title: Incorrect change point detection by FB Prophet
body: <p>I have a time series data as follows:</p>
  <pre><code>
             ds      y
  0  2016-10-31   2000
  1  2016-11-30   3000
  2  2016-12-31   5000
  3  2017-01-31   5000
  4  2017-02-28   4000
  5  2017-03-31   4500
  6  2017-04-30  10000
  7  2017-05-31   6500
  8  2017-06-30   3500
  9  2017-07-31   5500
  10 2017-08-31   2000
  11 2017-09-30   3000
  12 2017-10-31  10000
  13 2017-11-30   5000
  14 2017-12-31   4000
  15 2018-01-31   4500
  16 2018-02-28   5000
  17 2018-03-31   6500
  18 2018-04-30   3500
  19 2018-05-31   5500
  20 2018-06-30   2000
  21 2018-07-31   3000
  22 2018-08-31  10000
  23 2018-09-30   5000
  24 2018-10-31   4000
  25 2018-11-30   4500
  26 2018-12-31   5000
  27 2019-01-31   6500
  28 2019-02-28   3500
  29 2019-03-31   5500
  </code></pre>
  <p>I have applied FB Prophet change point detection algorithm to extract changepoints.</p>
  <p>When I specify 5 changepoints in the code, I get the following changepoints:</p>
  <pre><code>5    2017-03-31
  9    2017-07-31
  14   2017-12-31
  18   2018-04-30
  23   2018-09-30
  </code></pre>
  <p>When I specify 7 changepoints in the code, I get the following changepoints:</p>
  <pre><code>3    2017-01-31
  7    2017-05-31
  10   2017-08-31
  13   2017-11-30
  16   2018-02-28
  20   2018-06-30
  23   2018-09-30
  </code></pre>
  <p>Why the algorithm does not detect point 6, 12, 22 where there is maximum change in the value as compared to the previous point?</p>
  <p>My code below:</p>
  <pre><code>from fbprophet import Prophet
  import pandas as pd
  import matplotlib.pyplot as plt
  
  
  m = Prophet(growth='linear', n_changepoints = 7, changepoint_range=0.8, changepoint_prior_scale=0.5)
  m.fit(df)
  
  future = m.make_future_dataframe(freq = 'M', periods=3)
  fcst = m.predict(future)
  
  from fbprophet.plot import add_changepoints_to_plot
  fig = m.plot(fcst)
  a = add_changepoints_to_plot(fig.gca(), m, fcst)
  
  m.changepoints
  </code></pre>