TS实证分析案例1(ARMA).docx

时间序列实证分析案例分析举例案例1现有某国1952-1988年的国民收入指数数据，请用时间序列分析的方法对此进行分析。步骤：（1）准备工作：在Eviews中建立workfile文件1.wfl，选择Annual，1952-1988；主菜单object-series-x1，生成变量序列x1；edit+,将粘贴板中的数据粘贴过来；则在变量框中建立了研究对象：变量x1（2）序列x1的平稳性检验：方法一（观察法）：打开变量x1，view-graph-line，观察其折线图可明显发现其不平稳性。方法二（ACF图法）：选择：correlogram-level，观察其自相关图 Correlogram of X1=Date: 06/09/14 Time: 11:14 Sample: 1 37 Included observations: 37 = Autocorrelation Partial Correlation AC PAC Q-Stat Prob = . |*| . |*| 1 0.894 0.894 32.011 0.000 . |* | . *| . | 2 0.773-0.127 56.648 0.000 . |* | . | . | 3 0.654-0.056 74.799 0.000 . |* | . | . | 4 0.538-0.056 87.476 0.000 . |* | . | . | 5 0.430-0.041 95.815 0.000 . |* | . |* . | 6 0.354 0.085 101.65 0.000 . |*. | . | . | 7 0.297 0.015 105.89 0.000 . |*. | . | . | 8 0.254 0.014 109.09 0.000 . |*. | . *| . | 9 0.208-0.060 111.33 0.000 . |* . | . *| . | 10 0.150-0.109 112.53 0.000 . |* . | . | . | 11 0.099 0.020 113.08 0.000 . | . | . | . | 12 0.057 0.004 113.27 0.000 . | . | . | . | 13 0.013-0.043 113.28 0.000 . | . | . | . | 14-0.033-0.053 113.34 0.000 . *| . | . | . | 15-0.072-0.037 113.68 0.000 . *| . | . | . | 16-0.106-0.021 114.45 0.000 可发现其ACF呈现明显的强趋势性，所以序列x1不平稳；方法三（单位跟ADF检验法）Unit Root Test（单位根检验）结果如下： Augmented Dickey-Fuller Unit Root Test on X1=Null Hypothesis: X1 has a unit root Exogenous: Constant Lag Length: 1 (Automatic based on SIC, MAXLAG=9) = t-Statistic Prob.* =Augmented Dickey-Fuller test statistic 0.487806 0.9839 Test critical values1% level -3.632900 5% level -2.948404 10% level -2.612874 =*MacKinnon (1996) one-sided p-values. T检验的p值为0.9839，所以不能拒绝x1序列有单位根的原假设，所以x1不平稳。（3）现在对x1序列做一阶差分：y1=(x1) 观察其平稳性：在Eviews主命令窗口输入series y1=x1-x1(-1) ，或者主菜单选择objects-series-y1，然后主命令窗口输入 y1=x1-x1(-1)，这两个步骤效果一致。如此可得到差分后的序列y1.按照（2）的方法同样可检验序列y1的平稳性，单位根检验的结果显示 Augmented Dickey-Fuller Unit Root Test on Y1=Null Hypothesis: Y1 has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=9) = t-Statistic Prob.* =Augmented Dickey-Fuller test statistic -3.156056 0.0315 Test critical values1% level -3.632900 5% level -2.948404 10% level -2.612874 =*MacKinnon (1996) one-sided p-values. P值=0.03150.05，所以y1是平稳的。（4）对平稳序列y1分析其指标特征（ACF或PACF）通过观察y1序列的ACF图与PACF图： Correlogram of Y1=Date: 06/09/14 Time: 11:35 Sample: 1 37 Included observations: 36 = Autocorrelation Partial Correlation AC PAC Q-Stat Prob = . |* | . |* | 1 0.538 0.538 11.304 0.001 . |*. | . *| . | 2 0.208-0.115 13.039 0.001 . |* . | . | . | 3 0.090 0.039 13.376 0.004 . *| . | .*| . | 4-0.142-0.270 14.242 0.007 . *| . | . |* . | 5-0.101 0.162 14.694 0.012 . *| . | . *| . | 6-0.118-0.178 15.330 0.018 . *| . | . | . | 7-0.148 0.031 16.361 0.022 . |* . | . |*. | 8 0.091 0.210 16.764 0.033 . |* . | . | . | 9 0.166 0.029 18.156 0.033 . | . | .