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# Gap Inc. obtained significant growth of its business in last three decades…. 1 answer below »

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.

Page 3 of 3 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.

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.

Page 3 of 3 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.

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Gap Inc. obtained significant growth of its business in last three decades….
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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 |

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