4 (Requires StatTools) This data set has obvious seasonality, so Winters' exponential smoothing method is appropriate. When this method is used with smoothing constants 0.1 (for level), 0.1 (for trend), and 0.4 (for season), which of the following is true?

a. After using Winters' method, the graph of the forecast errors will typically still show a seasonal pattern.

b. To get future forecasts (i.e., beyond 2016), Winters' method starts with the last estimated level, keeps adding the last estimated trend, and finally multiplies the sum by the most recent relevant seasonal factor.

c. If the smoothing constant for season is set equal to 0, the forecasts from Winters' method will have no seasonal pattern, even though the data series does.

d. The MAPE indicates that the forecasts will be off, on average, by about 11.1%, but this applies only to the deseasonalized series, not the original series

B C D E A 1 Month 2 Jan-12 3 Feb-12 4 Mar-12 5 Apr-12 6 May-12 7 Jun-12 8 Jul-12 9 Aug-12 10 Sep-12 11 Oct-12 12 Nov-12 13 Dec-12 14 Jan-13 15 Feb-13 16 Mar-13 17 Apr-13 18 May-13 19 Jun-13 20 Jul-13 21 Aug-13 22 Sep-13 23 Oct-13 24 Nov-13 25 Dec-13 26 Jan-14 27 Feb-14 28 Mar-14 29 Apr-14 30 May-14 31 Jun-14 32 Jul-14 33 Aug-14 34 Sep-14 B Value 6001! 5702 10784 10004 12606 15300 18936 23240 18438 12424 6963 9202 11420 7622! 10177 10189 14166 13736 20912! 25546 15757 12897 8709 12632 10242 9466 10888 14205 16066 24185; 278711 36070 21900 www. 34 Sep-14 35 Oct-14 36 Nov-14 37 Dec-14 38 Jan-15 39 Feb-15 40 Mar-15 41 Apr-15 42 May-15 43 Jun-15 44 Jul-15 45 Aug-15 46 Sep-15 47 Oct-15 48 Nov-15 49 Dec-15 50 Jan-16 51 Feb-16 52 Mar-16 53 Apr-16 54 May-16 55 Jun-16 56 Jul-16 57 Aug-16 58 Sep-16 59 Oct-16 60 Nov-16 61 Dec-16 21900 16028 11198 13573 9958 12113 14488 18210 17427 28348 32036 42234 22413 15762 13085 16189 12347 12823 16182 23178 18621 27557 39899 39624 30104 19171 13147 18186 02