Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	12	15	11	18	13

a. Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Week	Time Series Value	Forecast
1	19
2	12
3	15
4	11
5	18
6	13

Compute MSE. (Round your answer to two decimal places.)

MSE =  

b. Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Week	Time Series Value	Forecast
1	19
2	12
3	15
4	11
5	18
6	13

Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.

The exponential smoothing using α = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.2.

The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.4.    

The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.

The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.4.

Answer 1

Using exponential smoothing for alpha =0.2

formula used

s_t = a.x_t-1+(1-a)s_t-1

with s₁ =19

α =0.2
Week	time series Forcast	Forcast Values	Error	Error sq
1	19	19	-	-
2	12	17.6	-5.6	31.36
3	15	17.08	-2.08	4.3264
4	11	15.864	-4.864	23.6585
5	18	16.2912	1.7088	2.919997
6	13	15.63296	-2.63296	6.932478
MSE =	Sum of Error Sq/5
	13.83947

Using exponential smoothing for alpha =0.4

formula used

s_t = a.x_t-1+(1-a)s_t-1

with s₁ =19

α= 0.4
Week	time series Forcast	Forcast Values	Error	Error sq
1	19	19	-	-
2	12	16.2	-4.2	17.64
3	15	15.72	-0.72	0.5184
4	11	13.832	-2.832	8.020224
5	18	15.4992	2.5008	6.254001
6	13	14.9952	-1.9952	3.980823
MSE =	Sum of Error Sq/5
	7.28269

For comparing two models we will compare MSE's of two models .. more the MSE lesser the efficiency of model ,Hence

The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.