Cross-correlation part 1

cross_corr1.py

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# Generate two series that are correlated
original_x = pd.Series(np.random.uniform(size=100))
original_y = 1.3*original_x + np.random.normal(0, 0.1, size=100)

# Now create shifted versions,
# I create two examples, one where x is shifted
# and one where y is.
shifted_versions = [
    (original_x.iloc[10:].reset_index(drop=True), original_y),
    (original_x, original_y.iloc[20:].reset_index(drop=True)),
]

# Function to calculate correlation
def correlation(x, y):
    shortest = min(x.shape[0], y.shape[0])
    return np.corrcoef(x.iloc[:shortest].values, y.iloc[:shortest].values)[0, 1]

# Function to plot time series and show the correlation
def plot_correlation(x, y, text):
    # plot 
    plt.subplots(figsize=(10, 6))
    x.plot(label="x")
    y.plot(label="y")
    plt.title(f"Correlation {text}: {correlation(x, y)}")
    plt.legend(loc="best")
    plt.show()

# Show results without shifting
for x, y in shifted_versions:
    plot_correlation(x, y, "before shifting")