https://www.quantopian.com/lectures/linear-correlation-analysis
This lecture corresponds to the Linear Correlation Analysis lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.
Part of the Quantopian Lecture Series:
In [1]:
# Useful Functions
def find_most_correlated(data):
n = data.shape[1]
keys = data.keys()
pair = []
max_value = 0
for i in range(n):
for j in range(i+1, n):
S1 = data[keys[i]]
S2 = data[keys[j]]
result = np.corrcoef(S1, S2)[0,1]
if result > max_value:
pair = (keys[i], keys[j])
max_value = result
return pair, max_value
In [2]:
# Useful Libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
In [3]:
A = np.random.rand(100)
B = -3 * A + np.random.exponential(0.05, 100)
#Your code goes here
covm = np.cov(A, B)
corrm = np.corrcoef(A, B)
print 'Covariance matrix: \n' + str(covm) + '\n'
print 'Correlation matrix: \n' + str(corrm) + '\n'
print 'Variance of A: ' + str(covm[0,0])
print 'Variance of B: ' + str(covm[1,1]) + '\n'
print 'Covariance of A and B: ' + str(covm[1,0])
print 'Correlation of A and B: ' + str(corrm[1,0])
In [4]:
C = np.random.rand(100)
D = np.random.normal(0, 0.5, 100)
#Your code goes here
covm = np.cov(C, D)
corrm = np.corrcoef(C, D)
print 'Covariance matrix: \n' + str(covm) + '\n'
print 'Correlation matrix: \n' + str(corrm) + '\n'
print 'Variance of C: ' + str(covm[0,0])
print 'Variance of D: ' + str(covm[1,1]) + '\n'
print 'Covariance of C and D: ' + str(covm[1,0])
print 'Correlation of C and D: ' + str(corrm[1,0])
In [5]:
X = np.random.rand(100)
#Your code goes here
Y = 2*X + np.random.normal(0, 0.1, 100)
plt.scatter(X,Y)
plt.xlabel('X Value')
plt.ylabel('Y Value')
print 'Correlation of X and Y: ' + str(np.corrcoef(X, Y)[0,1])
In [6]:
Z = np.random.rand(100)
#Your code goes here
W = -4*Z + np.random.normal(0, 10, 100)
plt.scatter(Z,W)
plt.xlabel('Z Value')
plt.ylabel('W Value')
print 'Correlation of Z and W: ' + str(np.corrcoef(Z, W)[0,1])
In [7]:
OKE = get_pricing('OKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')
LAKE = get_pricing('LAKE', fields='price', start_date='2013-01-01', end_date='2015-01-01')
benchmark = get_pricing('SPY', fields='price', start_date='2013-01-01', end_date='2015-01-01')
#Your code goes here
print "Correlation coefficient of OKE and LAKE: ", np.corrcoef(OKE, LAKE)[0,1]
print "Correlation coefficient of OKE and benchmark: ", np.corrcoef(OKE, benchmark)[0,1]
print "Correlation coefficient of LAKE and benchmark: ", np.corrcoef(LAKE, benchmark)[0,1]
In [8]:
symbol_list = ['GSK', 'SNOW', 'FB', 'AZO', 'XEC', 'AMZN']
data = get_pricing(symbol_list, fields=['price']
, start_date='2015-01-01', end_date='2016-01-01')['price']
data.columns = symbol_list
#Your code goes here
find_most_correlated(data)
Out[8]:
In [9]:
FB_15 = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2016-01-01')
AMZN_15 = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2016-01-01')
FB_16 = get_pricing('FB', fields='price', start_date='2016-01-01', end_date='2016-07-01')
AMZN_16 = get_pricing('AMZN', fields='price', start_date='2016-01-01', end_date='2016-07-01')
#Your code goes here
print "2015 correlation coefficient: ", np.corrcoef(FB_15, AMZN_15)[0,1]
print "2016 correlation coefficient: ", np.corrcoef(FB_16, AMZN_16)[0,1]
print "The strong correlation from 2015 did not hold outside of the 2015 pricing sample."
In [10]:
FB = get_pricing('FB', fields='price', start_date='2015-01-01', end_date='2017-01-01')
AMZN = get_pricing('AMZN', fields='price', start_date='2015-01-01', end_date='2017-01-01')
#Your code goes here
rolling_correlation = FB.rolling(window=60).corr(AMZN)
plt.plot(rolling_correlation)
plt.xlabel('Day')
plt.ylabel('60-day Rolling Correlation')
print "Upon further investigation, FB and AMZN do not consistently have the strong correlation suggested by our result from question 3b."
Congratulations on completing the Linear Correlation Analysis exercises!
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