Question

Question 3 part a & b. please show work!

3. The following time series shows the number of units of a particular product sold over the past six months. Units Sold Month (Thousands) 23 2 17 3 17 4 5 26 11 23 6 a. Use a = 0.2 to compute the exponential smoothing values for the time series, forecast the sales volume for month 7, and fill in the unknown spaces.

Answer 1

Note: Final answers are highlighted in colour.

a)

Ft = a At-1 + (1 - a) Ft-1

(i) Forecast for month 2= 0.2* Actual sales for Month 1+ 0.8* Forecasted sales for Month 1

Forecast for Month 1 can be assumed to be equal to Actual sales for Month 1.

Forecast for month 2= 0.2*23 + 0.8 * 23 = 23

(ii)Error = Actual sales volume- Forecasted Volume= 17-23= -6

(iii)Forecast for Month 7=0.2* Actual sales for Month 6+ 0.8* Forecasted sales for Month 6

= 0.2*23 + 0.8 * 19.698= 20.358

MSE= (36+23.04+26.6256+118.2004+10.9032)/5= 42.9538

Final Table

Month	Units Sold(Thousands)	Forecast(F)	Error	Squared Error
1	23	23	0	0
2	17	23(i)	-6(ii)	36
3	17	21.8	-4.8	23.04
4	26	20.84	5.16	26.6256
5	11	21.872	-10.872	118.2004
6	23	19.6976	3.3024	10.90585
7		20.35808(iii)	-20.3581	414.4514
Alpha	0.2		MSE	42.95437

b)

(i) Moving average = (23+11+26)/3= 20

ii) Forecast for Month 7= Moving average of Month 6= 20

iii) Error of month 6= Actual - Forecast= 23-18= 5

iv) Squared error for month 6= (Error of Month 6)^2= 5^2= 25

v) Mean square error(MSE)= Sum of Squared Errors/ n= (49+81+25)/3= 51.67

Final table

Month	Units Sold(Thousands)	3 Month moving average	Forecast(F)	Error	Squared Error
1	23
2	17
3	17	19	0
4	26	20	19	7	49
5	11	18	20	-9	81
6	23	20(i)	18	5(iii)	25(iv)
7			20(ii)		MSE= 51.66667(v)