Question

The quarterly demand for smartphones at a retailer is as show.

Year	Quarter	Demand
1	I	513
	II	932
	III	1509
	IV	1902
2	I	693
	II	1163
	III	1857
	IV	2469
3	I	846
	II	1439
	III	2271
	IV	3079
4	I	1070
	II	1751
	III	2785
	IV	3613

Forecast the quarterly demand for year 5 using the following models:

1. 4-week simple moving average.
2. Simple exponential smoothing with α = 0.1
3. Trend adjusted exponential smoothing with α = 0.1 and β = 0.1
4. Linear Regression with seasonality/

Answer 1

	four week moving Average
period	demand	forecast
t	Dt	Ft
1	513
2	932
3	1509
4	1902
5	693	1214.00
6	1163	1259.00
7	1857	1316.75
8	2469	1403.75
9	846	1545.50
10	1439	1583.75
11	2271	1652.75
12	3079	1756.25
13	1070	1908.75
14	1751	1964.75
15	2785	2042.75
16	3613	2171.25

year 5 forecast

Q1		2304.75
Q2		2037.25
Q3		1599.50
Q4		903.25

============================

Simple exponential smoothing with α = 0.1

period	demand	forecast
t	Dt	Ft
1	513	513
2	932	513
3	1509	554.9
4	1902	650.31
5	693	775.479
6	1163	767.2311
7	1857	806.80799
8	2469	911.827191
9	846	1067.54447
10	1439	1045.39002
11	2271	1084.75102
12	3079	1203.37592
13	1070	1390.93833
14	1751	1358.8445
15	2785	1398.06005
16	3613	1536.75404

year 5 forecast

Q1		1744.37864
Q2		1569.94077
Q3		1412.9467
Q4		1271.65203

====================

Trend adjusted exponential smoothing with α = 0.1 and β = 0.1

period	actual	Level	Trend	Forecast
1	513	513	419.00
2	932	932	419.00	932.00
3	1509	1366.8	420.58	1351.00
4	1902	1798.842	421.73	1787.38
5	693	2067.811	406.45	2220.57
6	1163	2343.136	393.34	2474.26
7	1857	2648.526	384.54	2736.47
8	2469	2976.662	378.90	3033.07
9	846	3104.608	353.81	3355.56
10	1439	3256.474	333.61	3458.42
11	2271	3458.178	320.42	3590.09
12	3079	3708.64	313.43	3778.60
13	1070	3726.859	283.91	4022.07
14	1751	3784.788	261.31	4010.76
15	2785	3919.986	248.70	4046.10
16	3613	4113.114	243.14	4168.68
17		3920.628	199.58	4356.25
18		3708.185	158.38	4120.21
19		3479.904	119.71	3866.56
20		3239.652	83.71	3599.61

Year 5 forecast

Q1				4356.25
Q2				4120.21
Q3				3866.56
Q4				3599.61

=======================

1. Linear Regression with seasonality/

QTR	Sales	Q1	Q2	Q3	t
1	513	1	0	0	1
2	932	0	1	0	2
3	1509	0	0	1	3
4	1902	0	0	0	4
1	693	1	0	0	5
2	1163	0	1	0	6
3	1857	0	0	1	7
4	2469	0	0	0	8
1	846	1	0	0	9
2	1439	0	1	0	10
3	2271	0	0	1	11
4	3079	0	0	0	12
1	1070	1	0	0	13
2	1751	0	1	0	14
3	2785	0	0	1	15
4	3613	0	0	0	16

Yt=1856.875+(-1712.5875)*Q1+(-1262.725)*Q2+(-569.3625)*Q3+(90.8875)*t          

Year 5		forecast
Q1		1689.38
Q2		2230.13
Q3		3014.38
Q4		3674.63