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Bollinger Bands

Bollinger Bands shows the levels of different highs and lows that a security price has reached in a particular duration.

Prequisites

  • python 3.6
  • pandas
  • numpy
  • math
  • matplotlib

What is Bollinger Band

Bollinger Bands encapsulate the price movement of a stock. It provides relative boundaries of highs and lows. The crux of the Bollinger Band indicator is based on a moving average that defines the intermediate-term "trend" based on the time frame you are viewing.

This trend indicator is known as the middle band. Most stock charting applications use a 20-period moving average for the default Bollinger Bands settings. The upper and lower bands are then a measure of volatility to the upside and downside. They are calculated as two standard deviations from the middle band.

How it Works

Bollinger Bands are volatility bands placed above and below a moving average. Volatility is based on the standard deviation, which changes as volatility increases and decreases. The bands automatically widen when volatility increases and narrow when volatility decreases. This dynamic nature of Bollinger Bands also means they can be used on different securities with the standard settings. For signals, Bollinger Bands can be used to identify M-Tops and W-Bottoms or to determine the strength of the trend. When the markets become more volatile, the bands widen; during less volatile periods, the bands contract.

Mathematical Description

Bollinger Bands indicator is calculated in three steps:

  • Calculate the Middle Band according to the SMA formula

20 days are default period for bollinger band.

  • Calculate the Standard Deviation

n is the period for finding standard deviation here it is 20.

  • Calculate Upper and Lower Band

Upper Band

Lower Band

Implementing Bollinger Bands

Importing Data

#Importing important libraries
import pandas as pd
import numpy as np
import math
from matplotlib import pyplot as plt
df = pd.read_csv('Put Your CSV File Here!!!')
# converting from UNIX timestamp to normal
array_date = np.array(df['date'])
array_close = np.array(df['close'])
array_open = np.array(df['open'])
array_high = np.array(df['high'])
array_low = np.array(df['low'])
array_volume = np.array(df['volume'])
print("High Array size",array_high.size)
print("Low Array size",array_low.size)
print("Open Array size",array_open.size)
print("Close Array size",array_close.size)

Finding Middle Band with Bperiods

Bperiods=19 # Bperiods are 20 array start with 0 index
y=0
array_Middleband=[None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None]
for x in range(0,array_close.size-Bperiods):
	sum=0
	for j in range(0,Bperiods+1): #upto 20 periods value
		z=array_close[y]
		sum=sum+z
		y=y+1
	print(sum)
	sum=sum/20
	print(sum)
	array_Middleband.append(sum)
	y=y-(Bperiods)
print(len(array_Middleband))
print(array_Middleband)

Finding Standard Deviation

stndrd_deviation=[None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None]
y=0
z=0
# taking periods for counting SD equal Bperiods
for x in range(0,array_close.size-Bperiods):
	sum=0
	for j in range(0,Bperiods+1): #upto 20 periods value
		z=array_Middleband[x+Bperiods]
		sum=sum+((z-array_close[y])*(z-array_close[y]))
		y=y+1
	print(sum)
	sum=sum/19
	sum=math.sqrt(sum)
	print(sum)
	stndrd_deviation.append(sum)
	y=y-(Bperiods)
print(len(stndrd_deviation))
print(stndrd_deviation)

Finding Upper and Lower Bands

upper_band=[None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None]
lower_band=[None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None,None]
for x in range(Bperiods,len(stndrd_deviation)-1):
	upper_band.append(array_Middleband[x]+(2*stndrd_deviation[x]))
	lower_band.append(array_Middleband[x]-(2*stndrd_deviation[x]))
print(upper_band)
print(len(upper_band))
print(lower_band)

Output

# Visualising the result
plt.plot(array_close,color='blue',label = 'close')
plt.plot(upper_band,color='red',label = 'Upper Band')
plt.plot(lower_band,color='green',label = 'lower Band')
plt.plot(array_Middleband,color='orange',label = 'Middle Band')
df['date'] = df['date'].reset_index()
x=df['date'].index
labels = array_date[0:]
plt.xticks(x, labels, rotation = 'vertical')
plt.ylabel('Bollinger_Bands')
plt.xlabel('dates')
plt.legend()
plt.show()

References