应用时间序列.docx
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应用时间序列.docx
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应用时间序列
生产总值模型
——应用时间序列分析期末论文
2014年11月
班级:
信计1202姓名:
孟奥学号:
1130112210
信计1202李朔1130112206
一、实验目的:
掌握用Box-Jeakins方法及Paudit-Wu方法建模及预测
二、实验内容:
某地区1983—2005年各季度的实际国际生产总值的分析与预测
某地区1983—2005年各季度生产总值前64个数据如下:
t
观测值
t
观测值
t
观测值
1
5253.8
23
6759.4
45
7715.1
2
5372.3
24
6848.6
46
7815.7
3
5478.4
25
6918.1
47
7859.5
4
5590.5
26
6963.5
48
7951.6
5
5699.8
27
7013.1
49
7973.7
6
5797.9
28
7030.9
50
7988.0
7
5854.3
29
7112.1
51
8053.1
8
5902.4
30
7130.3
52
8112.0
9
5956.9
31
7130.8
53
8169.2
10
6007.8
32
7076.9
54
8303.1
11
6101.7
33
7040.8
55
8372.7
12
6148.6
34
7086.5
56
8470.6
13
6207.4
35
7120.7
57
8536.1
14
6232.0
36
7154.1
58
8665.8
15
6291.7
37
7228.2
59
8773.7
16
6323.4
38
7297.7
60
8838.4
17
6365.0
39
7369.5
61
8936.2
18
6435.0
40
7450.7
62
8995.3
19
6493.4
41
7459.7
63
9098.9
20
6606.8
42
7497.5
64
9237.1
21
6639.1
43
7536.0
22
6723.5
44
7637.4
试对前60个数据进行建模分析,并预测61—64个数据。
三、数据检验
1、检验是否平稳
法一:
图形检验
(1)根据表中数据我们先画出序列图并对序列图进行平稳性分析。
(2)Matlab程序代码
clearall;
t=linspace(1,60,60);
y=[5253.85372.35478.45590.55699.85797.95854.35902.45956.96007.86101.76148.66207.46232.06291.76323.46365.06435.06493.46606.86639.16723.56759.46848.66918.16963.57013.17030.97112.17130.37130.87076.97040.87086.57120.77154.17228.27297.77369.57450.77459.77497.57536.07637.47715.17815.77859.57951.67973.77988.08053.18112.08169.28303.18372.78470.68536.18665.88773.78838.4];
plot(t,y);
xlabel('时间t');
ylabel('观测值y');
title('数据对应的序列图');
(3)得到图
(1)
图
(1)
(4)观察图形,发现数据存在长期向上的趋势。
表示序列是不平稳的。
法二:
利用样本自相关函数进行检验
(1)用matlab做出原数据自相关函数的图
(2)Matlab程序代码
clearall;
t=linspace(1,59,59);
y=[5253.85372.35478.45590.55699.85797.95854.35902.45956.96007.86101.76148.66207.46232.06291.76323.46365.06435.06493.46606.86639.16723.56759.46848.66918.16963.57013.17030.97112.17130.37130.87076.97040.87086.57120.77154.17228.27297.77369.57450.77459.77497.57536.07637.47715.17815.77859.57951.67973.77988.08053.18112.08169.28303.18372.78470.68536.18665.88773.78838.4];
autocorr(y);
[a,b]=autocorr(y);
xlabel('k');
ylabel('自相关函数ρ');
title('原序列对应的自相关函数图');
(3)得到图
(2)
图
(2)
(4)观察图形发现,数据是缓慢衰减的,所以序列是不平稳的。
法三:
利用单位根检验进行判断:
(1)用matlab求出原始数据的单位根
(2)Matlab程序代码:
clearall;
t=linspace(1,60,60);
y=[5253.85372.35478.45590.55699.85797.95854.35902.45956.96007.86101.76148.66207.46232.06291.76323.46365.06435.06493.46606.86639.16723.56759.46848.66918.16963.57013.17030.97112.17130.37130.87076.97040.87086.57120.77154.17228.27297.77369.57450.77459.77497.57536.07637.47715.17815.77859.57951.67973.77988.08053.18112.08169.28303.18372.78470.68536.18665.88773.78838.4];
[h,pValue]=adftest(y,'model','ar','Lags',0:
2);
(3)
结果分析:
根据h的值可以知道,检验表明时间序列存在单位根,原序列不平稳。
(如果h=[111],则表明时间序列不存在单位根,原序列平稳。
)
数据平稳性综合分析:
该序列用三种方法得到结果相同,所以认为原序列不平稳。
2、平稳化
差分方法:
程序编译:
clearall;
y=[5253.85372.35478.45590.55699.85797.95854.35902.45956.96007.86101.76148.66207.46232.06291.76323.46365.06435.06493.46606.86639.16723.56759.46848.66918.16963.57013.17030.97112.17130.37130.87076.97040.87086.57120.77154.17228.27297.77369.57450.77459.77497.57536.07637.47715.17815.77859.57951.67973.77988.08053.18112.08169.28303.18372.78470.68536.18665.88773.78838.4];
z=diff(y,1);
运行结果:
118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7共59个数据.
