1、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
2、后的五个数据是:0.6123 0.0034 0.4402 -0.4467 0.2232实验的结果和预测的数据近似四、实验结果(1)、y = Columns 1 through 15 0.8155 -0.4391 0.2045 -0.1154 -0.0922 -0.0081 -0.2689 0.2519 0.0992 -0.0336 0.1621 -0.3946 0.1324 0.1986 0.0537 Columns 16 through 30 -0.0733 0.1147 0.2208 -0.5821 0.4754 -0.7540 0.3979 -0.4497 0.6622 -0.9088
3、0.8496 -0.0729 0.5367 -0.0546 -0.0264 Columns 31 through 45 0.0152 -0.2958 0.3328 -0.3929 0.7116 -0.2288 0.0584 0.2072 -0.3647 0.1733 0.3225 -0.0230 -0.2727 0.5138 -0.2000 Columns 46 through 60 -0.2382 -0.1404 0.1971 0.0038 -0.1319 0.1596 -0.1507 -0.3597 -0.2426 -0.0320 -0.4666 0.1826 0.0662 -0.4496
4、 -0.1769 Columns 61 through 75 0.2256 -0.0359 -0.4613 -0.1884 -0.1893 0.2081 -0.5756 0.2360 -0.0196 0.2302 0.0454 -0.4450 0.2391 -0.2112 -0.0116 Columns 76 through 90 -0.3390 0.3926 -0.0520 0.2608 -0.1885 0.1755 -0.4913 0.2652 0.0462 0.3633 -0.4594 0.0488 0.3344 -0.4817 0.6131 Columns 91 through 105
5、 0.0160 -0.2783 -0.0825 -0.3974 -0.1673 0.2479 -0.4677 0.6432 -0.7378 0.1430 0.4028 -0.3180 0.0436 -0.2137 0.0018 Columns 106 through 120 -0.1079 0.1606 -0.4830 -0.1527 0.0563 0.3338 0.2206 -0.3767 -0.0986 0.4360 -0.5411 0.4922 0.1519 0.0677 0.3270 Columns 121 through 135 -0.6994 0.0846 0.2646 -0.23
6、92 0.5434 -0.1129 0.2596 -0.3200 -0.1292 -0.2617 -0.1414 0.0129 0.3477 -0.2323 0.4646 Columns 136 through 150 -0.3366 0.1728 -0.1599 0.0145 0.3923 -0.7455 0.2745 -0.6265 0.5942 -0.2302 0.6303 -0.3507 0.1245 -0.3809 0.3690 Columns 151 through 165 -0.0028 -0.1223 -0.4118 0.1834 0.1363 0.2067 0.2877 0.
7、1606 -0.2350 0.2712 0.0577 -0.3430 0.6244 -0.3304 0.3432 Columns 166 through 180 -0.4853 0.3593 0.2016 -0.2938 0.3436 -0.3280 0.3372 -0.0167 -0.0921 -0.0274 0.1728 0.2270 -0.2737 0.1004 0.0304 Columns 181 through 195 0.0463 0.1869 -0.1083 0.3457 -0.2319 -0.1657 0.3067 0.2864 0.1233 0.1246 -0.0948 -0
8、.3247 0.3727 -0.3731 -0.1211 Columns 196 through 210 0.1443 0.2307 0.0263 0.4826 0.1528 -0.5389 0.2052 -0.0828 -0.1852 0.2159 -0.5889 0.4479 -0.0858 0.5172 -0.0805 Columns 211 through 225 0.2915 -0.2547 0.2973 0.1128 -0.4883 0.7580 -0.0692 0.1462 -0.3400 0.5911 -0.3649 0.4662 -0.3761 0.7021 -0.8773
9、Columns 226 through 240 0.6149 -0.6015 0.7429 -0.6397 0.5896 -0.8239 0.3840 -0.2474 0.0928 0.0031 0.1147 -0.4600 0.6927 -0.1888 0.4119 Columns 241 through 255 0.0513 0.1372 -0.3869 0.0207 0.1130 -0.0355 -0.4178 -0.1436 -0.1368 -0.0034 -0.0238 0.4242 -0.1752 -0.0589 0.0159 Columns 256 through 270 0.0
10、870 -0.3942 0.5818 0.0838 0.0419 -0.4981 0.6309 -0.2937 0.3894 -0.6570 0.3454 -0.3455 -0.1127 0.4053 0.0792 Columns 271 through 285 -0.0991 0.5200 -0.6857 0.8088 -0.2482 0.1030 0.0547 0.4167 -0.1267 -0.1716 -0.0375 -0.2882 0.1751 -0.2028 0.0933 Columns 286 through 300 0.0512 -0.4616 0.1097 0.0382 -0
11、.3494 0.3446 -0.4746 0.3911 -0.2443 0.1211 -0.0361 0.4654 -0.4561 0.1937 -0.3163 Columns 301 through 315 0.1140 -0.2870 0.0778 -0.0468 0.2519 -0.3550 -0.1606 0.0461 -0.0627 -0.4452 0.4490 -0.0633 -0.1779 -0.1243 0.2881 Columns 316 through 330 0.0995 0.4225 -0.2970 0.5929 -0.4284 0.5787 -0.0415 -0.30
12、72 0.0905 -0.0372 0.2419 -0.0856 0.0156 -0.0647 -0.3709 Columns 331 through 345 0.1808 -0.2494 -0.0378 0.3761 0.0188 0.4377 -0.2222 -0.3436 0.3161 0.1139 0.4042 -0.5368 0.5472 -0.3282 0.6429 Columns 346 through 360 -0.1981 -0.1452 0.0426 -0.3550 0.6960 -0.5898 -0.0735 0.3024 0.2013 -0.3427 -0.0295 0
