# Undertanding cross correlation between two time series

I am trying to understand cross correlation between two time series. The time series are just sine and cos of 40 numbers between 0 to 100. When I plot the cross correlation between these two time series, the cross-correlation values increase with time as shown in figure

The python code to reproduce this figure is below


import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import ccf

a = np.linspace(0, 40, 100)
b = np.sin(a)
c = np.cos(b)
d = ccf_np(b,c)

def plot_autocorr(
x,
axis=None,
plot_marker=True
):

if not axis:
_, axis = plt.subplots()

if plot_marker:
axis.plot(x, 'o')

axis.vlines(range(len(x)), [0], x)
axis.axhline()

return axis

fig, axis = plt.subplots(2)
axis[0].plot(a, label='original')
axis[0].plot(b, label='b')
axis[0].plot(c, label='c')
axis[0].legend()
plot_autocorr(d, axis=axis[1], plot_marker=False)  # this function is not given for brevity
plt.show()


How does the correlation between these two time series increase with time?

I think you may have a typo in your code. Your time series $$c$$ is obtained by taking the cosine of your time series $$b$$ which is itself a sine transformation. I would change this and see if you obtain a more intuitive result.