 0.7 
T 4.89 0.48 4.44 0.72 
VLO 4.79 0.52 4.25 0.72 
WMB 4.8 0.49 4.35 0.73 
ARE 5.06 0.51 4.35 0.75 
AMT 4.8 0.55 3.9 0.76 
MO 5.16 0.45 4.1 0.76 

 

The quick observation reveals that the raw entropy for each raw HA is less than the raw entropy, 

and the probability of prediction for HA is greater than the calculated raw probability. 

The average results 

 

 



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Table 2: Mean data of entropy and prediction probability 

Mean entropy Raw 5.001 
Mean Prediction 
Raw 

0.491 

Mean entropy HA 4.2675 
Mean prediction HA 0.723 

 

The HA mean entropy is lower than the raw entropy. This means that the HA market is less 

uncertain than the original raw market. At the same time, we observe that with HA we have a 

mean 72% chance of predicting the next day, and with the raw market we have only a 49% 

chance of predicting the next day. So, using HA is good enough in a noisy environment. At this 

stage, we do not know if the cumulative probability we introduced in this study as a measure is 

good as criteria. That is why we evaluate it with the correlation study. 

 

 

 

 

 

Figure 3:  Entropy and Prediction Probability of Raw market with Pearson’s r. Correlation 

On the graph of Figure 3, we have a negative correlation, which means the higher the probability 

is, the lower the entropy is.. The dispersion we observe in the Heiken-Ashi case is due to the fact 

that the value of the entropy increases with the number of small trend periods and the reversal 

trend. This fact can explain why, with Heiken-Ashi, the negative correlation is not too much 

pronounced. 

In real life, predicting the next move with 70% accuracy is a good bet for a trader, so we will 

perform Hypothesis Testing. 



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3.3. Hypothesis Testing 

To validate the prediction rate, we perform hypothesis testing in the raw market and the Heiken-

Ashi transformed market. The necessity of this test is to provide investors more evidence of 

whether the Heiken-Ashi is acceptable for investors as a strategy or if the raw market is already 

set for that despite the noises. 

a) Null (H0) and Alternative (H1) Hypothesis 

In real life, if a trader can predict the next move with more than 50% accuracy, it is already a 

good task, but the goal of a financial analyst is to guarantee the investor better with a minimum 

possible. Thus, we will test a minimum guarantee of 70% accuracy to predict the next day's 

market move and compare the raw data with the Heiken-Ashi data. So we ran two hypothesis 

tests: 

 H0 :𝑝 ≥ 𝑝  and H1 : 𝑝 < 𝑝  

 p  ∈ {0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.80} 

 

b) Level of Significance and Confidence 

For our study we chose a significance 𝛼 = 0.05 this mean the Confidence C is:  

 𝐶 = 1 − 𝛼 = 0.95                                       (7) 

We apply this significance for the two Hypothesis testing to run. 

c) Computing of the different testing  

We stop the test when the null is rejected for the Left tail test. 

Table 3: p-value results 

p0 Stdraw Stdha Z-Score raw Z-Score ha P-value raw P-value ha Decision  
Raw a = 0.05 

Decision  
HA a = 0.05 

0.7 0.03 0.02 -7.0 1.0 0.0 0.1587 Rejet H0 Accept H0 
0.71 0.03 0.02 -7.33 0.5 0.0 0.3085 Rejet H0 Accept H0 
0.72 0.03 0.02 -7.67 0.0 0.0 0.5 Rejet H0 Accept H0 
0.73 0.03 0.02 -8.0 -0.5 0.0 0.3085 Rejet H0 Accept H0 
0.74 0.03 0.02 -8.33 -1.0 0.0 0.1587 Rejet H0 Accept H0 
0.75 0.03 0.02 -8.67 -1.5 0.0 0.0668 Rejet H0 Accept H0 



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0.76 0.03 0.02 -9.0 -2.0 0.0 0.0228 Rejet H0 Rejet H0 
0.77 0.03 0.02 -9.33 -2.5 0.0 0.0062 Rejet H0 Rejet H0 
0.78 0.03 0.02 -9.67 -3.0 0.0 0.0013 Rejet H0 Rejet H0 
0.79 0.03 0.02 -10.0 -3.5 0.0 0.0002 Rejet H0 Rejet H0 
0.8 0.03 0.02 -10.33 -4.0 0.0 0.0 Rejet H0 Rejet H0 
 

With a confidence of 95%, the result of this study reveals that with Heiken-Ashiwe can predict 

the next move with 75% accuracy. In conclusion of this study, Heiken-Ashi is recommendable 

for technical analysis as a trend indicator and can be coupled with other indicators to make 

trading decisions like: 

 Moving Average Convergence Divergence (MACD) is a measure of the divergence 

between two moving averages. 

 The Commodity Channel Index (CCI) 

 Exponential Moving Averages (EMA) 

 

4. Conclusion 
In this paper, we used HA to address the problem of market noise. The value of the noise is 

calculated by the measure of the entropy. We calculated the HA candle stick and the comparative 

study between the entropy of the HA candlestick and the entropy of the market candle stick. The 

mean entropy of HA for the studied sample is lower than the mean entropy of the raw price 

market, and the probability of prediction of the next move was also greater for HA than for the 

raw price market. Those results demonstrated that the HA is less noisy. The hypothesis test with 

a confidence level of 0.95 on the probability of predicting the next move of the market was 

accepted for HA at 0.70 until 0.75 and was rejected for the raw price market at 0.7. We 

concluded that using HA as a market mirror increases the chance of a good next move 

prediction. 