*| . | 10-0.012-0.258 18.163 0.052 . | . | . | . | 11-0.031 0.044 18.217 0.077 . | . | . | . | 12-0.045 0.043 18.331 0.106 . *| . | . | . | 13-0.084-0.039 18.752 0.131 . *| . | . *| . | 14-0.101-0.156 19.383 0.151 . *| . | . |*. | 15-0.061 0.219 19.627 0.187 . | . | . | . | 16 0.027 0.009 19.675 0.235 首先后面的Q统计量检验的p值拒绝了y1是白噪声，另外可以看到ACF近似是拖尾的，PACF的一阶截尾性比较明显，所以初步考虑模型：AR(1)（5）建模：主菜单：QuickEstimate EquationY1 ar(1)回车 （或者：d（x1） ar（1）；或者主命令窗口 ls d(x1) ar(1)）实验结果如下：=Dependent Variable: Y1 Method: Least Squares Date: 06/09/14 Time: 11:40 Sample(adjusted): 3 37 Included observations: 35 after adjusting endpoints Convergence achieved after 2 iterations = Variable CoefficientStd. Errort-Statistic Prob. = AR(1) 0.652119 0.131116 4.973593 0.0000 =R-squared 0.234740 Mean dependent var 5.080000 Adjusted R-squared 0.234740 S.D. dependent var 9.082686 S.E. of regression 7.945457 Akaike info criteri7.011233 Sum squared resid 2146.430 Schwarz criterion 7.055671 Log likelihood -121.6966 Durbin-Watson stat 1.944132 =Inverted AR Roots .65 通过对参数1的显著性t检验，p值=0，高度显著；AIC值=7.05567，模型的显式形式为：Y1=0.652119*Y1（-1）+at, 或者：d（x1）=0.652119*d（x1）（-1）+at其中白噪声的标准差为7.7198（6）模型检验：（残差resid的白噪声检验）运用 JB卡方检验，p值=0.608，不能拒绝resid是白噪声，模型适合。（7）拟合： 将真实值、预报值、残差等都放在一个图中的结果如下：可见，拟合效果还可以。真实值、拟合值及残差的数值如下所示：（y1序列）= obs Actual Fitted Residual Residual Plot = 3 1.70000 1.04339 0.65661 | . * . | 4 8.20000 1.10860 7.09140 | . | *. | 5 5.00000 5.34738 -0.34738 | . * . | 6 3.60000 3.26060 0.33940 | . * . | 7 0.20000 2.34763 -2.14763 | . *| . | 8 -19.7000 0.13042 -19.8304 |* . | . | 9 -17.0000 -12.8468 -4.15325 | . * | . | 10 1.10000 -11.0860 12.1860 | . | . * | 11 4.00000 0.71733 3.28267 | . | * . | 12 10.2000 2.60848 7.59152 | . | * | 13 13.0000 6.65162 6.34838 | . | *. | 14 11.0000 8.47755 2.52245 | . | * . | 15 9.00000 7.17331 1.82669 | . |* . | 16 2.30000 5.86908 -3.56908 | . * | . | 17 -2.60000 1.49987 -4.09987 | . * | . | 18 0.60000 -1.69551 2.29551 | . |* . | 19 7.60000 0.39127 7.20873 | . | *. | 20 2.20000 4.95611 -2.75611 | . * | . | 21 -1.50000 1.43466 -2.93466 | . * | . | 22 12.6000 -0.97818 13.5782 | . | . * | 23 6.10000 8.21671 -2.11671 | . *| . | 24 3.10000 3.97793 -0.87793 | . *| . | 25 -3.20000 2.02157 -5.22157 | . * | . | 26 -4.00000 -2.08678 -1.91322 | . *| . | 27 6.10000 -2.60848 8.70848 | . | * | 28 10.3000 3.97793 6.32207 | . | *. | 29 -3.10000 6.71683 -9.81683 | *. | . | 30 12.0000 -2.02157 14.0216 | . | . * | 31 21.2000 7.82543 13.3746 | . | . * | 32 17.1000 13.8249 3.27507 | . | * . | 33 28.3000 11.1512 17.1488 | . | . * | 34 6.70000 18.4550 -11.7550 | * . | . | 35 7.70000 4.36920 3.33080 | . | * . | 36 11.8000 5.02132 6.77868 | . | *. | 37 6.20000 7.69501 -1.49501 | . *| . | X1原始序列的预报值： X1F= Last updated: 06/09/14 Modified: 1 37 / fit( 1 NA 2 NA 3 102.6434 4 104.4086 5 116.8474 6 119.7606 7 122.4476 8 120.4304 9 87.75325 10 72.51397 11 85.41733 12 91.30848 13 105.5516 14 120.3776 15 130.0733 16 137.7691 17 135.6999 18 129.9045 19 132.5913 20 144.7561 21 143.4347 22 139.5218 23 161.3167 24 163.1779 25 164.3216 26 157.0132 27 152.4915 28 165.1779 29 178.2168 30 166.3784 31 188.2254 32 215.4249 33 229.8512 34 265.4550 35 258.0692 36 266.4213 37 280.8950 （8）预报：对1989-1993年的国民收入指数进行预测：首先将样本期进行扩充：在Eviews主命令窗口中输入：Expand 1952 1993回车选择：Forecast-将Forecast Sample（预测样本期限）改为：1989 1993 ，可得到后5年的预测值为：283.4431，286.0798，287.7991，288.9304，289.6516（9）模型的优化选取：通过观察其ACF图及PACF图，可见AR（1）已能比较好的反应序列的主要相关特性，当然也可选取ARMA（1，1）模型进行比较：D(x1) ar(1) ma(1) 结果如下：=Dependent Variab