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普通高等教育 “ 十一五 ” 国家级规划教材. 统计预测和决策 (第三版) 教 学 课 件( PowerPoint ). 对应于徐国祥教授主编的教材: 《 统计预测和决策 》 上海财经大学电子出版社. 目 录. 1 统计预测概述. 9 景气预测法. 10 灰色预测法. 2 定性预测法. 11 状态空间模型和卡尔曼滤波. 3 回归预测法. 12 预测精度测定与预测评价. 4 时间序列分解法和趋势外推法. 13 统计决策概述. 5 时间序列平滑预测法. 14 风险型决策方法. 6 自适应过滤法. - PowerPoint PPT Presentation
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PowerPoint
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 1.2 1.3 1.1
1.1
:
;
1.2
;
;
233
34
4 5
567
8 9
1011
1.3
2 2.1
2.2
2.3
2.4
2.5
2.1
1
2
2.2
1964
1
2
3
1
2
3
1
88
8
0.500.200.30
300 370 400 500 550 410 500 600 700 750 600 610 650 750 800 900 1250
400
600
750
0.500.200.30
2.3
=
2
200910
0.01010.12520.25030.37540.50050.62560.75070.87580.990912111214421562200222222442267227823112197821002133215622002222226722782500320442100213321442244226722892311244442156216721782189220022112222223322445220022112222224422782311233323562400
1200920831%
22009 23491%
322132009 50%
467
221367~2213+67 2146~2280
521462280 38 0.8750.250=0.625 2146~2280 62.5%
2.4
yt1t2t3t4t (
1
2
3
4
1
2
3
186000.11860111600.7781299200.21984111656124000.11240111600.8892893000.1930111098124000.33720105400.6632474400.1744110788
21
2.5
1
2
3
4
GDPGDP
19521977 19531957GDP119.4167.81961GDP
2. 19781991 5419781991GDP9%, :
3. 19922006 199220WTO20082010
Y: GDP X Z Y=17328.44+1.798X+23051.72Zt (23.1) (5.25)0.9816F639.3
2. 12006200523.9%120072007 109998.2123.9%136287.77 20072007 Y17328.44+1.798136287.77+23051.722 273820.41
2. 2200724.12%2007 109998.2124.12%136532.37 2 Y17328.44+1.798136532.37+23051.722 274260.2
2007
d
3 3.1
3.2
3.3
3.4
3.1
01
+11
~
~
DW DW0~4
DW2 DW,;,DW2, DW:,;,;,
, =
1 1 2 3=0.05 47595%
1.55 1.60 1.65 1.67 1.7 1.75 1.80 1.82 50 52 57 56 60 65 62 70
1n=8
2
3
4
3.2
y
y y
=
0.75 0.5,
3.3
S
3.4
4 4.1 4.2 4.3 4.4 4.5 4.6
4.1 1 T
2 S
3 C
4 I
y
1 TC S
2 T
3CTCT C
4TSC y
4.2
1
2
t
4.3
1
19521983
t yt t yt t yt 19521276.8196312604.51974231163.619532348.0196413638.21975241271.119543381.1196514670.31976251339.419554392.2196615732.81977261432.819565461.0196716770.51978271558.619576474.2196817737.31979281800.019587548.0196918801.51980292140.019598638.0197019858.01981302350.019609696.9197120929.21982312570.0196110607.71972211023.31983322849.4196211604.01973221106.7
1 yx
2
3
151.7
(4)
,175.37
5
4.4
4.5
lg ab
(2) lga1k k
(4) lga>0 b>1k kk
4.6
5.1 5.2 5.3 5.4 5.5 5.6 5
5.1
1N=1N=nn
NN
N
2
3 N
N tN+1 0
1 111N=3N=512
5.2
2 17=0.10.3 0.9=0.1=0.3=0.9
=0.1=0.3=0.9 MSE=3.93 MSE=3.98 MSE=4.2 =0.117
5.3 1
2m5.15.25.35.4
5.15.25.3 5.4NN
5.4
m
5.55.65.55.6
5.5
Chart5
12.9
14.91
15.96
14.41
14.57
14.6
15.35
15.84
16.9
18.26
17.4
18.71
19.53
20.82
22.87
24.59
25.93
28.04
29.45
31.47
33.99
39.56
48.08
53.67
n=1n=3n=5
1200.0
2135.0200.0
3195.0135.0
4197.5195.0176.7
5310.0197.5175.8
6175.0310.0234.2207.5
7155.0175.0227.5202.5
8130.0155.0213.3206.5
9220.0130.0153.3193.5
10277.5220.0168.3198.0
11235.0277.5209.2191.5
12235.0244.2203.5
