单方程第5题ARIMA模型例59建立中国GDP对数序列的ARIMA模型.docx

1、单方程第5题ARIMA模型例59建立中国GDP对数序列的ARIMA模型5.ARIMA模型第一步：gdp序列的平稳性检验。用ADF单位根检验：Null Hypothesis: GDP has a unit rootExogenous: Constant, Linear TrendLag Length: 4 (Automatic - based on SIC, maxlag=4)t-StatisticProb.*Augmented Dickey-Fuller test statistic1.9939371.0000Test critical values:1% level-4.3943095% l

2、evel-3.61219910% level-3.243079*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(GDP)Method: Least SquaresDate: 01/07/14 Time: 10:03Sample (adjusted): 1983 2006Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.GDP(-1

3、)0.0692060.0347081.9939370.0625D(GDP(-1)1.0788250.2399344.4963420.0003D(GDP(-2)-0.8609460.406194-2.1195450.0491D(GDP(-3)0.7283860.5018471.4514110.1649D(GDP(-4)-0.8137880.350036-2.3248690.0327C-402.47001591.446-0.2528960.8034TREND(1980)161.2485214.69150.7510710.4629R-squared0.944348Mean dependent var

4、8564.483Adjusted R-squared0.924706S.D. dependent var7687.518S.E. of regression2109.437Akaike info criterion18.38472Sum squared residSchwarz criterion18.72832Log likelihood-213.6167Hannan-Quinn criter.18.47588F-statistic48.07816Durbin-Watson stat2.069518Prob(F-statistic)0.000000gdp序列以最大的p值，即100%的显著性接

5、受原假设，即存在单位根。第二步检验gdp一阶差分的平稳性，结果如下：Null Hypothesis: GDP has a unit rootExogenous: Constant, Linear TrendLag Length: 4 (Automatic - based on SIC, maxlag=4)t-StatisticProb.*Augmented Dickey-Fuller test statistic1.9939371.0000Test critical values:1% level-4.3943095% level-3.61219910% level-3.243079*MacK

6、innon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(GDP)Method: Least SquaresDate: 01/07/14 Time: 10:03Sample (adjusted): 1983 2006Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.GDP(-1)0.0692060.0347081.9939370.0625D(GDP

7、(-1)1.0788250.2399344.4963420.0003D(GDP(-2)-0.8609460.406194-2.1195450.0491D(GDP(-3)0.7283860.5018471.4514110.1649D(GDP(-4)-0.8137880.350036-2.3248690.0327C-402.47001591.446-0.2528960.8034TREND(1980)161.2485214.69150.7510710.4629R-squared0.944348Mean dependent var8564.483Adjusted R-squared0.924706S.

8、D. dependent var7687.518S.E. of regression2109.437Akaike info criterion18.38472Sum squared residSchwarz criterion18.72832Log likelihood-213.6167Hannan-Quinn criter.18.47588F-statistic48.07816Durbin-Watson stat2.069518Prob(F-statistic)0.000000在16.66%的显著性水平下接受原假设，存在单位根，序列非平稳第三步：检验gdp二阶差分的平稳性，选择无常数项，趋势

9、项，滞后阶数为0，结果如下：Null Hypothesis: D2GDP has a unit rootExogenous: ConstantLag Length: 0 (Automatic - based on SIC, maxlag=0)t-StatisticProb.*Augmented Dickey-Fuller test statistic-3.2916260.0258Test critical values:1% level-3.7114575% level-2.98103810% level-2.629906*MacKinnon (1996) one-sided p-values

10、.Augmented Dickey-Fuller Test EquationDependent Variable: D(D2GDP)Method: Least SquaresDate: 01/07/14 Time: 10:15Sample (adjusted): 1981 2006Included observations: 26 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.D2GDP(-1)-0.6330420.192319-3.2916260.0031C687.3110496.77491.3835460.179

11、2R-squared0.311034Mean dependent var113.3808Adjusted R-squared0.282327S.D. dependent var2799.855S.E. of regression2371.914Akaike info criterion18.45459Sum squared resid1.35E+08Schwarz criterion18.55136Log likelihood-237.9096Hannan-Quinn criter.18.48245F-statistic10.83480Durbin-Watson stat1.868580Prob(F-statistic)0.003074T统计值小于相关临界值故认为是没有单位根的，由上述结果可见gdp序列是二阶单整序列第四步检验ln(gdp)稳定性Null Hypothesis: LNGDP has a unit rootExogenous: ConstantLag Length: 4 (Automatic - based on SIC, maxlag=6)t-StatisticProb.*Augmented Dickey-Fuller test statistic-1.0551470.7160Test critical values:1% level-3.73