时序第五章上机作业

5.1对原序列进行一阶差分：以线性模型为确定性模型，残差序列有：Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 0 0 0 0.184 0 0 0s.e. 0 0 0 0.096 0 0 0xt=xt-1+tt=0.18t-4+at5.2 程序如下： Box.test(tt,type=Box,lag=1) Box-Pierce testdata: ttX-squared = 7.2043, df = 1, p-value = 0.007273 非白噪声用AR（1）拟合 ttt tttCall:arima(x = tt, order = c(1, 0, 0), method = ML)Coefficients: ar1 intercept 均值不通过检验 0.6418 11.8016s.e. 0.1707 2.6969sigma2 estimated as 22.13: log likelihood = -62.58, aic = 131.16 ttt tttCall:arima(x = tt, order = c(1, 0, 0), include.mean = F, method = ML)Coefficients: ar1 0.9360s.e. 0.0672sigma2 estimated as 26.25: log likelihood = -65.15, aic = 134.3 Box.test(ttt$residuals,type=Ljung,lag=2) Box-Ljung testdata: ttt$residualsX-squared = 0.0196, df = 2, p-value = 0.9902 Box.test(ttt$residuals,type=Ljung,lag=3) Box-Ljung testdata: ttt$residualsX-squared = 3.9735, df = 3, p-value = 0.2643 Box.test(ttt$residuals,type=Ljung,lag=4) Box-Ljung testdata: ttt$residualsX-squared = 4.1526, df = 4, p-value = 0.3857 Box.test(ttt$residuals,type=Ljung,lag=5) Box-Ljung testdata: ttt$residualsX-squared = 4.2351, df = 5, p-value = 0.5161 Box.test(ttt$residuals,type=Ljung,lag=6) Box-Ljung testdata: ttt$residualsX-squared = 4.4922, df = 6, p-value = 0.6104 Box.test(ttt$residuals,type=Ljung,lag=7) Box-Ljung testdata: ttt$residualsX-squared = 4.5936, df = 7, p-value = 0.7094 Box.test(ttt$residuals,type=Ljung,lag=8) Box-Ljung testdata: ttt$residualsX-squared = 6.2873, df = 8, p-value = 0.6151 Box.test(ttt$residuals,type=Ljung,lag=9) Box-Ljung testdata: ttt$residualsX-squared = 6.7998, df = 9, p-value = 0.658 Box.test(ttt$residuals,type=Ljung,lag=10) Box-Ljung testdata: ttt$residualsX-squared = 8.0904, df = 10, p-value = 0.62残差为白噪声序列 tp tp$predTime Series:Start = 22 End = 26 Frequency = 1 1 11.232353 10.513812 9.841237 9.211687 8.6224095.3再做12步差分Coefficients: ma1 -0.4889s.e. 0.1205经过几个模型比较，最终参数通过显著性检验，残差项是白噪声。模型为：121xt=（1-0.49B）t5.4从自相关图和偏自相关图中可以看出，时间序列是平稳的。自相关系数1阶截尾，偏自相关系数1阶截尾，所以使用arma（1,1）模型。Coefficients: ar1 ma1 intercept 0.3020 0.2054 6.7394s.e. 0.1923 0.1952 0.8858sigma2 estimated as 26.6: log likelihood = -306.08, aic = 620.16可以发现，模型参数不显著 ar1 intercept 0.4616 6.7625s.e. 0.0885 0.9550sigma2 estimated as 26.88: log likelihood = -306.58, aic = 619.15Coefficients: ma1 intercept 0.4435 6.7102s.e. 0.0782 0.7504sigma2 estimated as 27.19: log likelihood = -307.15, aic = 620.3并且参数系数通过检验，残差序列可视为白噪声。所以，我们最终确定模型为AR（1）模型：xt=3.6409+0.4616*xt-1+t（2）画残差平方图，可以确定残差序列存在异方差：通过残差的acf，和残差平方的acf图，以及随机性检验得出残差非白噪声，可以假设残差有arch性质。得到条件异方差模型的残差项近似为白噪声，无arch效应。5.5一阶差分后，自相关系数图显示，除了延迟1阶和3阶，其他的自相关系数基本都在2倍标准差之内，有短期相关性，差分序列平稳。偏自相关系数图显示，除了前3期偏自相关系数在2倍标准差外，其他基本在内。arima(3,1,3）模型来模拟。arima(x = dsheep, order = c(3 1,4), method = CSS)Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 ma4 0.3394 0.0695 -0.6031 -0.9212 -0.4796 0.5143 -0.2698s.