R语言知识学习时间序列作业任务

**2016年第二学期时间序列分析及应用R语言课后作业第三章 趋势3.4(a) data(hours);plot(hours,ylab='MonthlyHours',type='o')谢谢阅读画出时间序列图5404s5H4y0M45930931983 1984 1985 1986 1987Timedata(hours);plot(hours,ylab='MonthlyHours',type='l')精品文档放心下载5.40.4s5H4yl0tM45930931983 1984 1985 1986 1987Timetype='o' 表示每个数据点都叠加在曲线上；type='b' 表示在曲线上叠加数据点，但是该谢谢阅读数据点附近是断开的；type='l' 表示只显示各数据点之间的连接线段；type='p'只想显感谢阅读示数据点。points(y=hours,x=time(hours),pch=as.vector(season(hours)))感谢阅读**5404s5H4y0M45.930.933.10(a)

DDDDJSNSNANJMMJSOJFOJFMMSNJJMMAOJAAOMAAAJJMFJMJAJDAFMNJAOJSF19831984198519861987Timedata(hours);hours.lm=lm(hours~time(hours)+I(time(hours)^2));summary(hou谢谢阅读rs.lm)用最小二乘法拟合二次趋势，结果显示如下：Call:lm(formula=hours~time(hours)+I(time(hours)^2))感谢阅读Residuals:Min 1Q Median 3Q Max-1.00603-0.25431-0.02267 0.22884 0.98358谢谢阅读Coefficients:EstimateStd.ErrortvaluePr(>|t|)精品文档放心下载(Intercept) -5.122e+05 1.155e+05 -4.4334.28e-05***精品文档放心下载time(hours) 5.159e+02 1.164e+02 4.4314.31e-05***精品文档放心下载I(time(hours)^2)-1.299e-01 2.933e-02 -4.4284.35e-05***谢谢阅读---**Signif.codes: 0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1精品文档放心下载Residualstandarderror:0.423on57degreesoffreedom谢谢阅读MultipleR-squared: 0.5921, AdjustedR-squared: 0.5778感谢阅读F-statistic:41.37on2and57DF, p-value:7.97e-12谢谢阅读(b)plot(y=rstudent(hours.lm),x=as.vector(time(hours)),type='l',ylab='Standardiz精品文档放心下载edResiduals')points(y=rstudent(hours.lm),x=as.vector(time(hours)),pch=as.vector(season(h精品文档放心下载ours)))标准残差的时间序列，应用月度绘图标志。（为了更容易识别季节性）精品文档放心下载带季节性图标的的残差-时间图D2DSDNODsAJ1JlFuJMJdNMiDASMSeMJNNJFd0ASJOOzNMAJMAiJJJAMAAdOJJMAn1Mt-SFAJJ2F-F19831984198519861987as.vector(time(hours))**runs(rstudent(hours.lm))对标准差进行游程检验$pvalue[1]0.00012$observed.runs[1]16$expected.runs30.96667$n131$n229$k0结果解释：P值为0.00012，表明非随机性是合理的。精品文档放心下载acf(rstudent(hours.lm))标准残差的样本自相关函数季节均值模型残差的样本自相关系数**Seriesrstudent(hours.lm)4020FC 002-4-5 10 15Lagqqnorm(rstudent(hours.lm));qqline(rstudent(hours.lm))精品文档放心下载（QQ图）NormalQ-QPlot21elitnQ 0epma-2--2 -1 0 1 2TheoreticalQuantiles正态性可以通过正态得分或者分位数-分位数（QQ）图来检验。此处的直线型图形支持了精品文档放心下载该模型中随机项是正态分布的假设。hist(rstudent(hours.lm),xlab='StandardizedResiduals')谢谢阅读标准残差的直方图（季节均值模型的标准残差直方图）Histogramofrstudent(hours.lm)感谢阅读02y510F150-3 -2 -1 0 1 2 3StandardizedResidualsshapiro.test(rstudent(hours.lm))谢谢阅读**正态性检验（Shapiro-Wilk检验）本质是：计算残差与相应的正态分位数之间的相关系数。谢谢阅读相关性越小，就越有理由否定正态性。Shapiro-Wilknormalitytest精品文档放心下载data: rstudent(hours.lm)W=0.99385,p-value=0.9909谢谢阅读根据上面的检验结果，我们不能拒绝模型的随机项是正态分布的假设。感谢阅读第四章 平稳时间序列模型4.4-112-第五章 非平稳时间序列模型5.1(a) ARMA(2,1) p=2,q=1,参数值φ和θ谢谢阅读φ1=1 φ2=-0.25 Θ1=0.1IMA(2,0)p=2,d=1,q=0,参数值φ和θ感谢阅读ARMA(2,2)p=2,q=2,参数值φ和θφ1=0.5φ2=-0.5Θ1=0.5Θ2=-0.255.7(a)A:AR(2)φ1=0.9φ2=0.09谢谢阅读B:IMA(1,1)Θ1=0.1(b)一个是固定的一个是不固定的。