单方程题ARIMA模型例建立中国GDP对数序列的ARIMA模型.doc

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 root Exogenous: Constant, Linear Trend Lag Length: 4 (Automatic - based on SIC, maxlag=4) t-Statistic ??Prob.* Augmented Dickey-Fuller test statistic ?1.993937 ?1.0000 Test critical values: 1% level -4.394309 5% level -3.612199 10% level -3.243079 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 01/07/14 Time: 10:03 Sample (adjusted): 1983 2006 Included observations: 24 after adjustments Variable Coefficient Std. Error t-Statistic Prob.?? GDP(-1) 0.069206 0.034708 1.993937 0.0625 D(GDP(-1)) 1.078825 0.239934 4.496342 0.0003 D(GDP(-2)) -0.860946 0.406194 -2.119545 0.0491 D(GDP(-3)) 0.728386 0.501847 1.451411 0.1649 D(GDP(-4)) -0.813788 0.350036 -2.324869 0.0327 C -402.4700 1591.446 -0.252896 0.8034 @TREND(1980) 161.2485 214.6915 0.751071 0.4629 R-squared 0.944348 ????Mean dependent var 8564.483 Adjusted R-squared 0.924706 ????S.D. dependent var 7687.518 S.E. of regression 2109.437 ????Akaike info criterion 18.38472 Sum squared resid????Schwarz criterion 18.72832 Log likelihood -213.6167 ????Hannan-Quinn criter. 18.47588 F-statistic 48.07816 ????Durbin-Watson stat 2.069518 Prob(F-statistic) 0.000000 gdp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 root Exogenous: Constant, Linear Trend Lag Length: 4 (Automatic - based on SIC, maxlag=4) t-Statistic ??Prob.* Augmented Dickey-Fuller test statistic ?1.993937 ?1.0000 Test critical values: 1% level -4.394309 5% level -3.612199 10% level -3.243079 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(GDP) Method: Least Squares Date: 01/07/14 Time: 10:03 Sample (adjusted): 1983 2006 Included observations: 24 after adjustments Variable Coefficient Std. Error t-Statistic Prob.?? GDP(-1) 0.069206 0.034708 1.993937 0.0625 D(GDP(-1)) 1.078825 0.239934 4.496342 0.0003 D(GDP(-2)) -0.860