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)), , x) axis.axhline() return axis fig, axis = plt.subplots(2) axis.plot(a, label='original') axis.plot(b, label='b') axis.plot(c, label='c') axis.legend() plot_autocorr(d, axis=axis, plot_marker=False) # this function is not given for brevity plt.show()
How does the correlation between these two time series increase with time?