1.Some ARIMA models do not require a constant term. What determines the need for it?
The t-value of the coefficients.
The LBQ values versus the Chi-square table.
The trend analysis intercept value of the last differenced data series used to determine the model type.
The mean value of the residuals.
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) .
(1,0, 1)(2,2,0)
(2,2,0)(0,1,1)
(2,2,1)(2,1,0)
(1,2,0)(2,1,0)
3.
Problem 15 Data
Q1 152
Q2 262
Q3 273
Q4 250
Q1 137
Q2 225
Q3 258
Q4 262
Q1 143
Q2 246
Q3 299
Q4 287
Q1 169
Q2 223
Q3 394
Q4 144
What is the first seasonal difference value of the data series?
-143
12
-15
-23
110
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SkyWest Airlines
Date Sales Rev.
3/31/1995 49.528
6/30/1995 60.381
9/29/1995 69.175
12/29/1995 58.991
3/29/1996 56.973
6/28/1996 70.569
9/30/1996 75.8
12/31/1996 63.651
3/31/1997 68.09
6/30/1997 72.115
9/30/1997 80.302
12/31/1997 66.975
3/31/1998 67.025
6/30/1998 81.959
9/30/1998 113.473
12/31/1998 102.255
3/31/1999 81.215
6/30/1999 123.098
9/30/1999 122.737
12/31/1999 138.631
3/31/2000 130.881
6/30/2000 131.194
9/29/2000 149.664
12/31/2000 111.258
3/31/2001 150.943
6/30/2001 129.918
9/28/2001 155.54
12/31/2001 165.467
3/29/2002 174.346
6/28/2002 187.396
9/30/2002 202.713
12/31/2002 208.155
3/31/2003 207.362
6/30/2003 212.694
9/30/2003 230.49
12/31/2003 237.48
3/31/2004 253.704
6/30/2004 267.387
9/30/2004 308.265
12/31/2004 326.688
3/31/2005 340.292
6/30/2005 384.043
9/30/2005 497.349
12/30/2005 742.364
3/31/2006 742.855
6/30/2006 790.404
9/29/2006 791.841
12/29/2006 789.556
3/30/2007 788.968
6/29/2007 855.048
9/28/2007 875.601
12/31/2007 854.715
3/31/2008 868.023
6/30/2008 950.82
9/30/2008 934.112
12/31/2008 743.294
3/31/2009 672.642
6/30/2009 698.823
9/30/2009 637.748
12/31/2009 604.401
3/31/2010 632.243
6/30/2010 649.759
9/30/2010 686.858
12/31/2010 796.284
3/31/2011 865.951
6/30/2011 933.697
9/30/2011 955.425
12/30/2011 899.85
3/30/2012 921.173
6/29/2012 937.214
9/28/2012 865.259
12/31/2012 810.725
3/29/2013 803.487
6/28/2013 839.13
9/30/2013 850.74
12/31/2013 804.368
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.
(0, 1, 1) (1, 1, 0)
(1, 0, 1)(0, 0, 0)
(0, 1, 2) (1, 0, 1)
(0, 1, 1)(0, 0, 0)
(1, 0, 0)(0, 0, 0)
5. Select the coefficient(s) that match the best ARIMA model that you developed in problem 17.
-.3924
.2314 AND .2370
1.8673 AND .2645
1.8673
6.What are the fit period RMSE and MAPE for the best ARIMA model for the data in problem 17?
RMSE = 25.2 MAPE = 1.3
RMSE = 46.7 MAPE = 9.7
RMSE = 31.5 MAPE = 12.4
RMSE = 24.503 MAPE = 1.4
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)
It follows the positive trend of the data.
It shows a decrease in the business cycle.
It is constant (stationary).
It shows seasonality.