3、再次检验
法一:
图形检验
(1)根据表中数据我们先画出序列图并对序列图进行平稳性分析。
(2)Matlab程序代码
clearall;
t=linspace(1,59,59);
z=[118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7];
plot(t,z);
plot(t,y);
xlabel('时间t');
ylabel('差分后的序列z');
title('差分后数据对应的序列图');
(3)得到图(4)
图(4)
(4)观察图形,发现数据存在上下波动。
表示序列是平稳的。
法二:
利用样本自相关函数进行检验
(1)用matlab做出原数据自相关函数的图
(2)Matlab程序代码
clearall;
t=linspace(1,59,59);
z=[118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7];
autocorr(z);
[a,b]=autocorr(z);
xlabel('k');
(3)得到图(5)
图(5)
(4)观察图形发现,当k增大时,自相关函数迅速衰减至蓝线内,所以序列是平稳的。
法三:
利用单位根检验进行判断:
(1)用matlab求出原始数据的单位根
(2)Matlab程序代码clearall;
clearall;
t=linspace(1,59,59);
z=[118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7];
[h,pValue]=adftest(z,'model','ar','Lags',0:
2);
图(6)
结果分析:
根据h的值可以知道,检验表明时间序列不存在单位根,原序列平稳。
数据平稳性综合分析:
该序列用三种方法得到结果相同,所以认为原序列平稳。
4、零均值化
程序编译:
clearall;
z=[118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7];
ave=mean(z);
fori=1:
59
z(1,i)=z(1,i)-ave;
end
得到:
57.744145.344151.344148.544137.3441-4.3559-12.6559-6.2559-9.855933.1441-13.8559-1.9559-36.1559-1.0559-29.0559-19.15599.2441-2.355952.6441-28.455923.6441-24.855928.44418.7441-15.3559-11.1559-42.955920.4441-42.5559-60.2559-114.6559-96.8559-15.0559-26.5559-27.355913.34418.744111.044120.4441-51.7559-22.9559-22.255940.644116.944139.8441-16.955931.3441-38.6559-46.45594.3441-1.8559-3.555973.14418.844137.14414.744168.944147.14413.9441
共59个数据。
四、模型建立及预测
Box-Jenkins方法建模
一、模型类型识别
(1)由平稳时间序列自相关和偏自相关函数的统计特性来初步确定时间序列模型的类型
(2)Matlab程序代码
z=[118.5106.1112.1109.398.156.448.154.550.993.946.958.824.659.731.741.67058.4113.432.384.435.989.269.545.449.617.881.218.20.5-53.9-36.145.734.233.474.169.571.881.2937.838.5101.477.7100.643.892.122.114.365.158.957.2133.969.697.965.5129.7107.964.7];
ave=mean(z);
fori=1:
59
z(1,i)=z(1,i)-ave;
endsubplot(1,2,1),autocorr(z);
[a,b]=autocorr(z);
title('差分序列的自相关函数图');
subplot(1,2,2),parcorr(z);
[c,d]=parcorr(z);
title('差分序列的偏自相关函数图');、
结果:
由图,初步判定差分后的序列适合MA(3)模型。
二、定阶
残差方差图定阶法
使用EViews工具,结果如下
(1)
DependentVariable:
AO
Method:
LeastSquares
Date:
11/29/14Time:
12:
13
Sample(adjusted):
1983Q11997Q3
Includedobservations:
59afteradjustments
Convergenceachievedafter33iterations
MABackcast:
1982Q4
Coefficient
Std.Error
t-Statistic
Prob.
MA
(1)
0.253309
0.126592
2.000983
0.0501
R-squared
0.102233
Meandependentvar
0.022542
AdjustedR-squared
0.102233
S.D.dependentvar
37.28685
S.E.ofregression
35.32950
Akaikeinfocriterion
9.984117
Sumsquaredresid
72394.05
Schwarzcriterion
10.01933
Loglikelihood
-293.5315
Hannan-Quinncriter.
9.997863
Durbin-Watsonstat
1.781594
InvertedMARoots
-.25
DependentVariable:
AO
Method:
LeastSquares
Date:
11/29/14Time:
12:
15
Sample(adjusted):
1983Q11997Q3
Includedobservations:
59afteradjustments
Convergenceachievedafter6iterations
MABackcast:
1982Q31982Q4
Coefficient
Std.Error
t-Statistic
Prob.
MA
(2)
0.453752
0.121221
3.743170
0.0004
R-squared
0.178204
Meandependentvar
0.022542
AdjustedR-squared
0.178204
S.D.dependentvar
37.28685
S.E.ofregression
33.80163
Akaikeinfocriterion
9.895699
Sumsquaredresid
66267.92
Schwarzcriterion
9.930912
Loglikelihood
-290.9231
Hannan-Quinncriter.
9.909445
Durbin-Watsonstat
1.349606
DependentVariable:
AO
Method:
LeastSquares
Date:
11/29/14Time:
12:
16
Sample(adjusted):
1983Q11997Q3
Includedobservations:
59afteradjustments
Convergenceachievedafter7iterations
MABackcast:
1982Q21982Q4
Coefficient
Std.Error
t-Statistic
Prob.
MA(3)
0.149485
0.134379
1.112415
0.2705
R-squared
0.014218
Meandependentvar
0.022542
AdjustedR-squared
0.014218
S.D.dependentvar
37.28685
S.E.ofregression
37.02083
Akaikeinfocriterion
10.07764
Sumsquaredresid
79491.41
Schwarzcriterion
10.11285
Loglikelihood
-296.2904
Hannan-Quinncriter.
10.09139
Durbin-Watsonstat
1.274100
InvertedMARoots
.27-.46i
.27+.46i
-.53
DependentVariable:
AO
Method:
LeastSquares
Date:
11/29/14Time:
12:
16
Sample(adjusted):
1983Q11997Q3
Includedobservations:
59afteradjustments
Convergenceachievedafter6iterations
MABackcast:
1982Q11982Q4
Coefficient
Std.Error
t-Statistic
Prob.
MA(4)
0.124299
0.133505
0.931043
0.3557
R-squared
0.011445
Meandependentvar
0.022542
AdjustedR-squared
0.011445
S.D.dependentvar
37.28685
S.E.
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