00.10.91
t00.1000.9000
t-100.0900.0900
t-200.0810.0090
t-300.0730.0010
t-400.0660.0000
0.10.50.9
1200.0
2135.0200.0200.0200.0
3195.0193.5167.5141.5
4197.5193.7181.3189.7
5310.0194.0189.4196.7
6175.0205.6249.7298.7
7155.0202.6212.3187.4
8130.0197.8183.7158.2
9220.0191.0156.8132.8
10277.5193.9188.4211.3
11235.0202.3233.0270.9
12205.6234.0238.6
M3M3abF
1200.0
2135.0
3195.0176.7
4197.5175.8
5310.0234.2195.6272.838.6
6175.0227.5212.5242.515.0311.4
7155.0213.3225.0201.7-11.7257.5
8130.0153.3198.1108.6-44.7190.0
9220.0168.3178.3158.3-10.063.9
10277.5209.2176.9241.432.2148.3
11235.0244.2207.2281.136.9273.6
12318.1
355.0
Brown
M3M3abF
1200.0200.0200.0
2135.0187.0200.0174.0-3.25
3195.0147.0189.4104.6-10.6170.8
4197.5195.5190.6200.41.2294.0
5310.0220.0196.5243.55.876201.6
6175.0283.0213.8352.217.3008249.4
7155.0171.0205.2136.8-8.55936369.5
8130.0150.0194.2105.8-11.047488128.2
9220.0148.0185.0111.0-9.237990494.8
10277.5231.5194.3268.79.30960768101.8
11235.0269.0209.2328.814.947686144278.0
12343.7
358.7
Holt
SbF
1200.0200.0-65.0
2135.0135.0-65.0135.0
3195.0132.5-15.070.0
4197.5157.517.0117.5
5310.0242.371.2174.5
6175.0244.215.8313.5
7155.0207.5-26.2260.0
8130.0155.7-46.7181.3
9220.0164.5-2.3108.9
10277.5219.843.8162.2
11235.0249.332.4263.7
12281.7
314.1
198312.9
198414.91
198515.96
198614.41
198714.57
198814.6
198915.35
199015.84
199116.9
199218.26
199317.4
199418.71
199519.53
199620.82
199722.87
199824.59
199925.93
200028.04
200129.45
200231.47
200333.99
200439.56
200548.08
200653.67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5.6
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6 6.1
6.2
6.1
i
i
K
t+1
xti+1ti+1
p
1
2
3
4
1
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6.2
5
20072008
p2
0.5
0.0002
k0.0002
t=2t+1
1 =44
2 = 4844=4
3
0.5+20.00024450.572
0.5+20.00024430.569
13t=3t+1
1 53
2 5053 3
3 0.572+20.0002(3)480.514
0.569+20.0002(3)450.515
t=4t+1
t=6t=5et+1t=2
20072008
0.54 0.541 0.5453+0.54150=56
0.5456+0.54153=59 200720085659
k1/p
=
7 7.1
7.2
7.3
7.4 ARMA
7.1
t,km
Box-Jenkins ARMA ARMA ARMA
ARMA
ARAuto-regressive
MAMoving-Average
ARMAAuto-regressive Moving-Average
,
p
1
q
MA(q)
ARMA(p,q) (p,q)
q=0AR(p)
p=0MA(q)
ARMA(p,q)
AB1
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7.2 ,
1 k
2
1 11
3k
k>3
ARMA AR(p)p
MA(q)q ARMA
ARMA(p,q)
7.3 Dickey-Fuller TestPhilips-Perron Test
1
2
3
Engle- GrangerJohansen
7.4 ARMA 1 ARMA(p,q)
q, .M M68.3%95.5% ()
. ,,,
M68.3%95.5%
ARMA
2F
3AICBIC
1 AR(p)Yule-WalkerAR(1) AR(2)
MA(q) MA(1)MA(2)
ARMA(p,q)
2 ARMA(p,q)
ARMA(p,q) ARMA(p,q) AR(p)
ARMA(p,q)
, t,ARMA(p,q)
95%
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2AR(2) 12195%,
1295%
8 8.1
8.2
8.3
8.1
T , ,
, ,
a. T
Yt
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b.
c.
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1
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2
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b.
c.
