In order to choose two variables as a candidate for time series modeling, we are required to perform a statistical correlation analysis between the said variables. Here each variable, the Gaussian curve, and Pearson's coefficient are used to identify the correlation that exists between two variables.

In time series analysis, the autocorrelation measures historic data called lags. An autocorrelation function (ACF) is used to plot such correlations with respect to lag.  In Python the autocorrelation function is computed as follows:

import matplotlib.pyplot as plt
import numpy as np
import pandas as p
from statsmodels.graphics.tsaplots import plot_acf
data = p.Series(0.7 * np.random.rand(1000) + 0.3 * np.sin(np.linspace(-9 * np.pi, 9 * np.pi, num=1000)))
plot_acf(data)
pyplot.show()

The output for the preceding code is as follows: