Question

Question 1. Consider the following time series data.

Week	1	2	3	4	5	6
Value	118	113	116	111	117	114

1. Construct a time series plot. What type of pattern exists in the data?

2. Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7.

3. Use a =0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.

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

Answer 1

The time series plot=

The time series plot shown above has a horizontal pattern.

Answer-

Week	Value	The 3-week moving average forecast	The 3-week moving average forecast	Error	Error^2
1	118
2	113
3	116
4	111	(118+113+116)/3	115.67	-4.67	21.78
5	117	(113+116+111)/3	113.33	3.67	13.44
6	114	(116+111+117)/3	114.67	-0.67	0.44
7		(111+117+114)/3	114	Sum	35.67

MSE=35.67/3=11.89

Forecast for week 7=114

Answer=

Week	Value	Exponential smoothening forecast	Exponential smoothening forecast	Error	Error^2
1	118		118.00	0.00	0.00
2	113	118+0.2*(118-118)	118.00	-5.00	25.00
3	116	118+0.2*(113-118)	117.00	-1.00	1.00
4	111	117+0.2*(116-117)	116.80	-5.80	33.64
5	117	116.8+0.2*(111-116.8)	115.64	1.36	1.85
6	114	115.64+0.2*(117-115.64)	115.91	-1.91	3.66
7		115.91+0.2*(114-115.91)	115.53	Sum	65.15

MSE=65.15/6=10.86

Forecast for week 7=115.53

Answer= Exponential smoothening with alpha 0.2 has the better forecast as it has less value of MSE