5.11(a) data(winnebago);win.graph(width=6.5,height=3,pointsize=8)谢谢阅读plot(winnebago,type='o',ylab='WinnebagoMonthlySales')谢谢阅读时间序列图**s00e51Sy0to0M1oga0be05niW01967 1968 1969 1970 1971 1972精品文档放心下载Time表明公司的休闲车的销量在逐渐增加。plot(log(winnebago),type='o',ylab='Log(MonthlySales)')感谢阅读取对数之后的时间序列图0.)7l0Sy.toM0(.L041967 1968 1969 1970 1971 1972感谢阅读Time仍然呈现增加的趋势，但是比没有取对数之前增加的缓慢一些。感谢阅读percentage=na.omit((winnebago-zlag(winnebago))/zlag(winnebago))win.graph(width=3,height=3,pointsize=8)精品文档放心下载plot(x=diff(log(winnebago))[-1],y=percentage[-1],ylab='Percentage感谢阅读Change',xlab='DifferenceofLogs')精品文档放心下载cor(diff(log(winnebago))[-1],percentage[-1])精品文档放心下载[1]0.9646886**5.e1gn0ah.C1eg5at.ecr0P.050--0.5 0.0 0.5 1.0DifferenceofLogs结果显示：0.96认为一致。第六章 模型识别6.29(a) set.seed(762534);series=arima.sim(n=60,list(ar=0.4,ma=0.6))感谢阅读phi=0.4;theta=0.6;ACF=ARMAacf(ar=phi,ma=-theta,lag.max=10)精品文档放心下载plot(y=ACF[-1],x=1:10,xlab='Lag',ylab='ACF',type='h',ylim=c(-.2,.2));abline(h精品文档放心下载=0)2010.010-20-2 4 6 8 10Lagacf(series)Seriesseries4020FCA020-5 10 15Lag**第八章 模型诊断8.7(a) data(hare);model=arima(sqrt(hare),order=c(3,0,0))精品文档放心下载win.graph(width=6.5,height=3,pointsize=8);acf(rstandard(model))谢谢阅读残差的样本自相关图FCA

Seriesrstandard(model)30101-3-2 4 6 8 10 12 14LagLB.test(model,lag=9)Box-Ljungtestdata: residualsfrom model精品文档放心下载X-squared=6.2475,df=6,p-value=0.396感谢阅读JB统计量结果表明不拒绝误差项的独立性。(c)对残差进行检验。runs(rstandard(model))$pvalue[1]0.602$observed.runs[1]18$expected.runs16.09677$n113**$n218$k0P值为0.602，不拒绝误差项的独立性。win.graph(width=3,height=3,pointsize=8)精品文档放心下载qqnorm(residuals(model))残差的正态QQ图NormalQ-QPlot1slauQe1l-maS2--2 -1 0 1 2TheoreticalQuantiles图看出有一点小的曲率，但是这种现象可能是俩个极端值造成的。感谢阅读(e)对残差的正态性进行shapiro-wilk检验精品文档放心下载shapiro.test(residuals(model))感谢阅读Shapiro-Wilknormalitytest感谢阅读data: residuals(model)W=0.93509,p-value=0.06043感谢阅读结果表明，我们不会拒绝通常意义水平的正态性。第九章预测9.2(a)Y(1)51.1Y0.5Y51.1(10)0.5(11)10.5200720072006**所以，Y2007(2)51.1Y0.5Y51.1(10.5)0.5(10)11.5520082007(b)从上式中看出1.1-0,1,1.1(c)Y1，11001195%预测极限为20077.67-13.33.(d)因为有，Y(t)Y(t1)YY(1)t1t1ttt1所以，Y2008(1)Y2007(2)YY2007(1)11.551.11210.513.212008第十章季节模型10.12(a) data(boardings);series=boardings[,1]感谢阅读plot(series,type='l',ylab='LightRail&BusBoardings')谢谢阅读points(series,x=time(series),pch=as.vector(season(series)))谢谢阅读0S15ONs1F0gM6SJS1OFMAM5SNsAONMMJOAMFD&1FJF0JAAANMJtJ1JJJDL5JJDDJJM1D0D1200120022003200420052006Timeacf(as.vector(series),ci.type='ma')精品文档放心下载Seriesas.vector(series)4.02.0FCA 00.20-40-5 10 15Lag**滞后期为1，5，6，12，时候，存在显著的自相关。