2.3 Consider the following noise-free data generated from the linear trend model dt = 2 + 3t. Show that using the method illustrated in Figure 2.9 to estimate the initial slope and level, a double exponential smoothing method will provide noise-free forecast no matter what α and β values are used.

Time 1

2 3

4 5

6 7

8 9

10 11 12 Demand 5

8 11 14 17 20 23 26 29 32 35 38