# Useful Functions
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

# Useful Libraries
import numpy as np
import pandas as pd

import statsmodels
import statsmodels.api as sm
from statsmodels.tsa.stattools import coint, adfuller
from quantopian.research.experimental import history, continuous_future
# just set the seed for the random number generator
np.random.seed(107)

import matplotlib.pyplot as plt

"""
Explanation: Exercises: Mean Reversion on Futures
By Chris Fenaroli, Delaney Mackenzie, and Maxwell Margenot
Lecture Link
https://www.quantopian.com/lectures/introduction-to-pairs-trading
https://www.quantopian.com/lectures/mean-reversion-on-futures
IMPORTANT NOTE:
This lecture corresponds to the Mean Reversion on Futures 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:

www.quantopian.com/lectures
github.com/quantopian/research_public


Key concepts
End of explanation
"""


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

"""
Explanation: Exercise 1: Testing Artificial Examples
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.
a. Cointegration Test I
Determine whether the following two artificial series $A$ and $B$ are cointegrated using the coint() function and a reasonable confidence level.
End of explanation
"""


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

"""
Explanation: b. Cointegration Test II
Determine whether the following two artificial series $C$ and $D$ are cointegrated using the coint() function and a reasonable confidence level.
End of explanation
"""


cn = continuous_future('CN', offset = 0, roll = 'calendar', adjustment = 'mul')
sb = continuous_future('SB', offset = 0, roll = 'calendar', adjustment = 'mul')

cn_price = history(cn, 'price', '2015-01-01', '2016-01-01', 'daily')
sb_price = history(sb, 'price', '2015-01-01', '2016-01-01', 'daily')

#Your code goes here

"""
Explanation: Exercise 2: Testing Real Examples
a. Real Cointegration Test I
Determine whether the following two assets CN and SB were cointegrated during 2015 using the coint() function and a reasonable confidence level.
End of explanation
"""


cl = continuous_future('CL', offset = 0, roll = 'calendar', adjustment = 'mul')
ho = continuous_future('HO', offset = 0, roll = 'calendar', adjustment = 'mul')

cl_price = history(cl, 'price', '2015-01-01', '2016-01-01', 'daily')
ho_price = history(ho, 'price', '2015-01-01', '2016-01-01', 'daily')

#Your code goes here

"""
Explanation: b. Real Cointegration Test II
Determine whether the following two underlyings CL and HO were cointegrated during 2015 using the coint() function and a reasonable confidence level.
End of explanation
"""



#Your code goes here

"""
Explanation: Exercise 3: Out of Sample Validation
a. Calculating the Spread
Using pricing data from 2015, construct a linear regression to find a coefficient for the linear combination of CL and HO that makes their spread stationary.
End of explanation
"""


cl_out = get_pricing(cl, fields='price', 
                        start_date='2016-01-01', end_date='2016-07-01')
ho_out = get_pricing(ho, fields='price', 
                        start_date='2016-01-01', end_date='2016-07-01')

#Your code goes here

"""
Explanation: b. Testing the Coefficient
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.
End of explanation
"""


# Your code goes here

"""
Explanation: Extra Credit Exercise: Hurst Exponent
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:

https://en.wikipedia.org/wiki/Hurst_exponent
https://www.quantopian.com/posts/pair-trade-with-cointegration-and-mean-reversion-tests
End of explanation
"""


