时间序列分析实验报告
Problem1:Estimate ARMA-ARCH model for financial series in arch序列.xls
◆create new integer-data workfile named arch1,import the data series named y
◆Estimate AR model by correlogram--eq01
◆Diagnostic checks:test whether there is serial correlation in the residuals by
Q-statistics and LM–test.
◆Test heteroskedasticity,give your reason briefly
◆Establish AR-ARCH(q)model for possible order q,and select the best one as your
final model(note:parameters,whether there is remaining ARCH effect in standardized
residuals and information criterions should be considered)
◆Write out the mean equation and variance equation---eq02
Problem2:Estimate ARMA-TGARCH(EGARCH)model for financial series in杠杆数据.xls
◆create a new integer-data workfile named杠杆;import data series named y
◆Estimate ARMA model by correlogram----eq01—
(sometimes the significance of coefficient can be omitted temporarily)
1.Diagnostic checks:test whether there is serial correlation in the residuals by
Q-statistics and LM–test.
2.Test heteroskedasticity(null hypothesis(H0):there is no ARCH in the residuals)
◆Correlogram of squared residuals----Q-statistic
◆ARCH-LM test:(In the Lag Specification dialog box you should specify
the lag order)
✧Establish ARMA-TGARCH--eq02,check whether there is leverage effect,give
your reason:
◆diagnostic checking on standardized residuals of eq02.
◆Write out mean equation and variance equation of eq02
◆You can try to establish ARMA-EGARCH model，check whether there is leverage effect and
give your reason:---eq03
◆diagnostic checking on standardized residuals of eq03.
◆Write out mean equation and variance equation---eq03
实验报告结果
Yt=0.477*Yt-1-0.208*Yt-2+Ut
（1-0.447*L+0.208*L^2）Yt=Ut
which is calculated with12correlation coefficients(and10
degrees of freedom)is Q(12)=12.101.Since p value(=0.278)is larger than0.05,there is
no serial correlation in the residuals under the5percent level
Establish an AR(1)-ARCH(1)model
Yt=0.439Yt-1+ξt
Ht^2=1.133+0.980ξt-1^2
the corresponding p value is0.318.This implies that the squared standardized residuals are not auto correlated.(12)11.525Q
(3.2)In LM test,the value of the test statistic is LM(2)=0.041,and the co80rresponding p value is 0.980.This implies that there exists no ARCH effect in the standardized residuals.
Ϭ^2=1.113/(1-0.980)=56.650
通过指定LM检验滞后的阶数为2，发现残差中不存在自相关性，截图如下：
(2.2)通过对残差平方的LBQ检验发现，残差平方中存在自相关性，截图如下：
（2.3）通过在ARCH-LM检验中指定滞后的阶数为2发现，条件异方差性存在
