Chapter 20
20.1 Time series Moving average
48
41 (48+41+37)/3 = 42.00
37 (41+37+32)/3 = 36.67
20.2 Time series Moving average
48
41
37 (48 +41+37+32+36)/5 = 38.8
20.3
50
60
70
Series1
Series2
20.4 Time series Moving average
16
22 (16+22+19)/3 = 19.00
19 (22+19+24)/3 = 21.67
20.5 Time series Moving average
16
22
19 (16+22+19+24+30)/5 = 22.2
20.6
25
30
35
Series1
20.7 Time series Exponentially smoothed time series
12 12
18 .1(18) +. 9(12) = 12.60
20.8 Time series Exponentially smoothed time series
12 12.00
18 .8(18) +. 2(12) = 16.80
16 .8(16) +. 2(16.80) = 16.16
20.9
20
25
30
Series1
Series2
20.10 Time series Exponentially smoothed time series
38 38.00
43 .1(43) +. 9(38) = 38.50
42 .1(42) +. 9(38.50) = 38.85
20.11 Time series Exponentially smoothed time series
38 38
43 .8(43) +. 2(38) = 42.00
20.12
45
50
55
Series1
Series2
20.13 & 20.14
Sales 3-Day moving average 5-Day moving average
43
45 (43+45+22)/3 = 36.67
22 (45+22+25)/3 = 30.67 (43+45+22+25+31)/5 = 33.20
25 (22+25+31)/3 = 26.00 (45+22+25+31+51)/5 = 34.80
31 (25+31+51)/3 = 35.67 (22+25+31+51+41)/5 = 34.00
30
40
50
60
70
Series1
Series2
20.15a Sales 4-quarter moving average Centered moving average
18
22
(18+22+27+31)/4 = 24.50
27 (24.50+28.25)/2 = 26.375
(22+27+31+33)/4 = 28.25
26 (27.25+31.25)/2 = 29.250
(38+26+25+36)/4 = 31.25
25 (31.25+32.75)/2 = 32.000
(26+25+36+44)/4 = 32.75
36 (32.75+33.50)/2 = 33.125
(25+36+44+29)/4 = 33.50
45
b
30
40
50
60
Series1
Series2
20.16 & 20.17
Sales Exponentially smoothed w = .4 Exponentially smoothed w = .8
18 18.00 18.00
22 .4(22)+.6(18) = 19.60 .8(22)+.2(18) = 21.20
27 .4(27)+.6(19.6) = 22.56 .8(27)+.2(21.2) = 25.84
31 .4(31)+.6(22.56) = 25.94 .8(31)+.2(25.84) = 29.97
20.16 b
40
50
60
Series1
20.17 b
Series2
20.18
40
50
60
Series1
20.19
20.20
20.21
20.22
Week
Day
Period t
y
y
ˆ
yy ˆ
/
1
1
1
12
17.2
0.699
2
2
18
17.5
1.027
3
3
16
17.9
0.894
4
4
25
18.3
1.369
5
5
31
18.6
1.664
2
1
6
11
19.0
0.579
2
7
17
19.4
0.878
3
8
19
19.7
0.963
4
9
24
20.1
1.194
5
10
27
20.5
1.320
2
12
16
21.2
0.755
3
13
16
21.6
0.742
4
14
28
21.9
1.277
5
15
25
22.3
1.122
4
1
16
17
22.7
0.750
2
17
21
23.0
0.912
3
18
20
23.4
0.855
4
19
24
23.8
1.010
5
20
32
24.1
1.327
Day
Week
Monday
Tuesday
Wednesday
Thursday
Friday
Total
1
.699
1.027
.894
1.369
1.664
2
.579
.878
.963
1.194
1.320
3
.672
.755
.742
1.277
1.122
4
.750
.912
.855
1.010
1.327
Average
.675
.893
.864
1.213
1.358
5.003
20.23
Year
Quarter
y
y
ˆ
yy ˆ
/
1
1
55
46.6
1.179
2
44
45.6
0.965
3
46
44.5
1.033
4
39
43.5
0.897
2
1
41
42.4
0.967
2
38
41.3
0.919
3
37
40.3
0.919
4
30
39.2
0.765
3
1
43
38.2
1.127
2
39
37.1
1.051
3
39
36.0
1.082
4
1
36
33.9
1.061
2
32
32.9
0.974
3
30
31.8
0.943
4
25
30.7
0.813
5
1
50
29.7
1.685
2
25
28.6
0.874
3
24
27.6
0.871
4
22
26.5
0.830
Quarter
Year
1
2
3
4
Total
1
1.179
0.965
1.033
0.897
2
0.919
0.919
3
1.127
1.051
1.082
1.001
4
1.061
0.974
0.943
0.813
5
0.874
0.871
1.204
0.957
0.970
0.861
3.991