精品文档放心下载(c)model=arima(series,order=c(0,0,3),seasonal=list(order=c(1,0,0),period=12));精品文档放心下载modelCall:arima(x=series,order=c(0,0,3),seasonal=list(order=c(1,0,0),period=12))谢谢阅读Coefficients:ma1ma2ma3sar1intercept0.72900.61160.29500.877612.5455s.e.0.11860.11720.11180.05070.0354sigma^2estimatedas0.0006542: loglikelihood=143.54, aic=-277.09谢谢阅读所有的变量都是显著的。(d)model2=arima(series,order=c(0,0,4),seasonal=list(order=c(1,0,0),period=12));精品文档放心下载model2Call:arima(x=series,order=c(0,0,4),seasonal=list(order=c(1,0,0),period=12))精品文档放心下载Coefficients:ma1ma2ma30.72770.66860.4244s.e.0.12120.13270.1681sigma^2estimatedas0.0006279:感谢阅读

ma4 sar1 intercept0.1414 0.8918 12.54590.1228 0.0445 0.0419loglikelihood=144.22, aic=-276.45感谢阅读**模型2中AIC=-276.45，模型1中的AIC=-277.09，AIC越小越好，所以模型是过度拟合感谢阅读的。第十二章异方差时间序列模型12.1 library(TSA)data(CREF)r.cref=diff(log(CREF))*100感谢阅读win.graph(width=4.875,height=2.5,pointsize=8)感谢阅读plot(abs(r.cref))win.graph(width=4.875,height=2.5,pointsize=8)感谢阅读plot(r.cref^2)12.9(a)>data(google)>plot(google)收益率数据的时间序列图**>acf(google)>pacf(google)根据ACF和PACF可以得知，无自相关。(b)计算google日收益率均值。t.test(google,alternative='greater')感谢阅读OneSamplet-testdata: googlet=2.5689,df=520,p-value=0.00524感谢阅读**alternativehypothesis:truemeanisgreaterthan0感谢阅读95percentconfidenceinterval:精品文档放心下载0.000962967 Infsampleestimates:meanofx0.002685589x的均值为0.002685589，备择假设为：均值异于0，根据P值显示，0.00524接受备择谢谢阅读假设。(c)McLeod-Li检验ARCH效应。win.graph(width=4.875,height=3,pointsize=8)感谢阅读McLeod.Li.test(y=google)根据图显示，所有滞后值在5%的水平上均显著。说明数据具有ARCH特征。感谢阅读(d)识别GARCH模型，估计识别的模型并对拟合的模型进行模型诊断检验。精品文档放心下载>eacf(google^2)取值平方的样本EACFAR/MA012345678910111213感谢阅读0xxoooooooxo o o x精品文档放心下载**1xooooooooxo o o x谢谢阅读2xooooooooxo o o x感谢阅读3xxxooooooxo o o x感谢阅读4xxxoooooooo o o o谢谢阅读5xxxoooooooo o o o感谢阅读6xxxxooooooo o o o感谢阅读7oxxooxooooo o o o感谢阅读>eacf(abs(google))绝对值的样本EACFAR/MA012345678910111213谢谢阅读0xxxoooxooxo o x x感谢阅读1xoooooooooo o o x感谢阅读2xxooooooooo o o x谢谢阅读3xxxoooooooo o o x感谢阅读4xoxoooooooo o o o谢谢阅读5xoxoxoooooo o o o精品文档放心下载**6oxxxxxooooo o o o感谢阅读7xoxxxoxoooo o o o谢谢阅读根据上图，得知设定GARCH(1,1)模型。Google日收益率的平方值相应的样本EACF也得知模精品文档放心下载GARCH(1,1)符合。检验模型：m1=garch(x=google,order=c(1,1))谢谢阅读summary(m1)Call:garch(x=google,order=c(1,1))谢谢阅读Model:GARCH(1,1)Residuals:Min1QMedian3QMax-3.64597-0.464860.082320.653795.73937Coefficient(s):EstimateStd.ErrortvaluePr(>|t|)a05.058e-051.232e-054.1064.03e-05***a11.264e-012.136e-025.9203.21e-09***b17.865e-013.578e-0221.980<2e-16***---Signif.codes:0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘’1**DiagnosticTests:JarqueBeraTestdata: R