R語(yǔ)言時(shí)間序列作業(yè)

R語(yǔ)言時(shí)間序列作業(yè)R語(yǔ)言時(shí)間序列作業(yè)R語(yǔ)言時(shí)間序列作業(yè)R語(yǔ)言時(shí)間序列作業(yè)編制僅供參考審核批準(zhǔn)生效日期地址：電話：傳真:郵編:2016年第二學(xué)期時(shí)間序列分析及應(yīng)用R語(yǔ)言課后作業(yè)第三章趨勢(shì)(a)data(hours);plot(hours,ylab='MonthlyHours',type='o')畫(huà)出時(shí)間序列圖(b)data(hours);plot(hours,ylab='MonthlyHours',type='l')type='o'表示每個(gè)數(shù)據(jù)點(diǎn)都疊加在曲線上；type='b'表示在曲線上疊加數(shù)據(jù)點(diǎn)，但是該數(shù)據(jù)點(diǎn)附近是斷開(kāi)的；type='l'表示只顯示各數(shù)據(jù)點(diǎn)之間的連接線段；type='p'只想顯示數(shù)據(jù)點(diǎn)。points(y=hours,x=time(hours),pch=(season(hours)))(a)data(hours);=lm(hours~time(hours)+I(time(hours)^2));summary用最小二乘法擬合二次趨勢(shì)，結(jié)果顯示如下：Call:lm(formula=hours~time(hours)+I(time(hours)^2))Residuals:Min1QMedian3QMaxCoefficients:EstimateStd.ErrortvaluePr(>|t|)(Intercept)+05+05***time(hours)+02+02***I(time(hours)^2)***---Signif.codes:0‘***’‘**’‘*’‘.’‘’1Residualstandarderror:on57degreesoffreedomMultipleR-squared:,AdjustedR-squared:F-statistic:on2and57DF,p-value:(b)plot(y=rstudent,x=(time(hours)),type='l',ylab='StandardizedResiduals')points(y=rstudent,x=(time(hours)),pch=(season(hours)))標(biāo)準(zhǔn)殘差的時(shí)間序列，應(yīng)用月度繪圖標(biāo)志。（為了更容易識(shí)別季節(jié)性）帶季節(jié)性圖標(biāo)的的殘差-時(shí)間圖(c)runs(rstudent)對(duì)標(biāo)準(zhǔn)差進(jìn)行游程檢驗(yàn)$pvalue[1]$[1]16$[1]$n1[1]31$n2[1]29$k[1]0結(jié)果解釋：P值為，表明非隨機(jī)性是合理的。(d)acf(rstudent)標(biāo)準(zhǔn)殘差的樣本自相關(guān)函數(shù)季節(jié)均值模型殘差的樣本自相關(guān)系數(shù)(e)qqnorm(rstudent);qqline(rstudent)（QQ圖）正態(tài)性可以通過(guò)正態(tài)得分或者分位數(shù)-分位數(shù)（QQ）圖來(lái)檢驗(yàn)。此處的直線型圖形支持了該模型中隨機(jī)項(xiàng)是正態(tài)分布的假設(shè)。hist(rstudent,xlab='StandardizedResiduals')標(biāo)準(zhǔn)殘差的直方圖（季節(jié)均值模型的標(biāo)準(zhǔn)殘差直方圖）(rstudent)正態(tài)性檢驗(yàn)（Shapiro-Wilk檢驗(yàn)）本質(zhì)是：計(jì)算殘差與相應(yīng)的正態(tài)分位數(shù)之間的相關(guān)系數(shù)。相關(guān)性越小，就越有理由否定正態(tài)性。Shapiro-Wilknormalitytestdata:rstudentW=,p-value=根據(jù)上面的檢驗(yàn)結(jié)果，我們不能拒絕模型的隨機(jī)項(xiàng)是正態(tài)分布的假設(shè)。第四章平穩(wěn)時(shí)間序列模型第五章非平穩(wěn)時(shí)間序列模型(a)ARMA(2,1)p=2,q=1,參數(shù)值φ和θφ1=1φ2=Θ1=(b)IMA(2,0)p=2,d=1,q=0,參數(shù)值φ和θ(c)ARMA(2,2)p=2,q=2,參數(shù)值φ和θφ1=φ2=Θ1=Θ2=(a)A:AR(2)φ1=φ2=B:IMA(1,1)Θ1=(b)一個(gè)是固定的一個(gè)是不固定的。(a)data(winnebago);(width=,height=3,pointsize=8)plot(winnebago,type='o',ylab='WinnebagoMonthlySales')時(shí)間序列圖表明公司的休閑車(chē)的銷(xiāo)量在逐漸增加。(b)plot(log(winnebago),type='o',ylab='Log(MonthlySales)')取對(duì)數(shù)之后的時(shí)間序列圖仍然呈現(xiàn)增加的趨勢(shì)，但是比沒(méi)有取對(duì)數(shù)之前增加的緩慢一些。(c)percentage=((winnebago-zlag(winnebago))/zlag(winnebago))(width=3,height=3,pointsize=8)plot(x=diff(log(winnebago))[-1],y=percentage[-1],ylab='PercentageChange',xlab='DifferenceofLogs')cor(diff(log(winnebago))[-1],percentage[-1])[1]結(jié)果顯示：認(rèn)為一致。