Question

Consider the following time series data. 

Week	1	2	3	4	5	6
Value	18	15	16	13	17	16

a. Choose the correct time series plot.

What type of pattern exists in the data? 

b. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. 

Week	Time Series Value	Forecast
1	18
2	15
3	16
4	13
5	17
6	16

 MSE:

 The forecast for week 7: 

c. Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places. 

Week	Time Series Value	Forecast
1	18
2	15
3	16
4	13
5	17
6	16

MSE: 

The forecast for week 7: 

d. Compare the three-week moving average forecast with the exponential smoothing forecast using a = 0.2. Which appears to provide the better forecast based on MSE?

 Explain. 

The input in the box below will not be graded, but may be reviewed and considered by your instructor. 

e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller MSE than what you calculated for a = 0.2. Find a value of a for the smallest MSE. Round your answer to three decimal places. 

α =

Answer 1

1. D. D is the correct plot for the dataset.

2. FORECAST = SIGMA(PREVIOUS N DEMANDS) / N

WHERE N = 3

FORECAST 4 = (18 + 15 + 16) / 3 = 16.33

FORECAST 5 = (15 + 16 + 13) / 3 = 14.67

FORECAST 6 = (16 + 13 + 17) / 3 = 15.33

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	DEVIATION ^2
1	18
2	15
3	16
4	13	16.33	-3.33	11.0889
5	17	14.67	2.33	5.4289
6	16	15.33	0.67	0.4489
SIGMA			-0.33	16.9667

MSE = SIGMA(DEVIATIONS^2) / N, WHERE N = 3

MSE = 16.9667 / 3 = 5.66

FORECAST 7 = (13 + 17 + 16) / 3 = 15.33

3. FORECAST(T + 1) = FORECAST + (ALPHA * (ACTUAL DEMAND - FORECAST))

FORECAST 2 = 18 + (0.2 * (18 - 18) = 18

FORECAST 3 = 18 + (0.2 * (15 - 18) = 17.4

FORECAST 4 = 17.4 + (0.2 * (16 - 17.4) = 17.12

FORECAST 5 = 17.12 + (0.2 * (13 - 17.12) = 16.3

FORECAST 6 = 16.3 + (0.2 * (17 - 16.3) = 16.44

FORECAST 7 = 16.44 + (0.2 * (16 - 16.44) = 16.35

PERIOD	ACTUAL DEMAND	FORECAST	DEVIATION(D - F)	DEVIATION ^2
1	18	18	0	0
2	15	18	-3	9
3	16	17.4	-1.4	1.96
4	13	17.12	-4.12	16.9744
5	17	16.3	0.7	0.49
6	16	16.44	-0.44	0.1936
SIGMA			-8.26	28.618

MSE = SIGMA(DEVIATIONS^2) / N, WHERE N = 6

MSE = 28.618 / 6 = 4.77

D. BASED ON THE MSE VALUE, EXPONENTIAL SMOOTHING IS CLOSER TO THE ACTUAL DATASET