Identify and Trade Cointegrated Pairs

				
					import warnings
warnings.filterwarnings('ignore')  # Ignore warnings for cleaner output
import yfinance as yf
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.api import VECM
from statsmodels.tsa.stattools import adfuller

# Check for stationarity of individual series using ADF test
adf_result1 = adfuller(aligned_data[ticker1])
adf_result2 = adfuller(aligned_data[ticker2])
# The adfuller function performs the Augmented Dickey-Fuller test
# It tests for a unit root in the time series and returns the test statistic and p-value

# Step 1: Perform Johansen cointegration test
from statsmodels.tsa.vector_ar.vecm import coint_johansen

def johansen_test(data, det_order=0, k_ar_diff=1):
    result = coint_johansen(data, det_order, k_ar_diff)
    return result.lr1, result.cvt
# The johansen_test function performs the Johansen cointegration test
# It returns the test statistics and critical values for cointegration

coint_test_stat, coint_critical_values = johansen_test(aligned_data)
# Apply the Johansen test on the aligned data to check for cointegration

# Step 2: If cointegration exists, proceed with VECM
vecm = VECM(aligned_data, k_ar_diff=1, coint_rank=1)
vecm_fit = vecm.fit()
# The VECM (Vector Error Correction Model) is fitted to the data if cointegration exists
# k_ar_diff is the number of lags and coint_rank is the cointegration rank

# Analyzing the residuals for stationarity
residuals = vecm_fit.resid
adf_residuals_1 = adfuller(residuals[:, 0])
adf_residuals_2 = adfuller(residuals[:, 1])
# The residuals from the VECM model are tested for stationarity using the ADF test

# Creating a DataFrame for residuals
residuals_df = pd.DataFrame(residuals, columns=[f'Residual_{ticker1}', f'Residual_{ticker2}'])
# Create a DataFrame to store the residuals for better visualization and analysis

# Plotting the residuals
plt.figure(figsize=(12, 6))
plt.plot(residuals_df, label=['Residual ASML.AS', 'Residual ASML'])
plt.axhline(0, color='red', linestyle='--', label='Zero Line')
plt.title('Residuals from VECM')
plt.xlabel('Date')
plt.ylabel('Residuals')
plt.legend()
plt.show()
# Plot the residuals to visualize their behavior over time
# The red line at y=0 helps identify deviations from the mean

# Print Statements to show ADF test results
print(f"ADF Statistic for {ticker1}: {adf_result1[0]}")
print(f"p-value for {ticker1}: {adf_result1[1]}")
print(f"ADF Statistic for {ticker2}: {adf_result2[0]}")
print(f"p-value for {ticker2}: {adf_result2[1]}")

# Interpretation of ADF results
if adf_result1[1] < 0.05:
    print(f"{ticker1} is stationary.")
else:
    print(f"{ticker1} is not stationary.")

if adf_result2[1] < 0.05:
    print(f"{ticker2} is stationary.")
else:
    print(f"{ticker2} is not stationary.")
# Interpretation of the ADF test results for each ticker
# A p-value less than 0.05 indicates stationarity

print(f"Cointegration Test Statistics: {coint_test_stat}")
print(f"Critical Values (90%, 95%, 99%): {coint_critical_values}")
# Print the test statistics and critical values from the Johansen cointegration test

# Summary of the VECM model (optional)
# print(vecm_fit.summary())

# Interpretation of Johansen test results
if coint_test_stat[0] > coint_critical_values[0, 1]:
    print(f"The two stocks {ticker1} and {ticker2} are cointegrated.")
else:
    print(f"The two stocks {ticker1} and {ticker2} are not cointegrated.")
# Check if the test statistic is greater than the critical value at the 95% confidence level
# If so, the stocks are cointegrated

print(f"ADF Statistic for VECM residuals of {ticker1}: {adf_residuals_1[0]}")
print(f"p-value for VECM residuals of {ticker1}: {adf_residuals_1[1]}")
print(f"ADF Statistic for VECM residuals of {ticker2}: {adf_residuals_2[0]}")
print(f"p-value for VECM residuals of {ticker2}: {adf_residuals_2[1]}")
# Print the ADF test results for the residuals from the VECM model

# Interpretation of VECM residuals
if adf_residuals_1[1] < 0.1:
    print(f"The residuals of the VECM model for {ticker1} are stationary, confirming cointegration.")
else:
    print(f"The residuals of the VECM model for {ticker1} are not stationary, suggesting no cointegration.")

if adf_residuals_2[1] < 0.1:
    print(f"The residuals of the VECM model for {ticker2} are stationary, confirming cointegration.")
else:
    print(f"The residuals of the VECM model for {ticker2} are not stationary, suggesting no cointegration.")
# Interpretation of the stationarity of the residuals from the VECM model
# A p-value less than 0.1 indicates stationarity, confirming cointegration

# Creating a table for Johansen test results
johansen_results = pd.DataFrame({
    'Test Statistic': coint_test_stat,
    '90% Critical Value': coint_critical_values[:, 0],
    '95% Critical Value': coint_critical_values[:, 1],
    '99% Critical Value': coint_critical_values[:, 2]
}, index=[f'Cointegration Test {i+1}' for i in range(len(coint_test_stat))])

print("\nJohansen Cointegration Test Results:\n")
print(johansen_results)
# Create a DataFrame to neatly display the Johansen test results with their critical values

# Comprehensive Interpretation

# ADF Test Results
print("\nADF Test Results Interpretation:")
if adf_result1[1] < 0.05:
    print(f"{ticker1} is stationary, indicating the series does not have a unit root.")
else:
    print(f"{ticker1} is not stationary, indicating the series has a unit root.")

if adf_result2[1] < 0.05:
    print(f"{ticker2} is stationary, indicating the series does not have a unit root.")
else:
    print(f"{ticker2} is not stationary, indicating the series has a unit root.")
# Detailed interpretation of the ADF test results for each ticker

# Johansen Cointegration Test Results
print("\nJohansen Cointegration Test Results Interpretation:")
if coint_test_stat[0] > coint_critical_values[0, 1]:
    print(f"The two stocks {ticker1} and {ticker2} are cointegrated at the 95% confidence level.")
else:
    print(f"The two stocks {ticker1} and {ticker2} are not cointegrated at the 95% confidence level.")
# Detailed interpretation of the Johansen test results

# VECM Residuals Stationarity Test Results
print("\nVECM Residuals Stationarity Test Results Interpretation:")
if adf_residuals_1[1] < 0.1:
    print(f"The residuals of the VECM model for {ticker1} are stationary, confirming cointegration.")
else:
    print(f"The residuals of the VECM model for {ticker1} are not stationary, suggesting no cointegration.")

if adf_residuals_2[1] < 0.1:
    print(f"The residuals of the VECM model for {ticker2} are stationary, confirming cointegration.")
else:
    print(f"The residuals of the VECM model for {ticker2} are not stationary, suggesting no cointegration.")
# Detailed interpretation of the VECM residuals' stationarity test results