第六章模型識(shí)別(a)(762534);series=(n=60,list(ar=,ma=)phi=;theta=;ACF=ARMAacf(ar=phi,ma=-theta,=10)plot(y=ACF[-1],x=1:10,xlab='Lag',ylab='ACF',type='h',ylim=c,.2));abline(h=0)(b)acf(series)第八章模型診斷(a)data(hare);model=arima(sqrt(hare),order=c(3,0,0))(width=,height=3,pointsize=8);acf(rstandard(model))殘差的樣本自相關(guān)圖(b)(model,lag=9)Box-Ljungtestdata:residualsfrommodelX-squared=,df=6,p-value=JB統(tǒng)計(jì)量結(jié)果表明不拒絕誤差項(xiàng)的獨(dú)立性。(c)對(duì)殘差進(jìn)行檢驗(yàn)。runs(rstandard(model))$pvalue[1]$[1]18$[1]$n1[1]13$n2[1]18$k[1]0P值為，不拒絕誤差項(xiàng)的獨(dú)立性。(d)(width=3,height=3,pointsize=8)qqnorm(residuals(model))殘差的正態(tài)QQ圖QQ圖看出有一點(diǎn)小的曲率，但是這種現(xiàn)象可能是倆個(gè)極端值造成的。(e)對(duì)殘差的正態(tài)性進(jìn)行shapiro-wilk檢驗(yàn)(residuals(model))Shapiro-Wilknormalitytestdata:residuals(model)W=,p-value=結(jié)果表明，我們不會(huì)拒絕通常意義水平的正態(tài)性。第九章預(yù)測(cè)(a)所以，(b)從上式中看出，(c)即2008年預(yù)測(cè)的95%預(yù)測(cè)極限為因?yàn)橛?，所以，第十章季?jié)模型(a)data(boardings);series=boardings[,1]plot(series,type='l',ylab='LightRail&BusBoardings')points(series,x=time(series),pch=(season(series)))(b)acf(series),='ma')滯后期為1，5，6，12，時(shí)候，存在顯著的自相關(guān)。(c)model=arima(series,order=c(0,0,3),seasonal=list(order=c(1,0,0),period=12));modelCall:arima(x=series,order=c(0,0,3),seasonal=list(order=c(1,0,0),period=12))Coefficients:ma1ma2ma3sar1intercept.sigma^2estimatedas:loglikelihood=,aic=所有的變量都是顯著的。(d)model2=arima(series,order=c(0,0,4),seasonal=list(order=c(1,0,0),period=12));model2Call:arima(x=series,order=c(0,0,4),seasonal=list(order=c(1,0,0),period=12))Coefficients:ma1ma2ma3ma4sar1intercept.sigma^2estimatedas:loglikelihood=,aic=模型2中AIC=，模型1中的AIC=，AIC越小越好，所以模型是過(guò)度擬合的。異方差時(shí)間序列模型library(TSA)data(CREF)=diff(log(CREF))*100(width=,height=,pointsize=8)plot(abs)(width=,height=,pointsize=8)plot^2)(a)>data(google)>plot(google)收益率數(shù)據(jù)的時(shí)間序列圖>acf(google)>pacf(google)根據(jù)ACF和PACF可以得知，無(wú)自相關(guān)。(b)計(jì)算google日收益率均值。>(google,alternative='greater') OneSamplet-testdata:googlet=,df=520,p-value=alternativehypothesis:truemeanisgreaterthan095percentconfidenceinterval:Infsampleestimates:meanofxx的均值為，備擇假設(shè)為：均值異于0，根據(jù)P值顯示，接受備擇假設(shè)。(c)McLeod-Li檢驗(yàn)ARCH效應(yīng)。>(width=,height=3,pointsize=8)>根據(jù)圖顯示，所有滯后值在5%的水平上均顯著。說(shuō)明數(shù)據(jù)具有ARCH特征。(d)識(shí)別GARCH模型，估計(jì)識(shí)別的模型并對(duì)擬合的模型進(jìn)行模型診斷檢驗(yàn)。>eacf(google^2)取值平方的樣本EACFAR/MA0123456789101112130xxoooooooxooox1xooooooooxooox2xooooooooxooox3xxxooooooxooox4xxxooooooooooo5xxxooooooooooo6xxxxoooooooooo7oxxooxoooooooo>eacf(abs(google))絕對(duì)值的樣本EACFAR/MA0123456789101112130xxxoooxooxooxx1xoooooooooooox2xxooooooooooox3xxxoooooooooox4xoxooooooooooo5xoxoxooooooooo6oxxxxxoooooooo7xoxxxoxooooooo根據(jù)上圖，得知設(shè)定GARCH(1,1)模型。Google日收益率的平方值相應(yīng)的樣本EACF也得知模型GARCH(1,1)符合。檢驗(yàn)?zāi)Ｐ停?gt;m1=garch(x=google,order=c(1,1))>summary(m1)Call:garch(x=google,order=c(1,1))Model:GARCH(1,1)Residuals:Min1QMedian3QMaxCoefficient(s):EstimateStd.ErrortvaluePr(>|t|)a0***a1***b1<2e-16***---Signif.codes:0‘***’‘**’‘*’‘.’‘’1DiagnosticTests: JarqueBeraTestdata:ResidualsX-squared=,df=2,p-va