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Cross-correlation part 1
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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") |
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