计量经济学上机作业答案(2)
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非平稳时间序列建模
一.确定消费与收入是否为平稳序列，如果是非平稳的，请确定单整的阶数；
对消费进行单位根检验
H0：r=1 H1：r<1
（常数）检验P值为0.2593，p值很大，接受原假设，消费是非平稳序列。
Null Hypothesis: CONS has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.665442 0.2593
Test critical values: 1% level -4.532598
5% level -3.673616
10% level -3.277364
另外，在同时有常数和变量或两者都没有（none）的检验中，p值都很大，所以也接受原假设，消费是非平稳序列。
Null Hypothesis: CONS has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.665442 0.2593
Test critical values: 1% level -4.532598
5% level -3.673616
10% level -3.277364
*MacKinnon (1996) one-sided p-values.
Warning: Probabilities and critical values calculated for 20 observations
and may not be accurate for a sample size of 19
Null Hypothesis: CONS has a unit root
Exogenous: None
Lag Length: 2 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic 2.082985 0.9874
Test critical values: 1% level -2.699769
5% level -1.961409
10% level -1.606610
*MacKinnon (1996) one-sided p-values.
Warning: Probabilities and critical values calculated for 20 observations
and may not be accurate for a sample size of 18
对消费数据一阶差分后回归的p值仍旧很大，所以仍不平稳
形式一：
Null Hypothesis: D(CONS) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.423252 0.1496 Test critical values: 1% level -3.857386
5% level -3.040391
10% level -2.660551
*MacKinnon (1996) one-sided p-values.
Warning: Probabilities and critical values calculated for 20 observations
And may not be accurate for a sample size of 18
形式二：
Null Hypothesis: D(CONS) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.757380 0.2283 Test critical values: 1% level -4.571559
5% level -3.690814
10% level -3.286909
*MacKinnon (1996) one-sided p-values.
Warning: Probabilities and critical values calculated for 20 observations
And may not be accurate for a sample size of 18
形式三：
Null Hypothesis: D(CONS) has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, maxlag=4)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.757380 0.2283 Test critical values: 1% level -4.571559
5% level -3.690814
10% level -3.286909
*MacKinnon (1996) one-sided p-values.
Warning: Probabilities and critical values calculated for 20 observations
and may not be accurate for a sample size of 18