单方程第5题ARIMA模型例5.9建立中国GDP对数序列的ARIMA模型

1、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% level-3.61219910% level-3.243079*Ma

2、cKinnon (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(G

3、DP(-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-squared0.924706

4、S.D. dependent var7687.518S.E. of regression2109.437Akaike info criterion18.38472Sum squared resid75645293Schwarz 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%的显著性接受原假设，即存在单位根。第二步检验gdp一阶差分的平

5、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*MacKinnon (1996) one-sided p-v

6、alues.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(-1)1.0788250.2399344.4963

7、420.0003D(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.D. dependent var7687.518S.

8、E. of regression2109.437Akaike info criterion18.38472Sum squared resid75645293Schwarz 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，趋势项，滞后阶数为0，结果如下：Null

9、 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.Augmented Dickey-

10、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)-0.6330420.192319-3.2916260.0031C687.3110496.77491.3835460.1792R-squared0.311034

11、Mean 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)0.00

12、3074T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-3.7378535% level-2.99187810% leve

13、l-2.635542*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNGDP)Method: Least SquaresDate: 01/07/14 Time: 10:22Sample (adjusted): 1983 2006Included observations: 24 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNGDP(-1)-0.0083510.00791

14、4-1.0551470.3053D(LNGDP(-1)1.0160550.2103394.8305620.0001D(LNGDP(-2)-0.7383300.292511-2.5241090.0212D(LNGDP(-3)0.5338620.2936181.8182190.0857D(LNGDP(-4)-0.4116380.202529-2.0324880.0571C0.1786970.0899491.9866450.0624R-squared0.669413Mean dependent var0.153297Adjusted R-squared0.577584S.D. dependent v

15、ar0.064378S.E. of regression0.041842Akaike info criterion-3.297535Sum squared resid0.031513Schwarz criterion-3.003021Log likelihood45.57042Hannan-Quinn criter.-3.219400F-statistic7.289734Durbin-Watson stat1.834540Prob(F-statistic)0.000685有上述结果认为lngdp是非平稳序列第五步检验lngdp一阶差分平稳性，结果如下：Null Hypothesis: DLNG

16、DP has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=1)t-StatisticProb.*Augmented Dickey-Fuller test statistic-2.9991090.0482Test critical values:1% level-3.7114575% level-2.98103810% level-2.629906*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test Equa

17、tionDependent Variable: D(DLNGDP)Method: Least SquaresDate: 01/07/14 Time: 10:26Sample (adjusted): 1981 2006Included observations: 26 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.DLNGDP(-1)-0.4429080.147680-2.9991090.0064D(DLNGDP(-1)0.4209610.1875742.2442400.0347C0.0653850.0232682.8

18、101450.0099R-squared0.311077Mean dependent var0.000950Adjusted R-squared0.251171S.D. dependent var0.051436S.E. of regression0.044510Akaike info criterion-3.278037Sum squared resid0.045566Schwarz criterion-3.132872Log likelihood45.61448Hannan-Quinn criter.-3.236235F-statistic5.192728Durbin-Watson sta

19、t1.852831Prob(F-statistic)0.013771由上述结果，认为lngdp的一阶差分是平稳的，lngdp一阶差分序列相关图如下。6. 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 statistic1.9939371.0000Te

20、st critical values:1% level-4.3943095% level-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 adjustmentsVariableCoe

21、fficientStd. Errort-StatisticProb.GDP(-1)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

22、.4629R-squared0.944348Mean dependent var8564.483Adjusted R-squared0.924706S.D. dependent var7687.518S.E. of regression2109.437Akaike info criterion18.38472Sum squared resid75645293Schwarz criterion18.72832Log likelihood-213.6167Hannan-Quinn criter.18.47588F-statistic48.07816Durbin-Watson stat2.06951

23、8Prob(F-statistic)0.000000gdp序列以最大的p值，即100%的显著性接受原假设，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-

24、4.3943095% level-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-Statisti

25、cProb.GDP(-1)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 d

26、ependent var8564.483Adjusted R-squared0.924706S.D. dependent var7687.518S.E. of regression2109.437Akaike info criterion18.38472Sum squared resid75645293Schwarz criterion18.72832Log likelihood-213.6167Hannan-Quinn criter.18.47588F-statistic48.07816Durbin-Watson stat2.069518Prob(F-statistic)0.000000在1

27、6.66%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-2.9810

28、3810% level-2.629906*MacKinnon (1996) one-sided p-values.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)-0.633

29、0420.192319-3.2916260.0031C687.3110496.77491.3835460.1792R-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.

30、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-1.0

31、551470.7160Test critical values:1% level-3.7378535% level-2.99187810% level-2.635542*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(LNGDP)Method: Least SquaresDate: 01/07/14 Time: 10:22Sample (adjusted): 1983 2006Included observations: 24 after adjustm

32、entsVariableCoefficientStd. Errort-StatisticProb.LNGDP(-1)-0.0083510.007914-1.0551470.3053D(LNGDP(-1)1.0160550.2103394.8305620.0001D(LNGDP(-2)-0.7383300.292511-2.5241090.0212D(LNGDP(-3)0.5338620.2936181.8182190.0857D(LNGDP(-4)-0.4116380.202529-2.0324880.0571C0.1786970.0899491.9866450.0624R-squared0.

33、669413Mean dependent var0.153297Adjusted R-squared0.577584S.D. dependent var0.064378S.E. of regression0.041842Akaike info criterion-3.297535Sum squared resid0.031513Schwarz criterion-3.003021Log likelihood45.57042Hannan-Quinn criter.-3.219400F-statistic7.289734Durbin-Watson stat1.834540Prob(F-statis

34、tic)0.000685有上述结果认为lngdp是非平稳序列第五步检验lngdp一阶差分平稳性，结果如下：Null Hypothesis: DLNGDP has a unit rootExogenous: ConstantLag Length: 1 (Automatic - based on SIC, maxlag=1)t-StatisticProb.*Augmented Dickey-Fuller test statistic-2.9991090.0482Test critical values:1% level-3.7114575% level-2.98103810% level-2.629906*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(DLNGDP)Method: Least SquaresDate: 01/07/14 Time: 10:26Sample (adjusted): 1981 2006Included observations: 26 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.DLNGDP(-