13、.4516 -0.6580 0.8620 -0.3498 Columns 361 through 375 0.5716 -0.6565 0.3753 -0.6591 0.7729 -0.4326 0.0962 -0.1867 0.4873 -0.4397 -0.1449 -0.2074 -0.3178 0.2701 -0.5509 Columns 376 through 390 0.3747 -0.6228 0.6685 -0.5528 0.6772 -0.8867 0.6654 0.0233 -0.2261 0.5335 -0.7399 0.0388 -0.2906 0.6191 -0.83
14、31 Columns 391 through 405 0.2974 0.3092 -0.4859 0.3094 -0.4075 0.4336 0.1805 0.1510 0.0695 -0.4135 -0.1399 -0.3956 0.0414 0.2903 0.2997 Columns 406 through 420 -0.6745 0.7510 -0.3595 0.2903 -0.4418 0.6047 -0.6238 0.6529 -0.2582 -0.1207 0.1794 -0.0099 0.1658 -0.4228 0.4071 Columns 421 through 435 -0
15、.5902 0.4174 -0.1437 0.2779 -0.0005 0.3771 -0.7285 0.2766 0.1020 -0.2580 0.5918 -0.2000 -0.2977 -0.2388 -0.3352 Columns 436 through 450 -0.0583 0.0536 -0.0761 0.2519 -0.0787 0.0596 -0.4638 -0.0099 -0.1141 -0.1506 0.3672 -0.4211 0.4077 0.2256 -0.1415 Columns 451 through 465 0.5383 -0.0165 0.4281 -0.6
16、609 0.7351 -0.0622 -0.3038 -0.1834 0.3801 -0.0214 0.1654 0.1482 0.0683 0.3398 -0.4453 Columns 466 through 480 0.2044 -0.4178 -0.1970 -0.2928 0.5379 -0.5041 0.2888 0.2290 -0.4180 0.6295 -0.2463 0.5488 -0.3631 0.7250 -0.5907 Columns 481 through 495 0.4094 -0.5807 0.3736 -0.3169 0.3632 -0.0588 0.4950 -
17、0.6249 0.0112 0.0579 0.4321 -0.7528 0.8520 -1.0184 0.6713 Columns 496 through 505 -0.7373 0.6876 -0.6894 0.8751 -0.9229 0.6123 0.0034 0.4402 -0.4467 0.2232(2)、r = 0.1431 -0.0942 0.0650 -0.0501 0.0385 -0.0339 0.0250 -0.0140 0.0079 -0.0027 0.0010 0.0004 -0.0003 0.0008 0.0018 0.0003 -0.0043 0.0038 -0.0
18、028 -0.0053 0.0123 -0.0132 0.0145 -0.0148 0.0154 -0.0116 0.0078 -0.0044 0.0021 -0.0009b = -0.6585 0.0364 -0.0670 0.0112 -0.0619 -0.0381 0.0557 -0.0091 0.0241 0.0075 0.0052 0.0187 0.0030 0.0378 0.0363 -0.0397 -0.0124 0.0042 -0.0922 0.0584 -0.0119 0.0252 -0.0114 0.0106 0.0510 -0.0183 0.0194 -0.0025 -0
19、.0008 0(3)、bic = -2.5006 -2.4896 -2.4818 -2.4696 -2.4611 -2.4502 -2.4410 -2.4288 -2.4170 -2.4047 -2.3924 -2.3805aic = -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 = Columns 16 through 29 -0.0397 -0.0124 0.0042 -0.0922 0.0584 -0.0119 0.0252 -0.0
20、114 0.0106 0.0510 -0.0183 0.0194 -0.0025 -0.0008p = 1.0e-003 * 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 0.
21、0000 0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 -
22、0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 0.0
23、000 -0.0000 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 0.0000 Columns 496 through 503 -0.0000 -0.0
24、000 0.0000 -0.0000 -0.0000 -0.0000 0.0027 -0.1059(5)、五、附录a1=-0.64;x(1)=0;r=zeros(1,30);for i=2:605 x(i)=a1*x(i-1)+unifrnd(-0.5,0.5);endfor i=1:505 y(i)=x(i+100);yybar=mean(y);30 for j=1:505-i r(i)=r(i)+(y(j)-ybar)*(y(j+i-1)-ybar); endr=r/505bar(r,r) b=zeros(1,30);for n=1:29 gamma=zeros(n,n); v=zeros
25、(n,1); for i=1:n v(i)=r(i+1); gamma(i,j)=r(abs(i-j)+1); a=inv(gamma)*v;t=0; for k=1: t=t+a(k)*r(k+1); sigma(n)=r(1)-t; b(n)=a(n);bfigurebar(b,b)axis(1,30,-1,1)%12 bic(i)=log(sigma(i)+i*log(505)/505; aic(i)=log(sigma(i)+2*i/505;bicaicsi=zeros(1,29);A=zeros(29);si(1)=r(1);a(1,1)=r(2)/si(1);for k=2: nu=0;de=0; si(k)=si(k-1)*(1-a(k-1,k-1);k-1 nu=nu+r(k-j+
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