Inverted MA Roots
Dependent Variable: AO Method: Least Squares
-.25
Date: 11/29/14 Time: 12:15 Sample (adjusted): 1983Q1 1997Q3 Included observations: 59 after adjustments Convergence achieved after 6 iterations MA Backcast: 1982Q3 1982Q4
MA(2)
R-squared
Coefficient
0.453752
Std. Error
0.121221
t-Statistic
3.743170
Prob.
0.0004
0.022542 37.28685 9.895699 9.930912 9.909445
0.178204 Mean dependent var 0.178204 S.D. dependent var 33.80163 Akaike info criterion 66267.92 Schwarz criterion -290.9231 Hannan-Quinn criter. 1.349606
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Dependent Variable: AO Method: Least Squares Date: 11/29/14 Time: 12:16 Sample (adjusted): 1983Q1 1997Q3 Included observations: 59 after adjustments Convergence achieved after 7 iterations MA Backcast: 1982Q2 1982Q4
MA(3)
R-squared
Coefficient
0.149485
Std. Error
0.134379
t-Statistic
1.112415
Prob.
0.2705
0.022542 37.28685 10.07764 10.11285
0.014218 Mean dependent var 0.014218 S.D. dependent var 37.02083 Akaike info criterion 79491.41 Schwarz criterion
Adjusted R-squared S.E. of regression Sum squared resid
Log likelihood Durbin-Watson stat
Inverted MA Roots
Dependent Variable: AO Method: Least Squares
-296.2904 Hannan-Quinn criter. 1.274100 .27-.46i
.27+.46i
-.53
10.09139
Date: 11/29/14 Time: 12:16 Sample (adjusted): 1983Q1 1997Q3 Included observations: 59 after adjustments Convergence achieved after 6 iterations MA Backcast: 1982Q1 1982Q4
MA(4)
R-squared
Coefficient
0.124299
Std. Error
0.133505
t-Statistic
0.931043
Prob.
0.3557
0.022542 37.28685 10.08045 10.11566 10.09420 -.42-.42i
0.011445 Mean dependent var 0.011445 S.D. dependent var 37.07285 Akaike info criterion 79715.00 Schwarz criterion -296.3733 Hannan-Quinn criter. 1.167643 .42+.42i
.42+.42i
-.42-.42i
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Inverted MA Roots
得到残差分别为：35.32950 33.80163 37.02083 37.07285 Matlab程序代码 clear all;
m=linspace(1,4,4);
cc=[35.32950 33.80163 37.02083 37.07285]; plot(m,cc);
37.53736.53635.53534.53433.511.522.533.54由图，可以判定为ma（2）模型
三、拟合
（1）使用EViews工具，最小二乘估计法，对ma(1),ma(2),ma(3)进行拟合，得出结果并进行分析
（2）利用Eviews软件，求出模型的参数，结果如下
Dependent Variable: AO Method: Least Squares Date: 11/29/14 Time: 12:35 Sample (adjusted): 1983Q1 1997Q3 Included observations: 59 after adjustments Convergence achieved after 8 iterations MA Backcast: 1982Q3 1982Q4
MA(1) MA(2)
R-squared
Coefficient
0.368233 0.484100
Std. Error
0.118032 0.119375
t-Statistic
3.119771 4.055283
Prob.
0.0028 0.0002
0.022542 37.28685 9.792365 9.862790 9.819856
0.283585 Mean dependent var 0.271016 S.D. dependent var 31.83572 Akaike info criterion 57770.25 Schwarz criterion -286.8748 Hannan-Quinn criter.
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood
Durbin-Watson stat
Inverted MA Roots
1.983636 -.18+.67i
-.18-.67i
（3）综上，模型可写为： xt?at?0.368at?1?0.484at?2
四、适应性检验
相关函数法 clear all;
z=[118.5 106.1 112.1 109.3 98.1 56.4 48.1 54.5 50.9 93.9 46.9 58.8 24.6 59.7 31.7 41.6 70 58.4 113.4 32.3 84.4 35.9 89.2 69.5 45.4 49.6 17.8 81.2 18.2 0.5 -53.9 -36.1 45.7 34.2 33.4 74.1 69.5 71.8 81.2 9 37.8 38.5 101.4 77.7 100.6 43.8 92.1 22.1 14.3 65.1 58.9 57.2 133.9 69.6 97.9 65.5 129.7 107.9 64.7]; ave=mean(z); for i=1:59
z(1,i)=z(1,i)-ave; end
a=zeros(1,59); a(1,1)=z(1,1); a(1,2)=z(1,2); for i=3:59
a(1,i)=a(1,i-1)*(-0.36)-a(1,i-2)*0.484 +z(1,i); end
autocorr(a); [a,b]=autocorr(a);
Sample Autocorrelation Function10.80.6Sample Autocorrelation0.40.20-0.2-0.40246810Lag1214161820
由图可知，在0.05的显著性水平下接受自相关函数等于零的假设，认为at是独立的
五、预测
（1）利用Eviews软件，根据后四个数据对模型进行预测，得到的预测值如下图
-3.4679411075
0196
-16.785095524
78437
0 0
（2）利用Matlab软件，对得出来的预测值进行求解零均值化和一阶差分的逆过程，得到最终的预测值，程序的代码为
x=[5253.8 5372.3 5478.4 5590.5 5699.8 5797.9 5854.3 5902.4 5956.9 6007.8 6101.7 6148.6 6207.4 6232.0 6291.7 6323.4 6365.0 6435.0 6493.4 6606.8 6639.1 6723.5 6759.4 6848.6 6918.1 6963.5 7013.1 7030.9 7112.1 7130.3 7130.8 7076.9 7040.8 7086.5 7120.7 7154.1 7228.2 7297.7 7369.5 7450.7 7459.7 7497.5 7536.0 7637.4