This is the code:
import numpy as np
import pandas as pd
import statsmodels
from statsmodels.tsa.stattools import coint
# just set the seed for the random number generator
np.random.seed(107)
import matplotlib.pyplot as plt
Generate a fake security X and model it’s daily returns by drawing from a normal distribution. Then perform a cumulative sum to get the value of X on each day.
# Generate daily returns
Xreturns = np.random.normal(0, 1, 100)
# sum them and shift all the prices up
X = pd.Series(np.cumsum(
Xreturns), name='X') + 50
X.plot(figsize=(15,7))
plt.show()
Generate Y which has deep economic link to X, so price of Y should vary pretty similarly as X.
noise = np.random.normal(0, 1, 100)
Y = X + 5 + noise
Y.name = 'Y'
pd.concat([X, Y], axis=1).plot(figsize=(15,7))
plt.show()
Plot the ratio between the two:
(Y/X).plot(figsize=(15,7))
plt.axhline((Y/X).mean(), color='red', linestyle='--')
plt.xlabel('Time')
plt.legend(['Price Ratio', 'Mean'])
plt.show()
# compute the p-value of the cointegration test
# will inform us as to whether the ratio between the 2 timeseries is stationary
# around its mean
score, pvalue, _ = coint(X,Y)
print (pvalue)
ret1 = np.random.normal(1, 1, 100)
ret2 = np.random.normal(2, 1, 100)
s1 = pd.Series( np.cumsum(ret1), name='X')
s2 = pd.Series( np.cumsum(ret2), name='Y')
pd.concat([s1, s2], axis=1 ).plot(figsize=(15,7))
plt.show()
print 'Correlation: ' + str(X_diverging.corr(Y_diverging))
score, pvalue, _ = coint(X_diverging,Y_diverging)
print 'Cointegration test p-value: ' + str(pvalue)
Error Message: File "", line 9 print 'Correlation: ' + str(X_diverging.corr(Y_diverging)) SyntaxError: invalid syntax
Y2 = pd.Series(np.random.normal(0, 1, 800), name='Y2') + 20
Y3 = Y2.copy()
Y3[0:100] = 30
Y3[100:200] = 10
Y3[200:300] = 30
Y3[300:400] = 10
Y3[400:500] = 30
Y3[500:600] = 10
Y3[600:700] = 30
Y3[700:800] = 10
Y2.plot(figsize=(15,7))
Y3.plot()
plt.ylim([0, 40])
plt.show()
# correlation is nearly zero
print 'Correlation: ' + str(Y2.corr(Y3))
score, pvalue, _ = coint(Y2,Y3)
print 'Cointegration test p-value: ' + str(pvalue)
Error message:File "", line 14 print 'Correlation: ' + str(Y2.corr(Y3)) SyntaxError: invalid syntax
def find_cointegrated_pairs(data):
n = data.shape[1]
score_matrix = np.zeros((n, n))
pvalue_matrix = np.ones((n, n))
keys = data.keys()
pairs = []
for i in range(n):
for j in range(i+1, n):
S1 = data[keys[i]]
S2 = data[keys[j]]
result = coint(S1, S2)
score = result[0]
pvalue = result[1]
score_matrix[i, j] = score
pvalue_matrix[i, j] = pvalue
if pvalue < 0.02:
pairs.append((keys[i], keys[j]))
return score_matrix, pvalue_matrix, pairs
pip install auquan-toolbox and execute following code snippet:
from backtester.dataSource.yahoo_data_source import YahooStockDataSource
from datetime import datetime
startDateStr = '2007/12/01'
endDateStr = '2017/12/01'
cachedFolderName = 'yahooData/'
dataSetId = 'testPairsTrading'
instrumentIds = ['SPY','AAPL','ADBE','SYMC','EBAY','MSFT','QCOM',
'HPQ','JNPR','AMD','IBM']
ds = YahooStockDataSource(cachedFolderName=cachedFolderName,
dataSetId=dataSetId,
instrumentIds=instrumentIds,
startDateStr=startDateStr,
endDateStr=endDateStr,
event='history')
data = ds.getBookDataByFeature()['Adj Close']
data.head(3)
Error message:File "C:\ProgramData\Anaconda3\lib\site-packages\backtester\dataSource\data_source_utils.py", line 25, in getCookieForYahoo return cookie, crumb # return a tuple of crumb and cookie
UnboundLocalError: local variable 'crumb' referenced before assignment
Complete article with code can be found here.
Any help is much appreciated. Thank you.
