2.2解：（1）因为是若平稳序列所以=即=0.0125（2）因为 , =1故=0.2, =0.04（3）=,其中为向前一步预测误差,h=100,=0.02*0.02同理故向前一步和两步的标准差分别为0.02和0.0200042.4解：代码：w=read.table(m-deciles08.txt)decile2=w,3;decile10=w,5Box.test(decile2,lag=12,type=Ljung)Box-Ljung testdata: decile2 X-squared = 55.7363, df = 12, p-value = 1.335e-07,从中可以看出拒绝原假设，即拒绝decile2前十二个间隔的自相关系数都为0Box.test(decile10,lag=12,type=Ljung) Box-Ljung testdata: decile10 X-squared = 10.6872, df = 12, p-value = 0.5559，因为P值大于0.5，不能拒绝原假设，即可认为Decile10前十二阶无序列自相关。b，decile2timeseris=ts(decile2,frequency=12,start=c(1970,1)plot(decile2timeseris)points(decile2timeseris,pch=*)从图中我们可以看出样本几乎是平稳的，我们对其做检验library(fUnitRoots)adfTest(decile2timeseris,lags=12,type=c(c)#平稳性检验Title: Augmented Dickey-Fuller TestTest Results: PARAMETER: Lag Order: 12 STATISTIC: Dickey-Fuller: -4.8996 P VALUE: 0.01从中可以看出无法拒绝原假设平稳性的假定acf(decile2timeseris,lag.max=36)pacf(decile2timeseris,lag.max=36)从自相关函数来看在间隔36,24,12以及1处显著不为0，如果接受季节性ARMA模型，m2=arima(decile2timeseris,order=c(1,0,0),seasonal=list(order=c(1,0,1),period=12)#结果如下Series: decile2timeseris ARIMA(1,0,0)(1,0,1)12 with non-zero mean Coefficients: ar1 sar1 sma1 intercept 0.1981 0.9891 -0.9389 0.0093s.e. 0.0454 0.0129 0.0392 0.0090sigma2 estimated as 0.003684: log likelihood=643.14AIC=-1276.28 AICc=-1276.15 BIC=-1255.54因此ARMA模型可以写成对残差进行检验看是否存在自相关Box.test(m2$residuals,lag=20,type=Ljung) Box-Ljung testdata: m2$residuals X-squared = 23.0335, df = 20, p-value = 0.2872从结果来看，无法拒绝残差无自相关的假设，因此可以认为该模型较好。（c），library(forecast)m2forecast=forecast.Arima(m2,h=12)Forecasts: Point Forecast Lo 80 Hi 80 Lo 95 Hi 95Jan 2009 0.048797473 -0.02900218 0.12659712 -0.07018682 0.1677818Dec 2009 0.012749089 -0.06662320 0.09212138 -0.10864035 0.1341385向前一步预测值为 0.048797473，向前十二步预测值为0.012749089。2.6代码：w=read.table(power6.txt)wtimeseries=ts(w)plot(wtimeseries)从图中可以看出序列是不平稳的，对其进行平稳性检验。plot(diff(wtimeseries)从图可以看出，差分后序列平稳，进行单位根检验发现确实拒绝存在单位根的假设。对其进行自相关和偏自相关检验。偏相关函数滞后期为24。建立ARIMA模型为ARMIA（24,1,0）wtimeseriesfor=arima(wtimeseries,order=c(24,1,0)Coefficients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 -0.3181 -0.1920 -0.0827 -0.2658 -0.0956 -0.0195 0.0603 -0.0869s.e. 0.0599 0.0629 0.0639 0.0636 0.0650 0.0651 0.0657 0.0659 ar9 ar10 ar11 ar12 ar13 ar14 ar15 ar16 ar17 0.0288 0.0149 0.0946 0.3286 0.2886 0.0911 0.1247 0.0578 -0.0107s.e. 0.0661 0.0662 0.0668 0.0640 0.0642 0.0665 0.0670 0.0675 0.0676 ar18 ar19 ar20 ar21 ar22 ar23 ar24 -0.0508 -0.0661 -0.1575 -0.0961 -0.0912 0.0534 0.2559s.e. 0.0677 0.0677 0.0674 0.0661 0.0667 0.0656 0.0617sigma2 estimated as 0.0004173: log likelihood=641.43AIC=-1232.87 AICc=-1227.36 BIC=-1143.66对残差进行自相关检验： Box-Ljung testdata: wtimeseriesfor$residuals X-squared = 7.3919, df = 12, p-value = 0.8307说明残差是在前十二个间隔期内是不自相关的，但是由于很多滞后项前面的系数很小，与0没有显著差别，我们应该将其剔除。m3=arima(wtimeseries,order=c(24,1,0),fixed=c(NA,NA,0,NA,NA,0,0,0,0,0,NA,NA,NA,NA,NA,0,0,0,0,NA,NA,NA,0,NA)icients: ar1 ar2 ar3 ar4 ar5 ar6 ar7 ar8 ar9 ar10 ar11 -0.2992 -0.1444 0 -0.2014 -0.0973 0 0 0 0 0 0.1476s.e. 0.0587 0.0562 0 0.0493 0.0494 0 0 0 0 0 0.0437 ar12 ar13 ar14 ar15 ar16 ar17 ar18 ar19 ar20 ar21 0.3789 0.3007 0.0912 0.0799 0 0 0 0 -0.1742 -0.0748s.e. 0.0520 0.0553 0.0539 0.0433 0 0 0 0 0.0478 0.0482 ar22 ar23 ar24 -0.0269 0 0.2428s.e. 0.0436 0 0.0585对残差做自相关性检验 Box-Ljung testdata: m3$residuals X-squared = 16.4389, df = 12, p-value = 0.172说明改进后的模型更合适故所求模型为: Rt=-0.2992ar1-0.1444ar2-0.2014ar4 -0.0973ar5 + 0.1476ar11 +0.3789ar12+0.3007ar13 +0.0912ar14+0.0799ar15-0.1742 ar20 -0.07ar21 -0.0269 ar22 +0.2428 ar242.8首先我们检验一下原序列是否存在单位根代码：w=read.table(d-ibm3dxwkdays8008.txt,header=T)names(w)w2=w,3w1=w,7w1timeseries=ts(w1)plot(w1timeseries)library(fUnitRoots)adfTest(w1timeseries,lag=12,type=c(c)通过散点图和单位根检验发现原序列确实是平稳的。将礼拜五设定为一个哑元,记t在礼拜五为1，在其他几天为0。F=rep(c(0,0,1,0,0),7320/5)F1=F-7320m1=lm(w1timeseriesF1)summary(m1)Call:lm(formula = w1timeseries F1)Residuals: Min 1Q Median 3Q Max -0.204956 -0.005169 0.000139 0.005349 0.115513 Coefficients: Estimate Std. Error t value Pr(|t|) (Intercept) 0.0002874 0.0001460 1.969 0.049 *F1 0.0003289 0.0003264 1.008 0.314 从中发现F前面系数并不显著无法说明不存在周五效应。建立模型m2=auto.arima(w1timeseries)m3=arima(w1timeseries,order=c(0,0