các bài tập san mũ tổng hợp

Ví dụ San mũ bất biến ( đơn giản)
Doanh thu của một Công ty:
Năm t Xt
2002 1 200
2003 2 135
2004 3 195
2005 4 197.5
2006 5 310
2007 6 175
2008 7 155
2009 8 130
2010 9 220
2011 10 277
2012 11 235
2013 12 ?
Ví dụ về san mũ Hotl's ( 2 tham số san) α β
Cầu về hàng hóa: 0.2 0.3
t Xt St bt
1 143 143 9 Chọn S1 = X1
2 152 152 9 b1 = X2-X1
3 161 161 9 St = α*Xt +(1-α)*(St-1 + bt-1)
4 139 163.8 7.14 bt = β*( St-St-1)+(1-β)* bt-1
5 137 164.152 5.1036
6 174 170.20448 5.388264 Dự báo: Ft+m = St + bt*m
7 142 168.8741952 3.3726994
8 141 165.9975156 1.4978857
9 162 166.3963211 1.1681616
10 180 170.0515861 1.9142926
11 164 170.372703 1.4363399
12 171 171.6472344 1.3877973
13 206 179.6280254 3.3656954

14 193 184.9949766 3.9660722
15 207 192.5688391 5.0484093
16 218 201.6937987 6.2713744
17 229 212.1721384 7.533464
18 225 220.7644819 7.8511278
19 204 223.6924878 6.3741913
20 227 229.4533432 6.1901905
21 223 233.114827 5.4315785
22 242 239.2371244 5.6387942 Dự báo:
23 239 243.7007348 5.286239
24 266 252.3895791 6.3070206 Dự báo: Dự báo:
1 258.70 261.37
2 Hàm dự báo: 265.00 267.75
3 Ft+m = St + bt*m 271.31 274.12
4 277.62 280.50
5 283.92 286.88
Hotl's Method
Estimate SE t Sig.
Alpha (Level)
.098 .135 .723 .478
Gamma
(Trend)
1.102E-06 .069 1.598E-05 1.000
25 26 27 28
Forecast
253.99 259.08 264.17 269.27
UCL
284.93 290.17 295.41 300.65
LCL
223.04 227.99 232.94 237.89

Dự báo Dân số Hà Giang - Hotl's method
Xt
St bt 0.9 0.5
1995 1 550.3
550.3 13.9
1996 2 564.2
564.2000 13.9000 Chọn S1 = X1
1997 3 577.7
577.7400 13.7200 b1 = X2-X1
1998 4 590.4
590.5060 13.2430 St = α*Xt +(1-α)*(St-1 + bt-1)
1999 5 605.9
605.6849 14.2110 bt = β*( St-St-1)+(1-β)* bt-1
2000 6 619.2
619.2696 13.8978
2001 7 631.6
631.7567 13.1925 Dự báo: Ft+m = St + bt*m
2002 8 643.9
644.0049 12.7203
2003 9 656.2
656.2525 12.4840
2004 10 669
668.9736 12.6025
2005 11 681.7
681.6876 12.6583
2006 12 693.4
693.4946 12.2326
Exponential Smoothing Model Parameters
Model
Doanh thu-

Model_1
No
Transformation
Năm
t
Forecast
Model
Doanh thu-
Model_1
For each model, forecasts start after the last non-missing in the range of the requested
estimation period, and end at the last period for which non-missing values of all the predictors
2007 13 704.9
704.9827 11.8604
2008 14 716.2
716.2643 11.5710
2009 15 727
727.0835 11.1951
Vậy ta có hàm dự báo:
X^t+m =
727.0835 + 11.1951004 * m
m Dự báo
2010 1 738.279
2011 2 749.474
2012 3 760.669
2013 4 771.864
2014 5 783.059
2015 6 794.254
Phương pháp san mũ xu thế tuyến tính Brown - Mayer (một tham số san) α
at bt 0.2778
t Xt 110.6026 87.20518 b0=X2-X1= 9

1 143 119.6026 96.20518 143 9 a0 =X1-b0= 134
2 152 128.6026 105.2052 152 9
3 161 137.6026 114.2052 161 9
S01 = a0-(1-α)/α*b0 =
110.6
4 139 137.9908 120.8128 155.1688 6.607642
S02= a0-2*(1-α)/α*b0=
87.205
5 137 137.7155 125.5084 149.9227 4.695577
6 174 147.7954 131.6997 163.891 6.19132
7 142 146.1854 135.7238 156.647 4.024126
8 141 144.7449 138.2299 151.2599 2.50605
9 162 149.5384 141.3714 157.7054 3.141494
10 180 158.0006 145.991 170.0102 4.619597
11 164 159.6672 149.7903 169.5442 3.799263
12 171 162.8155 153.4087 172.2223 3.618409
13 206 174.8121 159.3545 190.2697 5.945887
14 193 179.8647 165.0523 194.6772 5.697728
15 207 187.4029 171.2613 203.5445 6.209005
16 218 195.9028 178.1067 213.6989 6.845408
17 229 205.0972 185.6046 224.5897 7.49796
18 225 210.6262 192.5556 228.6967 6.950983
19 204 208.7854 197.0643 220.5066 4.508638
20 227 213.8454 201.7261 225.9648 4.661809
21 223 216.3886 205.7993 226.9778 4.073242
22 242 223.5034 210.7175 236.2893 4.918201
23 239 227.8084 215.4654 240.1514 4.747839
1
t
S

2
t
S
24 266 238.418 221.8416 254.9944 6.376246
1 261.3707
2 267.7469
3 274.1231
4 280.4994
5 286.8756
Hàm dự báo:
X^t+l = at + bt*l
Brown's Method
Estimate SE t Sig.
Doanh thu-
Model_1
No
Transformat
ion
Alpha (Level
and Trend)
.281 .069 4.091 .000
25 26 27 28
Forecast
261.37 267.75 274.12 280.49
UCL
295.24 306.60 318.63 331.26
LCL
227.51 228.89 229.60 229.73
Exponential Smoothing Model Parameters
Model

Forecast
Model
Doanh thu-
Model_1
For each model, forecasts start after the last non-missing in the range of the
requested estimation period, and end at the last period for which non-missing

0.2778