时间序列.docx
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时间序列.docx
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时间序列
实验报告
(2010/2011学年第二学期)
课程名称
应用时间序列分析
实验名称
时间序列分析
实验时间
2011-6-1至2011-6-13
指导单位
理学院
指导教师
唐诚
学生姓名
刘文文
班级学号
08005202
学院(系)
理学院
专业
统计学
一、实验题目
1、设
是[-0.5,0.5]上均匀分布的白噪声,
模型的参数为:
,
(1)在计算机上模拟产生一个符合此模型的长为505的序列片断
(2)用以上的前500个数据求出自协方差和篇相关系数,识别模型
(3)分别用AIC和BIC准则定阶,建立模型估计模型的参数
(4)检验模型的适应性
(5)用递推预测法预测后5个数据,与真实数据作比较,检验预测效果。
2、对问题的分析和所用原理Levinson递推公式法
首先计算样本的自协方差函数,接着画出自协方差函数的柱形图再用Yule-Walker方程求解偏相关系数并画出偏相关系数的柱形图
3、结论
以下的数据可以得知模型的残差是白噪声,可以通过检验
最后的五个数据是:
0.61230.00340.4402-0.44670.2232
实验的结果和预测的数据近似
四、实验结果
(1)、y=
Columns1through15
0.8155-0.43910.2045-0.1154-0.0922-0.0081-0.26890.25190.0992-0.03360.1621-0.39460.13240.19860.0537
Columns16through30
-0.07330.11470.2208-0.58210.4754-0.75400.3979-0.44970.6622-0.90880.8496-0.07290.5367-0.0546-0.0264
Columns31through45
0.0152-0.29580.3328-0.39290.7116-0.22880.05840.2072-0.36470.17330.3225-0.0230-0.27270.5138-0.2000
Columns46through60
-0.2382-0.14040.19710.0038-0.13190.1596-0.1507-0.3597-0.2426-0.0320-0.46660.18260.0662-0.4496-0.1769
Columns61through75
0.2256-0.0359-0.4613-0.1884-0.18930.2081-0.57560.2360-0.01960.23020.0454-0.44500.2391-0.2112-0.0116
Columns76through90
-0.33900.3926-0.05200.2608-0.18850.1755-0.49130.26520.04620.3633-0.45940.04880.3344-0.48170.6131
Columns91through105
0.0160-0.2783-0.0825-0.3974-0.16730.2479-0.46770.6432-0.73780.14300.4028-0.31800.0436-0.21370.0018
Columns106through120
-0.10790.1606-0.4830-0.15270.05630.33380.2206-0.3767-0.09860.4360-0.54110.49220.15190.06770.3270
Columns121through135
-0.69940.08460.2646-0.23920.5434-0.11290.2596-0.3200-0.1292-0.2617-0.14140.01290.3477-0.23230.4646
Columns136through150
-0.33660.1728-0.15990.01450.3923-0.74550.2745-0.62650.5942-0.23020.6303-0.35070.1245-0.38090.3690
Columns151through165
-0.0028-0.1223-0.41180.18340.13630.20670.28770.1606-0.23500.27120.0577-0.34300.6244-0.33040.3432
Columns166through180
-0.48530.35930.2016-0.29380.3436-0.32800.3372-0.0167-0.0921-0.02740.17280.2270-0.27370.10040.0304
Columns181through195
0.04630.1869-0.10830.3457-0.2319-0.16570.30670.28640.12330.1246-0.0948-0.32470.3727-0.3731-0.1211
Columns196through210
0.14430.23070.02630.48260.1528-0.53890.2052-0.0828-0.18520.2159-0.58890.4479-0.08580.5172-0.0805
Columns211through225
0.2915-0.25470.29730.1128-0.48830.7580-0.06920.1462-0.34000.5911-0.36490.4662-0.37610.7021-0.8773
Columns226through240
0.6149-0.60150.7429-0.63970.5896-0.82390.3840-0.24740.09280.00310.1147-0.46000.6927-0.18880.4119
Columns241through255
0.05130.1372-0.38690.02070.1130-0.0355-0.4178-0.1436-0.1368-0.0034-0.02380.4242-0.1752-0.05890.0159
Columns256through270
0.0870-0.39420.58180.08380.0419-0.49810.6309-0.29370.3894-0.65700.3454-0.3455-0.11270.40530.0792
Columns271through285
