Ft+1 is a weighted mean of all previous actual values Yt. The forecast Ft+1 is calculated using the simple exponential smoothing model Ft+1=Yt+(1-α)Ft, where α is the smoothing constant between 0 and 1. The document provides an example of using this model with α=0.2 to forecast month 9 sales of Blitz Beer based on the past 8 months of sales data. It also works through an example of using Holt's two-parameter exponential smoothing model, which includes a trend component, to forecast month 9 sales based on starting values for month 2.

1. Show all written workings a) Using the usual notation, the simple exponential smoothing model
is given by Ft+1=Yt+(1)Ft,0<<1 Show that the forecast for time t+1 is a weighted mean of all the
previous actual values of the time series. [6 marks] b) The sales (in thousands of bottles) of Blitz
Beer over the past eight months are shown in the table below. (i) Assume that the forecast for
month 2 is the actual sales for month 1. Use the simple exponential smoothing model with a
smoothing constant of =0.2 to forecast sales for month 9 . [5 marks] (ii) Assume that for month 2
the exponentially smoothed value is 489 and the smoothed trend value is 2 . Use Holt's two-
parameter exponential smoothing model with =0.2 and =0.3 to forecast sales for month 9 . [9
marks]