Calculating Parabolic SAR and Generating Position Signals
Summary
This notebook implements a recursive Parabolic SAR calculation and turns the indicator into position signals. It tracks trend direction, an extreme price, and an acceleration factor that rises in steps up to a cap. Each new SAR estimate is constrained by recent highs or lows; a crossing of price and SAR changes the trend state. The signal logic assigns a long position when SAR is below the close and no long position otherwise, then marks changes in that position. It also plots price, SAR, and signal markers.
The example downloads daily price data for EA over 2016–2018 and displays a shortened portion of the series. It does not calculate returns, compare benchmarks, or report strategy performance, so the plot is illustrative rather than evidence of profitability. The author notes that SAR’s calculation is involved and points readers to external explanations. The code uses particular initialization and acceleration settings and appears oriented to plotting signals; trading costs, execution, position sizing, and robustness across assets or periods are not addressed.
Key ideas
- The calculation advances SAR recursively using the prior SAR, an extreme price, and an acceleration factor.
- Recent highs or lows constrain the estimated SAR, and price crossing the indicator changes the trend state.
- The example maps SAR below the close to a long position and plots changes in that position.
- The EA example is visual only and reports no returns, benchmark comparison, costs, or execution assumptions.
Tags
Full text
# Parabolic SAR backtest
# Parabolic SAR backtest
## Source (Apache-2.0)
```python
# coding: utf-8
# In[1]:
#parabolic stop and reverse is very useful for trend following
#sar is an indicator below the price when its an uptrend
#and above the price when its a downtrend
#it is very painful to calculate sar, though
#and many explanations online including wiki cannot clearly explain the process
#hence, the good idea would be to read info on wikipedia
#and download an excel spreadsheet made by joeu2004
#formulas are always more straight forward than descriptions
#links are shown below
# https://en.wikipedia.org/wiki/Parabolic_SAR
# https://www.box.com/s/gbtrjuoktgyag56j6lv0
import matplotlib.pyplot as plt
import numpy as np
import fix_yahoo_finance as yf
import pandas as pd
# In[2]:
#the calculation of sar
#as rules are very complicated
#plz check the links above to understand more about it
def parabolic_sar(new):
#this is common accelerating factors for forex and commodity
#for equity, af for each step could be set to 0.01
initial_af=0.02
step_af=0.02
end_af=0.2
new['trend']=0
new['sar']=0.0
new['real sar']=0.0
new['ep']=0.0
new['af']=0.0
#initial values for recursive calculation
new['trend'][1]=1 if new['Close'][1]>new['Close'][0] else -1
new['sar'][1]=new['High'][0] if new['trend'][1]>0 else new['Low'][0]
new.at[1,'real sar']=new['sar'][1]
new['ep'][1]=new['High'][1] if new['trend'][1]>0 else new['Low'][1]
new['af'][1]=initial_af
#calculation
for i in range(2,len(new)):
temp=new['sar'][i-1]+new['af'][i-1]*(new['ep'][i-1]-new['sar'][i-1])
if new['trend'][i-1]<0:
new.at[i,'sar']=max(temp,new['High'][i-1],new['High'][i-2])
temp=1 if new['sar'][i]<new['High'][i] else new['trend'][i-1]-1
else:
new.at[i,'sar']=min(temp,new['Low'][i-1],new['Low'][i-2])
temp=-1 if new['sar'][i]>new['Low'][i] else new['trend'][i-1]+1
new.at[i,'trend']=temp
if new['trend'][i]<0:
temp=min(new['Low'][i],new['ep'][i-1]) if new['trend'][i]!=-1 else new['Low'][i]
else:
temp=max(new['High'][i],new['ep'][i-1]) if new['trend'][i]!=1 else new['High'][i]
new.at[i,'ep']=temp
if np.abs(new['trend'][i])==1:
temp=new['ep'][i-1]
new.at[i,'af']=initial_af
else:
temp=new['sar'][i]
if new['ep'][i]==new['ep'][i-1]:
new.at[i,'af']=new['af'][i-1]
else:
new.at[i,'af']=min(end_af,new['af'][i-1]+step_af)
new.at[i,'real sar']=temp
return new
# In[3]:
#generating signals
#idea is the same as macd oscillator
#check the website below to learn more
# https://github.com/je-suis-tm/quant-trading/blob/master/MACD%20oscillator%20backtest.py
def signal_generation(df,method):
new=method(df)
new['positions'],new['signals']=0,0
new['positions']=np.where(new['real sar']<new['Close'],1,0)
new['signals']=new['positions'].diff()
return new
# In[4]:
#plotting of sar and trading positions
#still similar to macd
def plot(new,ticker):
fig=plt.figure()
ax=fig.add_subplot(111)
new['Close'].plot(lw=3,label='%s'%ticker)
new['real sar'].plot(linestyle=':',label='Parabolic SAR',color='k')
ax.plot(new.loc[new['signals']==1].index,new['Close'][new['signals']==1],marker='^',color='g',label='LONG',lw=0,markersize=10)
ax.plot(new.loc[new['signals']==-1].index,new['Close'][new['signals']==-1],marker='v',color='r',label='SHORT',lw=0,markersize=10)
plt.legend()
plt.grid(True)
plt.title('Parabolic SAR')
plt.ylabel('price')
plt.show()
# In[5]:
def main():
#download data via fix yahoo finance library
stdate=('2016-01-01')
eddate=('2018-01-01')
ticker=('EA')
#slice is used for plotting
#a two year dataset with 500 variables would be too much for a figure
slicer=450
df=yf.download(ticker,start=stdate,end=eddate)
#delete adj close and volume
#as we dont need them
del df['Adj Close']
del df['Volume']
#no need to iterate over timestamp index
df.reset_index(inplace=True)
new=signal_generation(df,parabolic_sar)
#convert back to time series for plotting
#so that we get a date x axis
new.set_index(new['date'],inplace=True)
#shorten our plotting horizon and plot
new=new[slicer:]
plot(new,ticker)
#how to calculate stats could be found from my other code called Heikin-Ashi
# https://github.com/je-suis-tm/quant-trading/blob/master/heikin%20ashi%20backtest.py
# In[6]:
if __name__ == '__main__':
main()
```Shown in full with attribution under the source's licence. Licence: Apache-2.0
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.