# Simple shit

X = np.random.rand(50)

Y = 2 * X + np.random.normal(0, 0.1, 50)

print('Baseline covariance: %.5f' %np.cov(X, Y)[0, 1])

#

X = np.random.rand(50)

Y = 2 * X + 4

print('Covariance of X and Y: \n' + str(np.cov(X, Y)))

print('Correlation of X and Y: \n' + str(np.corrcoef(X, Y)))

#

cov_matrix = np.cov(X, Y)

# We need to manually set the degrees of freedom on X to 1, as numpy defaults to 0 for variance

# This is usually fine, but will result in a slight mismatch as np.cov defaults to 1

error = cov_matrix[0, 0] - X.var(ddof=1)

print('error: ' + str(error))

# Do a simple correlation comparison between custom, numpy as pandas

if X is None:

X = np.random.rand(50)

if Y is None:

Y = np.random.rand(50)

fig1 = plt.figure()

ax1 = fig1.add_subplot(221)

ax1.scatter(X,Y)

ax1.set_xlabel('X Value')

ax1.set_ylabel('Y Value')

# taking the relevant value from the matrix returned by np.cov

print('Correlation: ' + str(np.cov(X,Y)[0,1]/(np.std(X)*np.std(Y))))

# Let's also use the builtin correlation function

print('Built-in Correlation: ' + str(np.corrcoef(X, Y)[0, 1]))

#

X = np.random.rand(50)

Y = X + np.random.normal(0, 0.1, 50)

ax11 = fig1.add_subplot(222)

ax11.scatter(X,Y)

ax11.set_xlabel('X Value')

ax11.set_ylabel('Y Value')

print('Correlation: ' + str(np.corrcoef(X, Y)[0, 1]))

#

X = np.random.rand(50)

Y = X + np.random.normal(0, .2, 50)

ax2 = fig1.add_subplot(223)

ax2.scatter(X,Y)

ax2.set_xlabel('X Value')

ax2.set_ylabel('Y Value')

print('Correlation: ' + str(np.corrcoef(X, Y)[0, 1]))

#

X = np.random.rand(50)

Y = -X + np.random.normal(0, .1, 50)

ax3 = fig1.add_subplot(224)

ax3.scatter(X,Y)

ax3.set_xlabel('X Value')

ax3.set_ylabel('Y Value')

print('Correlation: ' + str(np.corrcoef(X, Y)[0, 1]))

plt.show()

# Pull the pricing data for our two stocks and S&P 500

start = datetime.datetime(2013, 1, 1) # '2013-01-01'

# end = '2015-01-01' # Fuck that I make my own end date

bench = pull_series(bench, start)

a1 = pull_series(sym1, start)

a2 = pull_series(sym2, start)

# Do a simple plot

fig = plt.figure()

ax1 = fig.add_subplot(211)

ax1.scatter(a1,a2)

ax1.set_xlabel(sym1)

ax1.set_ylabel(sym2)

ax1.set_title('Stock prices from %i-%i-%i to today' %(start.day,

start.month,

start.year))

print("Correlation coefficients")

print("%s and %s: %.5f" %(sym1, sym2, np.corrcoef(a1,a2)[0,1]))

print("%s and %s: %.5f" %(sym1, bench, np.corrcoef(a1,bench)[0,1]))

print("%s and %s: %.5f" %(sym2, bench, np.corrcoef(bench,a2)[0,1]))

# Get rolling correlation from pandas

rolling_correlation = pd.rolling_corr(a1, a2, 60)

ax2 = fig.add_subplot(222)

ax2.plot(rolling_correlation)

ax2.set_xlabel('Day')

ax2.set_ylabel('60-day Rolling Correlation')

# Get raw correlation

X = np.random.rand(100)

Y = X + np.random.poisson(size=100)

ax3 = fig.add_subplot(223)

ax3.scatter(X, Y)

print('X-Y correlation coefficient: %.5f' %np.corrcoef(X, Y)[0, 1])

plt.show()