Davis Company is interested in using exponential smoothing for short-range forec

Question

Davis Company is interested in using exponential smoothing for short-range forecasting table for the past two years. Month Jan. Feb. Mar. Apr. May June 3. purposes for inventory control. Monthly inventories data are presented in the accompanying 2009 8.5 7.9 7.7 8.1 7.7 7.3 2010 11.5 11.9 11.3 12.5 12.9 13.3 2009 Month 7.1 7.5 7.8 8.1 9.3 2010 6.7 8.7 °July 9.4 9.9 10.3 10.5 11.3 Aug. Sep. Oct. Nov. Dec. Use an appropriate naïve model, and forecast inventory for January 2011. Using a smoothing constant of 0.2, prepare an exponential smoothing of the data. Use the mean of the first four months as a starting value, Fs, and start the smoothing process in the fifth month. Using smoothing constants of alpha equals 0.2 and gamma equals 0.4, prepare an exponential smoothing adjusted for trend of the data (Holt Model). Use the mean of the first four months as initial value, and assume T, equals zero. Start the smoothing process in the fifth month. a. b. c. d. Use the RMSE as a basis for evaluating the methods used in parts b and c e. Forecast inventory for January 2011. 4. Boeing Company sales, in millions of dollars, for 2008-2010 are reported in the arcomnantino

Explanation / Answer

a) In case of Naive model, we simply put the past value as the forecast for the current period. For ex, forecast for Feb-09 would be the value of Jan-09. Forecast for Jan-11 is 13.3.

b) and c) As shown in the table below

d) RMSE for Exp_Smoothing= 1.98 and for Holt's method= 0.77. Holt's method is better

e) Forecast for Jan-11 is 11.739 as per exponential smoothing and 13.87 as per Holt's method.

Month Data Naïve Exp_Smoothing a b Holt's Abs(error)-Exp_Smoothing Abs(error)-Holt's (Abs(error)-Exp_Smoothing)^2 (Abs(error)-Holt's)^2 Jan-09 6.7 Feb-09 7.1 6.7 Mar-09 7.5 7.1 Apr-09 7.8 7.5 May-09 8.1 7.8 7.275 7.275 0 0.825 0.680625 Jun-09 9.3 8.1 7.440 7.68 0.162 7.275 1.86 2.025 3.4596 4.100625 Jul-09 8.5 9.3 7.812 7.9736 0.21464 7.842 0.688 0.658 0.473344 0.432964 Aug-09 7.9 8.5 7.950 8.130592 0.1915808 8.18824 0.0496 0.28824 0.00246016 0.083082298 Sep-09 7.7 7.9 7.940 8.19773824 0.141806976 8.3221728 0.23968 0.6221728 0.057446502 0.387098993 Oct-09 8.1 7.7 7.892 8.291636173 0.122643359 8.339545216 0.208256 0.239545216 0.043370562 0.057381911 Nov-09 7.7 8.1 7.933 8.271423625 0.065500996 8.414279532 0.2333952 0.714279532 0.054473319 0.510195249 Dec-09 7.3 7.7 7.887 8.129539697 -0.017452974 8.336924621 0.58671616 1.036924621 0.344235852 1.07521267 Jan-10 8.7 7.3 7.769 8.229669379 0.029580089 8.112086724 0.930627072 0.587913276 0.866066747 0.345642021 Feb-10 9.4 8.7 7.955 8.487399574 0.120840131 8.259249467 1.444501658 1.140750533 2.086585039 1.301311777 Mar-10 9.9 9.4 8.244 8.866591764 0.224180955 8.608239705 1.655601326 1.291760295 2.741015751 1.668644659 Apr-10 10.3 9.9 8.576 9.332618175 0.320919137 9.090772719 1.724481061 1.209227281 2.973834929 1.462230617 May-10 10.5 10.3 8.920 9.82282985 0.388636152 9.653537312 1.579584849 0.846462688 2.495088294 0.716499081 Jun-10 11.3 10.5 9.236 10.4291728 0.475718872 10.211466 2.063667879 1.088533998 4.258725115 1.184906264 Jul-10 11.5 11.3 9.649 11.02391334 0.523327538 10.90489167 1.850934303 0.595108326 3.425957795 0.35415392 Aug-10 11.9 11.5 10.019 11.6177927 0.551548268 11.54724088 1.880747443 0.352759123 3.537210943 0.124438999 Sep-10 11.3 11.9 10.395 11.99547278 0.48200099 12.16934097 0.904597954 0.86934097 0.818297458 0.755753722 Oct-10 12.5 11.3 10.576 12.48197901 0.483803089 12.47747377 1.923678363 0.022526234 3.700538445 0.000507431 Nov-10 12.9 12.5 10.961 12.95262568 0.478540521 12.9657821 1.938942691 0.065782102 3.759498757 0.004327285 Dec-10 13.3 12.9 11.349 13.40493296 0.468047225 13.4311662 1.951154152 0.131166203 3.807002527 0.017204573 Jan-11 13.3 11.739 11.09838415 -0.64179119 13.87298019 RMSE RMSE 1.97926886 0.767483183

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