Question

Suppose ten weeks of data on the Commodity Futures Index are 7.34, 7.39, 7.54, 7.56, 7.61, 7.52, 7.51, 7.71, 7.63, and 7.55.

(a) What type of pattern exists in the data?

The data appear to follow a seasonal pattern.

The data appear to follow a cyclical pattern.     

The data appear to follow a trend pattern.

The data appear to follow a horizontal pattern.

(b)Compute the exponential smoothing forecasts for α = 0.2. (Round your answers to two decimal places.)

Week	Time Series Value	α = 0.2 Forecast
1	7.34
2	7.39
3	7.54
4	7.56
5	7.61
6	7.52
7	7.51
8	7.71
9	7.63
10	7.55

(c)Compute the exponential smoothing forecasts for α = 0.3. (Round your answers to two decimal places.)

Week	Time Series Value	α = 0.3 Forecast
1	7.34
2	7.39
3	7.54
4	7.56
5	7.61
6	7.52
7	7.51
8	7.71
9	7.63
10	7.55

(d) Which exponential smoothing constant provides more accurate forecasts based on MSE?

A.Exponential smoothing with α = 0.3 provides more accurate forecasts since its MSE is smaller than the MSE for α = 0.2.

B.Exponential smoothing with α = 0.2 provides more accurate forecasts since its MSE is larger than the MSE for α = 0.3.

C. Exponential smoothing with α = 0.2 provides more accurate forecasts since its MSE is smaller than the MSE for α = 0.3.

D. Exponential smoothing with α = 0.3 provides more accurate forecasts since its MSE is larger than the MSE for α = 0.2.

Using the more accurate approach, forecast week 11. (Round your answer to two decimal places.)

Answer 1

b)

week	value	Forecast	error^2
1	7.34
2	7.39	7.34	0.0025
3	7.54	7.35	0.0361
4	7.56	7.39	0.0296
5	7.61	7.42	0.0352
6	7.52	7.46	0.0036
7	7.51	7.47	0.0014
8	7.71	7.48	0.0531
9	7.63	7.53	0.0109
10	7.55	7.55	0.0000
		average	0.0192

c)

week	value	Forecast	error^2
1	7.34
2	7.39	7.34	0.0025
3	7.54	7.36	0.0342
4	7.56	7.41	0.0224
5	7.61	7.46	0.0239
6	7.52	7.50	0.0003
7	7.51	7.51	0.0000
8	7.71	7.51	0.0408
9	7.63	7.57	0.0038
10	7.55	7.59	0.0014
		average	0.0144

d)

A.Exponential smoothing with α = 0.3 provides more accurate forecasts since its MSE is smaller than the MSE for α = 0.2.

forecast week 11 = 7.58