How to find (and select) a specific point of a graph in Python

Question

The code below computes the autocorrelation using plt.acorr for a time-series. My aim is to find the first value (vertical bar) on the x-axis where the graph of the autocorrelation goes below 1/e (= 0.3679).

In the example shown below (see image), the x-axis value the code had to select would be the very first vertical bar located on the x-axis at x=1 (or at x=-1), since the graph of the autocorrelation passes below 1/e here.

In other words, the code would have to select the value 1 (the negative counterpart -1 is not needed).

What would be an appropriate way to code this?

import numpy as np
import matplotlib.pyplot as plt

Timeseries = [-0.213399, 0.383858, 0.162265, 0.393239, 0.018605, 
              -0.241237, 0.0230115, 0.226046, 0.137763, -0.0818484, 0.0341396,
              -0.460055, -0.201813, 0.0728111, -0.259836, -0.0302774, 0.125858]

Threshold = 0.367879441171
plt.axhline(y=Threshold, color='r', linestyle='-')
    
# Autocorrelation (AC)
plt.acorr(x=Timeseries, maxlags=4, normed=True, color="blue", lw=1.5)
plt.title("Autocorrelation")
plt.show()

Answer 1

plt.acorr can return the resulting AC like so:

lags, c, line, b = plt.acorr(x=Timeseries, maxlags=4, normed=True, color="blue", lw=1.5)

Hence, you can do:

indices_below = np.where(c < 1/np.exp(1))[0]
index_zero = np.where(lags == 0)[0]

first_point = lags[np.argmin(np.abs(indices_below - index_zero))] # = -1

The above returns -1 because it is the "first" from left to right between -1 and +1, but you could just flip the arrays or add another condition if you really want to get 1.