White检验

一、White检验

、用OLS法估计，并求出e2、x2序列。 、回归e2 c x x2得： Dependent Variable: E^2 Method: Least Squares Date: 11/11/11 Time: 21:06 Sample: 1 21

Included observations: 21

Coefficient Std. Error t-Statistic Prob. C 823375.5 130273.4 6.320365 0.0000 X -3605.578 553. -6.513091 0.0000 X2 4.742387 0.532352 8.908366 0.0000

R-squared 0.860705 Mean dependent var 351198.3 Adjusted R-squared 0.845228 S.D. dependent var 4261.0 S.E. of regression 178711.1 Akaike info criterion 27.159 Sum squared resid 5.75E+11 Schwarz criterion 27.30571 Log likelihood -282.1432 Hannan-Quinn criter. 27.18888 F-statistic 55.61118 Durbin-Watson stat 2.015035 Prob(F-statistic) 0.000000 X和X2的t检验值很显著。

、计算统计量n*R2，n*R2=21*0.860705=18.074805。由white 检验知，在ａ=0.05，查X2分布表得X20.05(2)=5.9915，n*R2=18.074805>X20.05(2)=5.9915,所以拒绝原假设，表明模型存在异方差

二、ARCH检验 、提出假设：

H0：ａ1=ａ2=ａ3，H1:ａj(j=1，2)中至少有一个不为0。 、回归原模型，求出残差e，并计算出残差平方序e2t-1、e2t-2,

并回归e2 c e2(-1) e2(-2)得

Dependent Variable: E2 Method: Least Squares Date: 11/11/11 Time: 22:09 Sample (adjusted): 3 21

Included observations: 19 after adjustments Coefficient Std. Error t-Statistic Prob. C 204070.3 100029.5 2.040101 0.0582 E2(-1) -0.078393 0.223052 -0.351457 0.7298 E2(-2) 0.267413 0.118184 2.262681 0.0379

R-squared 0.279746 Mean dependent var 279134.7 Adjusted R-squared 0.1714 S.D. dependent var 251501.6 S.E. of regression 226391.4 Akaike info criterion 27.186 Sum squared resid 8.20E+11 Schwarz criterion 27.79098 Log likelihood -259.5976 Hannan-Quinn criter. 27.66710 F-statistic 3.107188 Durbin-Watson stat 2.119843 Prob(F-statistic) 0.072425

、在H0成立的条件下，（n-p）*R渐进服从X2（p）。 （n-p）*R2=17*0.279746=4.755682>X20.1(2)=4.60517。拒绝原假设，说明存在异方差。