text: Title: Python does not seem to correctly report fitted values in statmodels ARIMA when differencing is involved
  Body: When fitting an ARIMA model using the statsmodels python implementation I see the following behaviour, python does not seem to correctly provide the values for the differenced lags. I am comparing the results with the ones obtained using the R ARIMA implementation.
  
  ```python
  import pandas as pd
  
  df=pd.read_csv('ffp2\datasets\euretail.csv')
  df.index=pd.date_range(start=df['index'].str[:4].min(),freq='1Q',periods=df.shape[0])
  df=df['value']
  
  from statsmodels.tsa.arima.model import ARIMA
  model=ARIMA(df, order=(0,1,1), seasonal_order=(0,1,1,4)).fit()
  pd.concat((df,model.fittedvalues, model.resid), axis=1).rename(columns={0:'py_fit',1:'py_resid'}).head(10)
  ```
  <details>
  
  Scenario:
  - Seasonal non-stationary data which requires
  - Single differencing
  - Seasonal first differencing of period 4
  - We end up with a ARIMA(0,1,1)(0,1,1,4) model
  
  Please note the issue occurs when using the python ARIMA implementation when importing from `statsmodels.tsa.arima.model import ARIMA` I've seen webtutorials where it seems to function correctly but they seem to be using the previous implementation `from statsmodels.tsa.arima_model import ARIMA`, this implementation seems to currently be deprecated https://github.com/statsmodels/statsmodels/issues/3884
  
  Python fitted model below (for reference)
  ```
                                      SARIMAX Results                                    
  =======================================================================================
  Dep. Variable:                           value   No. Observations:                   64
  Model:             ARIMA(0, 1, 1)x(0, 1, 1, 4)   Log Likelihood                 -34.642
  Date:                         Thu, 01 Dec 2022   AIC                             75.285
  Time:                                 14:09:56   BIC                             81.517
  Sample:                             03-31-1996   HQIC                            77.718
                                    - 12-31-2011                                         
  Covariance Type:                           opg                                         
  ==============================================================================
                   coef    std err          z      P>|z|      [0.025      0.975]
  ------------------------------------------------------------------------------
  ma.L1          0.2903      0.155      1.872      0.061      -0.014       0.594
  ma.S.L4       -0.6912      0.132     -5.250      0.000      -0.949      -0.433
  sigma2         0.1810      0.034      5.316      0.000       0.114       0.248
  ===================================================================================
  Ljung-Box (L1) (Q):                   0.25   Jarque-Bera (JB):                 1.91
  Prob(Q):                              0.62   Prob(JB):                         0.38
  Heteroskedasticity (H):               0.76   Skew:                            -0.22
  Prob(H) (two-sided):                  0.54   Kurtosis:                         3.77
  ===================================================================================
  
  Warnings:
  [1] Covariance matrix calculated using the outer product of gradients (complex-step).
  ```
  
  R model code for reference below
  ```r
  chooseCRANmirror(graphics=FALSE, ind=70)
  # # Install if needed
  # install.packages("fpp2")
  # install.packages("readr")
  # install.packages("tsibble")
  library("fpp2")
  library("readr")
  library("tsibble")
  
  fit <- Arima(euretail, order=c(0,1,1), seasonal=c(0,1,1))
  fitted(fit)
  resid(fit)
  ```
  
  
  </details>
  
  #### Expected Output
  
  I would expect R and Python implementations to provide much closer results, it seems as if the Python implementation might have a bug
  
  ```
              value      py_fit   py_resid      r_fit   r_resid
  1996-03-31  89.13    0.000000  89.130000  89.078541  0.051459 <---- (Issue Here)
  1996-06-30  89.52   89.130003   0.389997  89.496685  0.023315
  1996-09-30  89.88   89.520000   0.360000  89.864432  0.015568
  1996-12-31  90.12   89.879998   0.240002  90.143352 -0.023352
  1997-03-31  89.19  134.685000 -45.495000  89.380354 -0.190354 <---- (Issue Here)
  1997-06-30  89.78   89.579993   0.200007  89.621984  0.158016
  1997-09-30  90.03   90.193547  -0.163547  90.164354 -0.134354
  1997-12-31  90.38   90.222837   0.157163  90.251028  0.128972
  1998-03-31  90.27   89.463010   0.806990  89.602346  0.667654
  1998-06-30  90.77   90.951737  -0.181737  90.937687 -0.167687
  1998-09-30  91.85   91.019609   0.830391  91.077857  0.772143
  1998-12-31  92.51   92.389250   0.120750  92.397782  0.112218
  1999-03-31  92.21   92.044928   0.165072  92.056141  0.153859
  1999-06-30  92.52   92.752252  -0.232252  92.744481 -0.224481
  1999-09-30  93.62   93.066856   0.553144  93.083940  0.536060
  ```
  Dataset
  [euretail.csv](https://github.com/statsmodels/statsmodels/files/10134041/euretail.csv)
  
  #### Output of ``import statsmodels.api as sm; sm.show_versions()``
  
  <details>
  
  
  
  INSTALLED VERSIONS
  ------------------
  Python: 3.9.6.final.0
  
  statsmodels
  ===========
  
  Installed: 0.13.5 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\statsmodels)
  
  Required Dependencies
  =====================
  
  cython: Not installed
  numpy: 1.21.4 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\numpy)
  scipy: 1.7.3 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\scipy)
  pandas: 1.3.5 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\pandas)
      dateutil: 2.8.2 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\dateutil)
  patsy: 0.5.2 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\patsy)
  
  Optional Dependencies
  =====================
  
  matplotlib: 3.5.1 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\matplotlib)
      backend: module://matplotlib_inline.backend_inline 
  cvxopt: Not installed
  joblib: 1.1.0 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\joblib)
  
  Developer Tools
  ================
  
  IPython: 7.30.1 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\IPython)
      jinja2: Not installed
  sphinx: Not installed
      pygments: 2.10.0 (c:\Users\alber\Documents\forecasting-principles-and-practice\venv\lib\site-packages\pygments)
  pytest: Not installed
  virtualenv: Not installed
  
  </details>
  