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8.3
1 : 1952~1993,19781978
t123456789101112xt100114.0120.6128.3146.4153.0186.7202.0199.1140.0130.9144.9
t131415161718192021222324xt168.8197.4231.0214.3200.3239.0294.6315.3324.3351.2355.2384.7
t252627282930313233 3435xt374.5403.7453.4485.1516.3541.5585.8644.2731.9830.6894.5
t36373839404142xt985.71097.21133.41191.71283.41480.91704.6
:11952~1977
txt Zt
1952~1977
21978~1993, Zt
t19781979198019811982198319841985Zt3.805.153.736.040.8319.2364.25117.49
t19861987198819891990199119921993Zt133.04172.89229.94212.28209.60237.50354.96404.24
:
:
3
9 9.1
9.2 9.3
9.4
9.1
12
1234
9.2 1
2
3
4
9.3
1GNPGDP
2
3
4
5
1
2
3KL
4
5
6
TCSI Y=TCSI T=T+C+S+I Y=TC+SI
DI12 TC C3
10<
3100%> >50%
450%> >0
1 52000671
1I I=1 I=0I=0.5
2
3
9.4
1
2
3
4
5
10 10.1 10.2 GM(1,1) 10.3 GM(1,1)GM (n, h)
10.1 1
2
3
1
:
1m
1
2
,
=0.5
10.2 GM(1,1)GM11 n GM11
1
2=0.50.6
3a.:
b. c.
10.3 GM(1,1)GM (n, h) GM11GM11GM(1,1)
GMnh GMnhNGM
11
11.1 11.2 11.3
11.1
12
12
12
k=k0kk0
k=12ni
i=12r)
i=12m)
1 1Xkk3
2
p1p2p3p1=0.1p2=0.13p3=0.083
4C33
11.2
Xk) k>j k=j k
11.3 1. 2. 3.
12 12.1 12.2 12.3 12.4
12.1
?, ? ,?
12.2
1Makridakis
2
,
Spivey Wrobleski:
33 ,
McNees:SpiveyWrobleski11
12.3
,
,
()();
12.4
Bates Granger
(1)
2.
n R2>0.9,n,,
2
tn t n
n=2:in>2:i
n
nn1
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Box-Jenkins
nARIMAARIMA
,,
2080
13 13.1
13.2
13.3
13.1
1.
2.
1 2
3. :
13.2
13.3
14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8
14.1
14.2
1 2 3
1.
2.
3.
14.3
1.
2.
3.
d1d2dm
14.4
1.
2.
3.
14.5
1.
2.
14.6
1. 2. 3.
1.0-+
14.7
1. 2.
14.8
121
1 2 3
1. 2. 3. 4.
1 700210403300906034000.70.3370.90.110
145789623606090402104021040 0.7 0.3 0.7 0.3 0.9 0.1 0.9 0.1 0.9 0.1 3 7 1227.51247.51295-280895420895609
42100.97400.17=12955407=280212950.7+2100.732800.3400.33=1227.582100.97400.17400=8959900.97+600.17=60968968957607=42038950.7+2100.73+4200.3+600.33=1247.5
2333
15 15.1
15.2
15.1
1 2 3, 4
AiBn n
1 2
3 4
1 2
15.2
1
2
1 9090%70%40%60%5
0.70.3
16 16.1 16.2 16.3 16.4 16.5
16.1
1 2 3
,
4
5
16.2
16.4
nndin
:
:
16.5
1 :
S1S2200150100202060
1 23 4
1 200
2 60
3
4 max(200200,60+20)=80
max(200150,6020)=50
max(200100,6060)=100
50
17 17.1 17.2 17.3 17.4 17.5
17.1
1
2
1
2 3
1. 123 2.
17.2 AHP
1 (2)
123 4 5
WiiiA
n 0(1) aii=1max=n
135792468
12
3 4
17.3
17.4
1
1 0
17.5 )
) xi
)
1 D1D2D3: A1:A2:A3:A4:A5:A6:
A1 A2 A3 A4 A5 A6 A1 1 1 4 3 3 4 A2 1 1 1/3 5 1 1/3 A3 1/4 3 1 7 1/5 1 A4 1/3 1/5 1/7 1 1/5 1/6 A5 1/3 1 5 5 1 3 A6 1/4 3 1 6 1/3 1
A1 D1 D2 D3 D1 1 1/3 1/2 D2 3 1 3 D3 2 1/3 1
A2 D1 D2 D3 D1 1 9 7 D2 1/9 1 1/5 D3 1/7 5 1
A3 D1 D2 D3 D1 1 1 1 D2 1 1 1 D3 1 1 1
A5 D1 D2 D3 D1 1 1/2 1 D2 2 1 2 D3 1 1/2 1
A6 D1 D2 D3 D1 1 6 4 D2 1/6 1 1/3 D3 1/4 3 1
A4 D1 D2 D3 D1 1 5 1 D2 1/5 1 1/5 D3 1 5 1
A1-A6
0.1 =0.37 0.38 0.25 D2