title: R Arima works but Python statsmodels SARIMAX throws invertibility error
body: <p>I am comparing SARIMAX fitting results between R (3.3.1) forecast package (7.3) and Python's (3.5.2) statsmodels (0.8).</p>
  
  <p>The R-code is:</p>
  
  <pre><code>    library(forecast)
      data("AirPassengers")
      Arima(AirPassengers, order=c(2,1,1), seasonal=list(order=c(0,1,0), 
      period=12))$aic
      [1] 1017.848
  </code></pre>
  
  <p>The Python code is:</p>
  
  <pre><code>    from statsmodels.tsa.statespace import sarimax
      import pandas as pd
      AirlinePassengers = 
      pd.Series([112,118,132,129,121,135,148,148,136,119,104,118,115,126,
                141,135,125,149,170,170,158,133,114,140,145,150,178,163,                       
                172,178,199,199,184,162,146,166,171,180,193,181,183,218,
                230,242,209,191,172,194,196,196,236,235,229,243,264,272,
                237,211,180,201,204,188,235,227,234,264,302,293,259,229,
                203,229,242,233,267,269,270,315,364,347,312,274,237,278,
                284,277,317,313,318,374,413,405,355,306,271,306,315,301,
                356,348,355,422,465,467,404,347,305,336,340,318,362,348,
                363,435,491,505,404,359,310,337,360,342,406,396,420,472,
                548,559,463,407,362,405,417,391,419,461,472,535,622,606,
                508,461,390,432])
      AirlinePassengers.index = pd.DatetimeIndex(end='1960-12-31', 
                                periods=len(AirlinePassengers), freq='1M')
      print(sarimax.SARIMAX(AirlinePassengers,order=(2,1,1),
            seasonal_order=(0,1,0,12)).fit().aic)
  </code></pre>
  
  <p>Which throws an error: ValueError: Non-stationary starting autoregressive parameters found with <code>enforce_stationarity</code> set to True. </p>
  
  <p>If I set enforce_stationarity (and enforce_invertibility, which is also required) to False, the model fit works but AIC is very poor (>1400). </p>
  
  <p>Using some other model parameters for the same data, e.g., ARIMA(0,1,1)(0,0,1)[12] I can get identical results from R and Python with stationarity and invertibility checks enabled in Python. </p>
  
  <p>My main question is: What explains the difference in behavior with some model parameters? Are statsmodels' invertibility checks different from forecast's Arima and is the other somehow "more correct"?</p>
  
  <p>I also found a pull request related to fixing an invertibility calculation bug in statsmodels: <a href="https://github.com/statsmodels/statsmodels/pull/3506" rel="noreferrer">https://github.com/statsmodels/statsmodels/pull/3506</a></p>
  
  <p>After re-installing statsmodels with the latest source code from Github, I still get the same error with the code above, but setting enforce_stationarity=False and enforce_invertibility=False I get aic of around 1010 which is lower than in the R case. But model parameters are also vastly different. </p>