ⅲ自回归项数为3（p=3） 同理得：

L2前的系数显著性检验无法通过,建模停止，确定ARCH模型的自回归项数为1或2： p=1时,h(t)=ω+（Stata语句）

. arch Dp,noconstant arch(1/1) arima(0,0,1) nolog . predict ehat,residual (1 missing value generated) . wntestq ehat

Portmanteau test for white noise ---------------------------------------

Portmanteau (Q) statistic = 45.1366 Prob > chi2(40) = 0.2659 . wntestb ehat

1.00?1εt?12

Cumulative Periodogram White-Noise Test0.000.000.200.400.600.800.100.200.30Frequency0.400.50Bartlett's (B) statistic = 0.91 Prob > B = 0.3754

P值均大于α，残差列通过白噪声检验。

. estat ic

Akaike's information criterion and Bayesian information criterion -----------------------------------------------------------------------------

Model | Obs ll(null) ll(model) df AIC BIC -------------+---------------------------------------------------------------

. | 251 . -1599.71 3 3205.42 3215.997 ----------------------------------------------------------------------------- 之前的ARIMA(0，1，1)(noconstant)模型的AIC/BIC如下：

ARCH(1)的AIC/BIC更小，模型更优。

p=2时,h(t)=ω+（Stata语句）

. arch Dp,noconstant arch(1/2) arima(0,0,1) nolog . predict eehat,residual . wntestq eehat

Portmanteau test for white noise ---------------------------------------

Portmanteau (Q) statistic = 45.1990 Prob > chi2(40) = 0.2638 . wntestb eehat

?1εt?12+?2εt?22

0.000.200.400.600.801.00Cumulative Periodogram White-Noise Test0.000.100.200.30Frequency0.400.50Bartlett's (B) statistic = 0.73 Prob > B = 0.6595

P值均大于α，残差列通过白噪声检验。 . estat ic

-----------------------------------------------------------------------------

Model | Obs ll(null) ll(model) df AIC BIC -------------+---------------------------------------------------------------

. | 251 . -1594.913 4 3197.826 3211.928 -----------------------------------------------------------------------------

ARCH(2)的AIC值和BIC值均小于ARCH(1)的，我们根据最小信息量准则选择ARCH(2)模型。回看：

★写出模型：

ARIMA(0,1,1) (noconstant):(1?B)xt=(1?0.33B)εt

εt=√htet

ARCH(2):h(t)=13710.6+0.27εt?12+0.13εt?22

预测（未来一年的月度水平） 手动延长时间至264期（252+12）： （Stata语句） . set obs 253

obs was 252, now 253

. replace n = 253 in 253 (1 real change made) …

. set obs 264

obs was 263, now 264

. replace n = 264 in 264 (1 real change made)

. predict x ,dynamic(时间)

(option xb assumed; linear prediction)