非平稳时间序列实验报告.docx

实验报告 时间序列分析08 经济统计I60814030王思瑶、实验简介针对我国1978〜2002年中国支出法GDP （单位：亿元）进行非平稳性检验、平稳化方法、模型建立及预测，从而掌握对非平稳时间序列的分析 数据如下：1978~2002年中国支出法GDP （单位：亿元）年份GDP零均值化后GDP19783605.6-32539.9519794073.9-32071.6519804551.3-31594.2519814901.4-31244.1519825489.2-30656.3519836076.3-30069.2519847164.4-28981.1519858792.1-27353.45198610132.8-26012.75198711784-24361.55198814704-21441.55198916466-19679.55199018319.5-17826.05199121280.4-14865.15199225863.6-10281.95199334500.6-1644.95199446690.710545.15199558510.522364.95199668330.432184.85199774894.338748.75199879003.342857.75199982673.146527.55200089340.953195.35200198592.962447.352002107897.671752.05二、非平稳性检验进行非平稳性检验，先用两种方法检验零均值化GDP的平稳性:1 、 自相关、偏自相关函数检验法Date: 06/09/11 Time: 22:00Sample: 1978 2002Included observations: 25AutocorrelationPartial CorrelationACPACQ-StatProb. |****** |. |****** |10.7270.72714.8770.000. |**** |. | . |20.5300.00123.1110.000. |*** |. | . |30.365-0.04427.1990.000. |**. |. | . |40.240-0.02229.0550.000* . | .| . | 50.1780.04830.1290.000* . | .| . | 60.1590.05731.0220.000* . | .| . | 70.1480.02031.8380.000* . | .| . | 80.1360.00632.5720.000* . | .| . | 90.119-0.00133.1650.000* . | .| . | 100.091-0.01433.5400.000. | .| . | 110.057-0.02233.6990.000. | .| . | 120.020-0.03133.7190.001从上图可以看出：自相关函数是拖尾的，偏自相关函数是截尾的，但自相关函数是缓慢衰减 的，这说明序列存在一定的非平稳性。

2、单位根检验法在零均值化后数据窗口依次按Views-U nit Root Text进行单位根检验，如下：Null Hypothesis: GDP has a unit rootExogenous: ConstantLag Length: 5 (Automatic based on SIC, MAXLAG=5)t-StatisticProb.*Augme nted Dickey-Fuller test statistic-1.7657860.3847Test critical values:1% level-3.8315115% level-3.02997010% level-2.655194*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 19Augmented Dickey-Fuller Test EquationDependent Variable: D(GDP)Method: Least SquaresDate: 06/09/11 Time: 22:07Sample (adjusted): 1984 2002Included observations: 19 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.GDP(-1)-0.0701450.039725-1.7657860.1028D(GDP(-1))1.7803480.2582726.8933010.0000D(GDP(-2))-1.0152820.474855-2.1380880.0538D(GDP(-3))0.5564340.5527061.0067440.3339D(GDP(-4))-0.7314370.537091-1.3618480.1983D(GDP(-5))0.9944990.4185282.3761830.0350C-1668.8691507.690-1.1069050.2900一 一R-squared0.93364iMean dependent var5359.0i6Adjusted R-squared0.90046iS.D. dependent var3778.i65S.E. of regressionii92.002Akaike info criterioni7.28i97Sum squared residi705042iSchwarz criterioni7.62992Log likelihood-i57.i787F-statistic28.i3902Durbin-Watson stat2.ii0286Prob(F-statistic)0.000002原假设：零均值化后数据有单位根。

由结果知假设成立的概率为0.3847，大于显著性水 平 0.05，则不能拒绝原假设：序列存在单位根由于平稳性数据的单位根的绝对值均是小于1 的，现在序列出现了单位根，说明序列不 是平稳的通过上面两种方法说明：序列不是平稳的三、对序列进行平稳化处理把不平稳数据变为平稳化数据的方法是进行差分，在命令行中输入genr d1=d(gdp )对序列进 行一阶差分，得到差分后的数据di，然后对di进行单位根检验，得到如下结果：Null Hypothesis: D1 has a unit rootExogenous: ConstantLag Length: 2 (Automatic based on SIC, MAXLAG=5)t-StatisticProb.*Augme nted Dickey-Fuller test statistic-1.3857310.5693Test critical values:1% level-3.7880305% level-3.012363i0% level-2.646119*MacKinnon (i996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(Di)Method: Least SquaresDate: 06/09/ii Time: 22:28Sample (adjusted): i982 2002Included observations: 2i after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D1(-1)-0.1183970.085440-1.3857310.1837D(D1(-1))0.9295200.1897724.8980860.0001D(D1(-2))-0.5045280.219858-2.2947910.0347C717.1676455.27911.5752270.1336R-squared0.610638Mean dependent var426.4095Adjusted R-squared0.541927S.D. dependent var1863.610S.E. of regression1261.312Akaike info criterion17.28734Sum squared resid27045415Schwarz criterion17.48629Log likelihood-177.5170F-statistic8.887063Durbin-Watson stat2.188072Prob(F-statistic)0.000913由结果知假设成立的概率为 0.5693，大于显著性水平 0.05，则不能拒绝原假设：序列 存在单位根。

继续进行差分，在命令行中输入genr d2=d(d1)对序列进行一阶差分，得到差分后的数据d2, 然后对d2进行单位根检验，得到如下结果：Null Hypothesis: D2 has a unit rootExogenous: ConstantLag Length: 1 (Automatic based on SIC, MAXLAG=4)t-StatisticProb.*Augme nted Dickey-Fuller test statistic-3.9697560.0067Test critical values:1% level-3.7880305% level-3.01236310% level-2.646119*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(D2)Method: Least。