By Chris Fenaroli, Delaney Mackenzie, and Maxwell Margenot
This exercise notebook refers to this lecture. Please use the lecture for explanations and sample code.
https://www.quantopian.com/lectures#Introduction-to-Pairs-Trading
Part of the Quantopian Lecture Series:
Notebook released under the Creative Commons Attribution 4.0 License.
import numpy as np
import pandas as pd
import statsmodels
import statsmodels.api as sm
from statsmodels.tsa.stattools import coint, adfuller
# just set the seed for the random number generator
np.random.seed(107)
import matplotlib.pyplot as plt
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 < 0.05:
pairs.append((keys[i], keys[j]))
return score_matrix, pvalue_matrix, pairs
We'll use some artificially generated series first as they are much cleaner and easier to work with. In general when learning or developing a new technique, use simulated data to provide a clean environment. Simulated data also allows you to control the level of noise and difficulty level for your model.
Determine whether the following two artificial series $A$ and $B$ are cointegrated using the coint() function and a reasonable confidence level.
A_returns = np.random.normal(0, 1, 100)
A = pd.Series(np.cumsum(A_returns), name='X') + 50
some_noise = np.random.exponential(1, 100)
B = A - 7 + some_noise
#Your code goes here
Determine whether the following two artificial series $C$ and $D$ are cointegrated using the coint() function and a reasonable confidence level.
C_returns = np.random.normal(1, 1, 100)
C = pd.Series(np.cumsum(C_returns), name='X') + 100
D_returns = np.random.normal(2, 1, 100)
D = pd.Series(np.cumsum(D_returns), name='X') + 100
#Your code goes here
ual = get_pricing('UAL', fields=['price'],
start_date='2015-01-01', end_date='2016-01-01')['price']
aal = get_pricing('AAL', fields=['price'],
start_date='2015-01-01', end_date='2016-01-01')['price']
#Your code goes here
Determine whether the following two assets FCAU and HMC were cointegrated during 2015 using the coint() function and a reasonable confidence level.
fcau = get_pricing('FCAU', fields=['price'],
start_date='2015-01-01', end_date='2016-01-01')['price']
hmc = get_pricing('HMC', fields=['price'],
start_date='2015-01-01', end_date='2016-01-01')['price']
#Your code goes here
Use the find_cointegrated_pairs function, defined in the "Helper Functions" section above, to find any cointegrated pairs among a set of metal and mining securities.
symbol_list = ['MTRN', 'CMP', 'TRQ', 'SCCO', 'HCLP','SPY']
prices_df = get_pricing(symbol_list, fields=['price']
, start_date='2015-01-01', end_date='2016-01-01')['price']
prices_df.columns = map(lambda x: x.symbol, prices_df.columns)
#Your code goes here
S1 = prices_df['MTRN']
S2 = prices_df['SCCO']
#Your code goes here
Use your coefficient from part a to plot the weighted spread using prices from the first half of 2016, and check whether the result is still stationary.
S1_out = get_pricing('MTRN', fields=['price'],
start_date='2016-01-01', end_date='2016-07-01')['price']
S2_out = get_pricing('SCCO', fields=['price'],
start_date='2016-01-01', end_date='2016-07-01')['price']
#Your code goes here
This exercise is more difficult and we will not provide initial structure.
The Hurst exponent is a statistic between 0 and 1 that provides information about how much a time series is trending or mean reverting. We want our spread time series to be mean reverting, so we can use the Hurst exponent to monitor whether our pair is going out of cointegration. Effectively as a means of process control to know when our pair is no longer good to trade.
Please find either an existing Python library that computes, or compute yourself, the Hurst exponent. Then plot it over time for the spread on the above pair of stocks.
These links may be helpful:
# Your code goes here
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