 



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Appendix 

1. Heiken Ashi plot code  
import matplotlib.pyplot as plt 
from mpl_finance import candlestick_ohlc 
import pandas as pd 
import matplotlib.dates as mpl_dates 
import numpy as np 
 
 
ticker = "AAPL" 
data =  pd.read_csv("PortfolioData/02_apple_ohlc.csv")  
 
 
 
def get_heiken_ashi_ohlc(df):     
    ha_close = (df['open'] + df['close'] + df['high'] + df['low']) / 4 
     
    ha_open = [(df['open'].iloc[0] + df['close'].iloc[0]) / 2] 
    for close in ha_close[:-1]: 
        ha_open.append((ha_open[-1] + close) / 2)     
    ha_open = np.array(ha_open) 
    date = df['date'] 
 
    elements = df['high'], df['low'], ha_open, ha_close 
    ha_high, ha_low = np.vstack(elements).max(axis=0), 
np.vstack(elements).min(axis=0) 
     
    ha_ohlc = pd.DataFrame({ 
        'open': ha_open, 
        'high': ha_high,     
        'low': ha_low, 
        'close': ha_close, 
        'date': date 
    }) 
     
    return ha_ohlc 
 
 
#def get_heiken_ashi_ohlc(data): 
#    ha_ohlc = pd.DataFrame() 
#    ha_ohlc['date'] =  data['date'] 
#    ha_ohlc['HaClose'] = 
(data['close']+data['open']+data['high']+data['low'])/4 
   # ha_ohlc['HaOpen'] =  
     
#    return ha_ohlc 
 
ha_ohlc = get_heiken_ashi_ohlc(data) 
 
 



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def plot_candle_stick(data,ticker,color1,color2): 
    plt.style.use('ggplot') 
    ohlc = data.loc[:, ['date', 'open', 'high', 'low', 'close']] 
    ohlc['date'] = pd.to_datetime(ohlc['date']) 
    ohlc['date'] = ohlc['date'].apply(mpl_dates.date2num) 
    ohlc = ohlc.astype(float) 
     
    # Creating Subplots 
    fig, ax = plt.subplots(figsize = (10, 5)) 
     
    candlestick_ohlc(ax, ohlc.values, width=0.6, colorup=color1, 
colordown=color2, alpha=0.8) 
     
    # Setting labels & titles 
    ax.set_xlabel('Date') 
    ax.set_ylabel('Price') 
    fig.suptitle('Daily Candlestick Chart of '+ ticker) 
     
    # Formatting Date 
    date_format = mpl_dates.DateFormatter('%d-%m-%Y') 
    ax.xaxis.set_major_formatter(date_format) 
    fig.autofmt_xdate() 
     
    fig.tight_layout() 
     
    plt.show() 
     
#plot_candle_stick(data,ticker,"green","red") 
 
def 
plot_candle_stick_ha_ma(data,data_ha,ticker,color1,color2,colorma,typema): 
     
    plt.style.use('ggplot') 
    ohlc = data.loc[:, ['date', 'open', 'high', 'low', 'close']] 
    ohlc_ha = data_ha.loc[:, ['date', 'open', 'high', 'low', 'close']] 
    ohlc_ha['date'] = pd.to_datetime(ohlc_ha['date']) 
    ohlc_ha['date'] = ohlc_ha['date'].apply(mpl_dates.date2num) 
     
    ohlc_ha = ohlc_ha.astype(float) 
     
    # Creating Subplots 
    fig, ax = plt.subplots(figsize = (10, 5)) 
     
    candlestick_ohlc(ax, ohlc_ha.values, width=0.6, colorup=color1, 
colordown=color2, alpha=0.9) 
     
    # Setting labels & titles 
    ax.set_xlabel('Date') 
    ax.set_ylabel('Price') 
    fig.suptitle('Daily Candlestick Chart of'+ ticker) 
     
    # Formatting Date 



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    date_format = mpl_dates.DateFormatter('%d-%m-%Y') 
    ax.xaxis.set_major_formatter(date_format) 
    fig.autofmt_xdate() 
     
    fig.tight_layout() 
     
    ohlc[typema] = ohlc['close'].rolling(10).mean() 
    ax.plot(ohlc_ha['date'], ohlc[typema], color=colorma, label=typema) 
     
    fig.suptitle('Daily Candlestick Chart of '+ ticker +' with '+typema) 
     
    plt.legend() 
     
    plt.show() 
     
 
plot_candle_stick(data,ticker,"green","red") 
plot_candle_stick(ha_ohlc,ticker,"blue","red")  
plot_candle_stick_ha_ma(data,ha_ohlc,ticker,"blue","red",'black', 'EMA10')  
 

 

References 

[1] Gray, Robert M. Entropy and Information Theory. Springer Science & Business Media, 

2013. 

[2] Roy Trivedi, S. Technical analysis using Heiken Ashi Stochastic: To catch a trend, use a 

HASTOC. Int J Fin Econ. 2022; 27: 1836– 1847. https://doi.org/10.1002/ijfe.2245