Question

The following data shows the quarterly profit (in thousands of dollars) made by a particular company in the past 3 years.

Year	Quarter	Profit ($1000s)
1	1	45
1	2	51
1	3	72
1	4	50
2	1	49
2	2	45
2	3	79
2	4	54
3	1	42
3	2	58
3	3	70
3	4	56

a. Use α = 0.3 to compute the exponential smoothing values for the time series. Compute MSE and the forecast of profit (in $1000s) for the next quarter.

Answer 1

a:

Formulae to be used:

Absolute deviation= |Forecast - Actual|

MSE= Mean square error = sum of squares of deviation/ no. of periods

· the formula to be used in Simple Exponential smoothing is

Ft+1= alpha*At + (1-alpha) Ft

At means Actual demand of t'th period, if you want to find out the Forecast through exponential smoothing= forecast of 3rd period = alpha*actual demand of 2nd period +(1-alpha) *forecast demand of 2nd period

· remember forecast of 1st period is 45, alpha= 0.3

Period, t	Actual , At	Ft, Exponential Forecast	Absolute deviation= |Forecast - Actual|	squared deviation= (absolute deviation)^2
1	45	45.00
2	51	45.00	6.00	36.00
3	72	46.80	25.20	635.04
4	50	54.36	4.36	19.01
5	49	53.05	4.05	16.42
6	45	51.84	6.84	46.74
7	79	49.79	29.21	853.49
8	54	58.55	4.55	20.70
9	42	57.18	15.18	230.58
10	58	52.63	5.37	28.84
11	70	54.24	15.76	248.36
12	56	58.97	2.97	8.81
				194.91
				MSE