title: python statsmodels: Help using ARIMA model for time series
body: <p>ARIMA from statsmodels is giving me inaccurate answers for my output. I was wondering whether someone could help me understand what's wrong with my code.</p>
  
  <p>This is a sample:</p>
  
  <pre><code>import pandas as pd
  import numpy as np
  import datetime as dt
  from statsmodels.tsa.arima_model import ARIMA
  
  # Setting up a data frame that looks twenty days into the past,
  # and has linear data, from approximately 1 through 20
  counts = np.arange(1, 21) + 0.2 * (np.random.random(size=(20,)) - 0.5)
  start = dt.datetime.strptime("1 Nov 01", "%d %b %y")
  daterange = pd.date_range(start, periods=20)
  table = {"count": counts, "date": daterange}
  data = pd.DataFrame(table)
  data.set_index("date", inplace=True)
  
  print data
  
                 count
  date
  2001-11-01   0.998543
  2001-11-02   1.914526
  2001-11-03   3.057407
  2001-11-04   4.044301
  2001-11-05   4.952441
  2001-11-06   6.002932
  2001-11-07   6.930134
  2001-11-08   8.011137
  2001-11-09   9.040393
  2001-11-10  10.097007
  2001-11-11  11.063742
  2001-11-12  12.051951
  2001-11-13  13.062637
  2001-11-14  14.086016
  2001-11-15  15.096826
  2001-11-16  15.944886
  2001-11-17  17.027107
  2001-11-18  17.930240
  2001-11-19  18.984202
  2001-11-20  19.971603
  </code></pre>
  
  <p>The rest of the code sets up the ARIMA model. </p>
  
  <pre><code># Setting up ARIMA model
  order = (2, 1, 2)
  model = ARIMA(data, order, freq='D')
  model = model.fit()
  print model.predict(1, 20)
  
  2001-11-02    1.006694
  2001-11-03    1.056678
  2001-11-04    1.116292
  2001-11-05    1.049992
  2001-11-06    0.869610
  2001-11-07    1.016006
  2001-11-08    1.110689
  2001-11-09    0.945190
  2001-11-10    0.882679
  2001-11-11    1.139272
  2001-11-12    1.094019
  2001-11-13    0.918182
  2001-11-14    1.027932
  2001-11-15    1.041074
  2001-11-16    0.898727
  2001-11-17    1.078199
  2001-11-18    1.027331
  2001-11-19    0.978840
  2001-11-20    0.943520
  2001-11-21    1.040227
  Freq: D, dtype: float64
  </code></pre>
  
  <p>As you could see, the data is just constant around <code>1</code> instead of increasing. What am I doing wrong here?</p>
  
  <p>(On a side note, I can't pass in string dates like <code>"2001-11-21"</code> into the predict function for some reason. It would be helpful to know why.)</p>