Example7_5.py

"""
# Example 7-5
# Calculation of the Half-Life of a Mean-Reverting Time Series
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import coint
from statsmodels.api import OLS

df1 = pd.read_excel("miscFiles/GLD.xls")
df2 = pd.read_excel("miscFiles/GDX.xls")
df = pd.merge(df1, df2, on="Date", suffixes=("_GLD", "_GDX"))
df.set_index("Date", inplace=True)
df.sort_index(inplace=True)
"""
## Run cointegration (Engle-Granger) test
"""
coint_t, pvalue, crit_value = coint(df["Adj Close_GLD"], df["Adj Close_GDX"])
(
    coint_t,
    pvalue,
    crit_value,
)  # abs(t-stat) > critical value at 95%. pvalue says probability of null hypothesis (of no cointegration) is only 1.8%
"""
## Determine hedge ratio
"""
model = OLS(df["Adj Close_GLD"], df["Adj Close_GDX"])
results = model.fit()
hedgeRatio = results.params
print(hedgeRatio)
"""
##  z = GLD - hedgeRatio*GDX
"""
z = df["Adj Close_GLD"] - hedgeRatio[0] * df["Adj Close_GDX"]
plt.plot(z)
plt.show()
prevz = z.shift()
dz = z - prevz
dz = dz[
    1:,
]
prevz = prevz[
    1:,
]
model2 = OLS(dz, prevz - np.mean(prevz))
results2 = model2.fit()
theta = results2.params
print(theta)
halflife = -np.log(2) / theta
print(halflife)