-0.09910.5200-0.68570.8088-0.24820.10300.05470.4167-0.1267-0.1716-0.0375-0.28820.1751-0.20280.0933
Columns286through300
0.0512-0.46160.10970.0382-0.34940.3446-0.47460.3911-0.24430.1211-0.03610.4654-0.45610.1937-0.3163
Columns301through315
0.1140-0.28700.0778-0.04680.2519-0.3550-0.16060.0461-0.0627-0.44520.4490-0.0633-0.1779-0.12430.2881
Columns316through330
0.09950.4225-0.29700.5929-0.42840.5787-0.0415-0.30720.0905-0.03720.2419-0.08560.0156-0.0647-0.3709
Columns331through345
0.1808-0.2494-0.03780.37610.01880.4377-0.2222-0.34360.31610.11390.4042-0.53680.5472-0.32820.6429
Columns346through360
-0.1981-0.14520.0426-0.35500.6960-0.5898-0.07350.30240.2013-0.3427-0.02950.4516-0.65800.8620-0.3498
Columns361through375
0.5716-0.65650.3753-0.65910.7729-0.43260.0962-0.18670.4873-0.4397-0.1449-0.2074-0.31780.2701-0.5509
Columns376through390
0.3747-0.62280.6685-0.55280.6772-0.88670.66540.0233-0.22610.5335-0.73990.0388-0.29060.6191-0.8331
Columns391through405
0.29740.3092-0.48590.3094-0.40750.43360.18050.15100.0695-0.4135-0.1399-0.39560.04140.29030.2997
Columns406through420
-0.67450.7510-0.35950.2903-0.44180.6047-0.62380.6529-0.2582-0.12070.1794-0.00990.1658-0.42280.4071
Columns421through435
-0.59020.4174-0.14370.2779-0.00050.3771-0.72850.27660.1020-0.25800.5918-0.2000-0.2977-0.2388-0.3352
Columns436through450
-0.05830.0536-0.07610.2519-0.07870.0596-0.4638-0.0099-0.1141-0.15060.3672-0.42110.40770.2256-0.1415
Columns451through465
0.5383-0.01650.4281-0.66090.7351-0.0622-0.3038-0.18340.3801-0.02140.16540.14820.06830.3398-0.4453
Columns466through480
0.2044-0.4178-0.1970-0.29280.5379-0.50410.28880.2290-0.41800.6295-0.24630.5488-0.36310.7250-0.5907
Columns481through495
0.4094-0.58070.3736-0.31690.3632-0.05880.4950-0.62490.01120.05790.4321-0.75280.8520-1.01840.6713
Columns496through505
-0.73730.6876-0.68940.8751-0.92290.61230.00340.4402-0.44670.2232
(2)、r=
Columns1through15
0.1431-0.09420.0650-0.05010.0385-0.03390.0250-0.01400.0079-0.00270.00100.0004-0.00030.00080.0018
Columns16through30
0.0003-0.00430.0038-0.0028-0.00530.0123-0.01320.0145-0.01480.0154-0.01160.0078-0.00440.0021-0.0009
b=
Columns1through15
-0.65850.0364-0.06700.0112-0.0619-0.03810.0557-0.00910.02410.00750.00520.01870.00300.03780.0363
Columns16through30
-0.0397-0.01240.0042-0.09220.0584-0.01190.0252-0.01140.01060.0510-0.01830.0194-0.0025-0.00080
(3)、bic=
-2.5006-2.4896-2.4818-2.4696-2.4611-2.4502-2.4410-2.4288-2.4170-2.4047-2.3924-2.3805
aic=
-2.5090-2.5063-2.5069-2.5030-2.5029-2.5004-2.4996-2.4957-2.4923-2.4884-2.4845-2.4808
(4)、c=
Columns1through15
-0.65850.0364-0.06700.0112-0.0619-0.03810.0557-0.00910.02410.00750.00520.01870.00300.03780.0363
Columns16through29
-0.0397-0.01240.0042-0.09220.0584-0.01190.0252-0.01140.01060.0510-0.01830.0194-0.0025-0.0008
p=
1.0e-003*
Columns1through15
