Gap Inc. Sales Case: Gap Inc. obtained significant growth of its business in last three decades. Attached Minitab dataset, “Gap data.MTW” contains 22 years’ (1985 to 2006) quarterly sales values...

Gap Inc. Sales Case:


Gap Inc. obtained significant growth of its business in last three decades. Attached Minitab dataset, “Gap data.MTW” contains 22 years’ (1985 to 2006) quarterly sales values (measured in $1,000’s) of the company. Suppose we are at the end of year 2006, and we are interested in conducting time series analysis and forecasting for the sales in future quarters. Based on the data given, please,
a). Obtain a time series plot of the sales data and discuss any patterns you can identify.
b). Using Bartlett test, conduct hypothesis test to check whether there exists significant autocorrelation at lag 4. In so doing, list your null and alternative hypotheses and show your test statistics which lead you to the conclusion
c). Discuss in details whether the sales series is stationary or not
d). Due to existence of trend and seasonality, we are constructing a Winters’ model for predicting purpose. In carry out the modeling, we use the following parameter values:
a
= 0.25, ß = 0.25 and ? = 0.3


The following Excel results are modeling results using the Winters’ method, based on these, please obtain your estimates and forecasts for relevant periods. In so doing, please
list the formulas and calculations you used.

Note: You must maintain precision level of at least three digits after the decimal point.

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d-1). Calculate estimates of level, trend and seasonal factor for the 4th quarter of 2006 (for Cells E95:G95).
d-2). Obtain your forecasts for the 3rd and the 4th quarters of year 2007.

Year	Quarter	GapSales($1,000_s)
1985	1	105715
1985	2	120136
1985	3	181669
1985	4	239813
1986	1	159980
1986	2	164760
1986	3	224800
1986	4	298469
1987	1	211060
1987	2	217753
1987	3	273616
1987	4	359592
1988	1	241348
1988	2	264328
1988	3	322752
1988	4	423669
1989	1	309925
1989	2	325939
1989	3	405601
1989	4	545131
1990	1	402368
1990	2	404996
1990	3	501690
1990	4	624726
1991	1	490300
1991	2	523056
1991	3	702052
1991	4	803485
1992	1	588864
1992	2	614114
1992	3	827222
1992	4	930209
1993	1	643580
1993	2	693192
1993	3	898677
1993	4	1060230
1994	1	751670
1994	2	773131
1994	3	988346
1994	4	1209790
1995	1	848688
1995	2	868514
1995	3	1155930
1995	4	1522120
1996	1	1113150
1996	2	1120340
1996	3	1383000
1996	4	1667900
1997	1	1231186
1997	2	1345221
1997	3	1765939
1997	4	2165479
1998	1	1719712
1998	2	1904970
1998	3	2399900
1998	4	3029900
1999	1	2277734
1999	2	2453339
1999	3	3045386
1999	4	3858939
2000	1	2731990
2000	2	2947714
2000	3	3414668
2000	4	4579088
2001	1	3179656
2001	2	3245219
2001	3	3333373
2001	4	4089625
2002	1	2890840
2002	2	3268309
2002	3	3644956
2002	4	4650604
2003	1	3352771
2003	2	3685299
2003	3	3929456
2003	4	4886264
2004	1	3667565
2004	2	3720789
2004	3	3980150
2004	4	4898000
2005	1	3626000
2005	2	3716000
2005	3	3860000
2005	4	4821000
2006	1	3441000
2006	2	3716000
2006	3	3856000
2006	4	4930000