Question

Round all intermediate calculations to at least 4 decimal places. Consider the following sample data, consisting of 20 observations. t 1 23 4 5 67 8 9 10 yt 8.1 15.1 12.4 11.2 8.9 10.2 13.2 9.1 13.3 13.3 t 11 12 13 14 15 16 17 18 19 20 yt 14.0 9.0 14.3 12.1 11.3 13.412.1 11.0 15.2 12.1 picture Click here for the Excel Data File The data are plotted below. 15.5 14.5 13.5 12.5 11.5 10.5 9.5 8.5 7.5 0 2 48 0 2 14 18 20 a-2. Discuss the presence of random variations. The smoother appearance of the graph suggests the presence of random variations O The smoother appearance of the graph suggests the absence of random variations. The jagged appearance of the graph suggests the presence of random variations O The jagged appearance of the graph suggests the absence of random variations.

Answer 1

Solution:

Solution(a-2): The option selected by you is right. The correct option is Option(c).

Solution(b-1): The solution to this is given in column C in the above snapshot.

Solution(b-2): MSE = 6.65 and MAD = 2.02

Solution(c-1): The solution to this is given in column F in the above snapshot.

Solution(c-2): MSE = 6.70 and MAD = 2.05

Solution(d): For $\alpha = 0.2$ , the MSE and MAD are less. Hence the more appropriate value of $\alpha$ is 0.2

Forecasting for the period 21 can be computed as,

$F_{21} = \alpha D_{20} + (1-\alpha)F_{20}$