Reconsider Prob. 27.7-15. The economy is beginning to boom so the management of Transcontinental Airlines is predicting that the number of people flying will steadily increase this year over the relatively flat (seasonally adjusted) level of last year. Since the forecasting methods considered in Prob. 27.7-15 are relatively slow in adjusting to such a trend, consideration is being given to switching to exponential smoothing with trend. Subsequently, as the year goes on, management€™s prediction proves to be true. The following table shows the average number of the passengers under consideration in each month of the New Year.

(a) Repeat part (a) of Prob. 27.7-15 for the two years of data.
In Part a 27.7-15
After considering seasonal effects, compare both the MAD and MSE values for the last-value method, the averaging method, the moving-average method (based on the most recent three months), and the exponential smoothing method (with an initial estimate of 80 and a smoothing constant of α = 0.2) when they are applied retrospectively to the past year.
(b) After considering seasonal effects, apply exponential smoothing with trend to just the New Year. Use initial estimates of 80 for the expected value and 2 for the trend, along with smoothing constants of α = 0.2 and β = 0.2. Compare MAD for this method to the MAD values obtained in part (a). Then do the same with MSE.
(c) Repeat part (b) when exponential smoothing with trend is begun at the beginning of the first year and then applied to both years, just like the other forecasting methods in part (a). Use the same initial estimates and smoothing constants except change the initial estimate of trend to 0.
(d) Based on these results, which forecasting method would you recommend that Transcontinental Airlines use hereafter?

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Average Average Average Number Month Nunber Month Nunber Month anuary 75 May February 76 June March 85 Seber 94 90 107 November106 99 October 81 July 84 Augst 108 December 110 April