000000000000000
Columns16through30
000000000000000
Columns31through45
000000000000000
Columns46through60
000000000000000
Columns61through75
000000000000000
Columns76through90
000000000000000
Columns91through105
000000000000000
Columns106through120
000000000000000
Columns121through135
000000000000000
Columns136through150
000000000000000
Columns151through165
000000000000000
Columns166through180
000000000000000
Columns181through195
000000000000000
Columns196through210
000000000000000
Columns211through225
000000000000000
Columns226through240
000000000000000
Columns241through255
000000000000000
Columns256through270
000000000000000
Columns271through285
000000000000000
Columns286through300
000000000000000
Columns301through315
000000000000000
Columns316through330
000000000000000
Columns331through345
000000000000000
Columns346through360
000000000-0.00000.0000-0.0000-0.0000-0.0000-0.0000
Columns361through375
0.00000.0000-0.00000.0000-0.00000.0000-0.0000-0.00000.00000.00000.0000-0.00000.0000-0.00000.0000
Columns376through390
0.00000.0000-0.00000.00000.00000.00000.00000.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000
Columns391through405
0.00000.0000-0.0000-0.0000-0.00000.00000.0000-0.0000-0.0000-0.0000-0.0000-0.00000.0000-0.0000-0.0000
Columns406through420
-0.0000-0.0000-0.00000.0000-0.0000-0.00000.00000.0000-0.00000.00000.0000-0.0000-0.00000.0000-0.0000
Columns421through435
0.00000.00000.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000-0.00000.00000.0000-0.0000
Columns436through450
0.00000.00000.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.0000-0.00000.0000
Columns451through465
0.00000.0000-0.0000-0.0000-0.00000.0000-0.00000.00000.00000.0000-0.00000.00000.00000.00000.0000
Columns466through480
-0.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.00000.00000.0000-0.00000.0000
Columns481through495
-0.0000-0.00000.0000-0.0000-0.00000.0000-0.00000.00000.00000.0000-0.00000.0000-0.00000.00000.0000
Columns496through503
-0.0000-0.00000.0000-0.0000-0.0000-0.00000.0027-0.1059
(5)、
五、附录
a1=-0.64;x
(1)=0;r=zeros(1,30);
fori=2:
605
x(i)=a1*x(i-1)+unifrnd(-0.5,0.5);
end
fori=1:
505
y(i)=x(i+100);
end
y
ybar=mean(y);
fori=1:
30
forj=1:
505-i
r(i)=r(i)+(y(j)-ybar)*(y(j+i-1)-ybar);
end
end
r=r/505
bar(r,'r')
b=zeros(1,30);
forn=1:
29
gamma=zeros(n,n);
v=zeros(n,1);
fori=1:
n
v(i)=r(i+1);
forj=1:
n
gamma(i,j)=r(abs(i-j)+1);
end
end
a=inv(gamma)*v;t=0;
fork=1:
n
t=t+a(k)*r(k+1);
end
sigma(n)=r
(1)-t;
b(n)=a(n);
end
b
figure
bar(b,'b')
axis([1,30,-1,1])%
fori=1:
12
bic(i)=log(sigma(i))+i*log(505)/505;
aic(i)=log(sigma(i))+2*i/505;
end
bic
aic
si=zeros(1,29);A=zeros(29);si
(1)=r
(1);a(1,1)=r
(2)/si
(1);
fork=2:
29
nu=0;de=0;
si(k)=si(k-1)*(1-a(k-1,k-1));
forj=1:
k-1
nu=nu+r(k-j+
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