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1.Some ARIMA models do not require a constant term.  What determines the need for it? 

      


      


      


      

 

2.

A data series required one seasonal difference and two non seasonal differences to make it stationary.  You have found two early spikes in the PACF after the non seasonal differences with converging ACFs.  In addition, you found one early spike in the ACF for the seasonal differenced data along with converging PACFs.    Which is the appropriate ARIMA menu for the model given the non seasonal and seasonal menu form (p, d, q)(P, D, Q) . (Points : 4)

      
      
      
      

 

 

3.

 
Problem 15 Data 
  
    Q1152
    Q2262
    Q3273
    Q4250
    Q1137
    Q2225
    Q3258
    Q4262
    Q1143
    Q2246
    Q3299
    Q4287
    Q1169
    Q2223
    Q3394
    Q4144
What is the first seasonal difference value of the data series?

      
      
      
      
      

 

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SkyWest Airlines 
DateSales Rev.
3/31/199549.528
6/30/199560.381
9/29/199569.175
12/29/199558.991
3/29/199656.973
6/28/199670.569
9/30/199675.8
12/31/199663.651
3/31/199768.09
6/30/199772.115
9/30/199780.302
12/31/199766.975
3/31/199867.025
6/30/199881.959
9/30/1998113.473
12/31/1998102.255
3/31/199981.215
6/30/1999123.098
9/30/1999122.737
12/31/1999138.631
3/31/2000130.881
6/30/2000131.194
9/29/2000149.664
12/31/2000111.258
3/31/2001150.943
6/30/2001129.918
9/28/2001155.54
12/31/2001165.467
3/29/2002174.346
6/28/2002187.396
9/30/2002202.713
12/31/2002208.155
3/31/2003207.362
6/30/2003212.694
9/30/2003230.49
12/31/2003237.48
3/31/2004253.704
6/30/2004267.387
9/30/2004308.265
12/31/2004326.688
3/31/2005340.292
6/30/2005384.043
9/30/2005497.349
12/30/2005742.364
3/31/2006742.855
6/30/2006790.404
9/29/2006791.841
12/29/2006789.556
3/30/2007788.968
6/29/2007855.048
9/28/2007875.601
12/31/2007854.715
3/31/2008868.023
6/30/2008950.82
9/30/2008934.112
12/31/2008743.294
3/31/2009672.642
6/30/2009698.823
9/30/2009637.748
12/31/2009604.401
3/31/2010632.243
6/30/2010649.759
9/30/2010686.858
12/31/2010796.284
3/31/2011865.951
6/30/2011933.697
9/30/2011955.425
12/30/2011899.85
3/30/2012921.173
6/29/2012937.214
9/28/2012865.259
12/31/2012810.725
3/29/2013803.487
6/28/2013839.13
9/30/2013850.74
12/31/2013804.368

 

4.Given the quarterly data for SkyWest Airline determine the best ARIMA model that applies in (p, d, q)(P, D, Q) form.  I will accept an ARIMA model with insignificant coefficients or non significant residuals.  Also, remember to apply the rule of parsimony. (Points : 4)

      
      
      
      
      

 

5.

Select the coefficient(s) that match the best ARIMA model that you developed in problem 17. (Points : 4)

      
      
      
      

 

6.What are the fit period RMSE and MAPE for the best ARIMA model for the data in problem 17? (Points : 4)

      
      
      
      

 

7.

 Develop an 8 quarter forecast with the best ARIMA model you developed in problem 17.  What do you note about the forecast? (Points : 4)

      
      
      
      

 

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