R在水文时间序列分析的应用Word格式文档下载.docx
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whereitistheminimumofthisquantityand12.
method
Characterstringgivingthemethodusedtofitthemodel.Mustbeoneofthestringsinthedefaultargument(thefirstfewcharactersaresufficient).Defaultsto"
.
na.action
functiontobecalledtohandlemissingvalues.
series
namesfortheseries.Defaultstodeparse(substitute(x)).
在概率论中,一个时间序列是一串随机变量。
在统计学中,这样一些变量都会受时间影响:
比如每天在变的股票价格,每月一测的空气温度,每分钟病人的心率等等
数据:
北美五大湖之一的LakeHuron的1875-1972年每年的水位值这个时间序列大致的图像:
plot(LakeHuron,
ylab="
"
main="
LevelofLakeHuron"
)
AR
(1)模型:
x<
-LakeHuron
op<
-par(mfrow=c(2,1))
y<
-filter(x,.8,method="
recursive"
plot(y,main="
AR
(1)"
ylab="
acf(
y,
main=paste(
"
p="
signif(dwtest(y~1)$p.value,3)
)
par(op)
ACF和PCF图
-par(mfrow=c(3,1),
mar=c(2,4,1,2)+.1)
acf(x,xlab="
pacf(x,xlab="
spectrum(x,xlab="
main="
AR(p)模型使用Yule-walker法得出估计的参数值
y<
-ar(x,aic=TRUE,method="
regr=ar.ols(x,order=2,demean=FALSE,intercept=FALSE)
regr
结果:
Call:
ar.ols(x=x,order.max=2,demean=FALSE,intercept=FALSE)
Coefficients:
12
1.1319-0.1319
Orderselected2sigma^2estimatedas0.5281
预测1973值
>
1.1319*x[98]-0.1319*x[97]
[1]579.9692
参考书目:
IntroductoryTimeSerieswithR,AnalysisofTimeSeriesDataUsingR,TimeSeriesAnalysisandItsApplications--withRexamples,TimeSeriesAnalysisandItsApplications--withRexamples
参考网站:
http:
//zoonek2.free.fr/UNIX/48_R/15.html#2
MA(MovingAveragemodels)
Hereisasimplewayofbuildingatimeseriesfromawhitenoise:
justperformaMovingAverage(MA)ofthisnoise.
n<
-200
x<
-rnorm(n)
-(x[2:
n]+x[2:
n-1])/2
-par(mfrow=c(3,1),mar=c(2,4,2,2)+.1)
plot(ts(x),xlab="
whitenoise"
plot(ts(y),xlab="
MA
(1)"
acf(y,main="
-(x[1:
(n-3)]+x[2:
(n-2)]+x[3:
(n-1)]+x[4:
n])/4
MA(3)"
Youcanalsocomputethemovingaveragewithdifferentcoefficients.
-x[2:
n]-x[1:
(n-1)]
momentum
(1)"
-x[3:
n]-2*x[2:
(n-1)]+x[1:
(n-2)]
Momentum
(2)"
Insteadofcomputingthemovingaveragebyhand,youcanusethe"
filter"
function.
-filter(x,c(1,-2,1))
Whitenoise"
acf(y,na.action=na.pass,main="
TODO:
the"
side=1"
argument.
AR(Auto-Regressivemodels)
Anothermeansofbuildingatimeseriesistocomputeeachtermbyaddingnoisetotheprecedingterm:
thisiscalledarandomwalk.
Forinstance,
-200
-rep(0,n)
for(iin2:
n){
x[i]<
-x[i-1]+rnorm
(1)
}
Thiscanbewritten,moresimply,withthe"
cumsum"
-cumsum(x)
Moregenerally,onecanconsider
X(n+1)=aX(n)+noise.
Thisiscalledanauto-regressivemodel,orAR
(1),becauseonecanestimatethecoefficientsbyperformingaregressionofxagainstlag(x,1).
a<
-.7
-a*x[i-1]+rnorm
(1)
-x[-1]
-x[-n]
r<
-lm(y~x-1)
plot(y~x)
abline(r,col='
red'
abline(0,.7,lty=2)
Moregenerally,anAR(q)processisaprocessinwhicheachtermisalinearcombinationoftheqprecedingtermsandawhitenoise(withfixedcoefficients).
for(iin4:
-.3*x[i-1]-.7*x[i-2]+.5*x[i-3]+rnorm
(1)
AR(3)"
acf(x,main="
xlab="
pacf(x,main="
Youcanalsosimulatethosemodelswiththe"
arima.sim"
-arima.sim(list(ar=c(.3,-.7,.5)),n)
acf(x,xlab="
main="
pacf(x,xlab="
PACF
ThepartialAutoCorrelationFunction(PACF)providesanestimationofthecoefficientsofanAR(infinity)model:
wehavealreadyseenitonthepreviousexamples.Itcanbeeasilycomputedfromtheautocorrelationfunctionwiththe"
Yule-Walker"
equations.
Yule-WalkerEquations
Tocomputetheauto-correlationfunctionofanAR(p)processwhosecoefficientsareknown,
(1-a1B-a2B^2-...-apB^p)Y=Z
wejusthavetocomputethefirstautocorrelationsr1,r2,...,rp,andthenusetheYule-Walkerequations:
r(j)=a1r(j-1)+a2r(j-2)+...+apr(j-p).
YoucanalsousethemintheotherdirectiontocomputethecoefficientsofanARprocessfromitsautocorrelations.
FitanARMAmodeltoaunivariatetimeseriesbyconditionalleastsquares.Forexactmaximumlikelihoodestimationsee
arima0.
arma(x,order=c(1,1),lag=NULL,coef=NULL,
include.intercept=TRUE,series=NULL,qr.tol=1e-07,...)
anumericvectorortimeseries.
order
atwodimensionalintegervectorgivingtheordersofthemodeltofit.
order[1]
correspondstotheARpartand
order[2]
totheMApart.
lag
alistwithcomponents
ar
and
ma.Eachcomponentisanintegervector,specifyingtheARandMAlagsthatareincludedinthemodel.Ifboth,
order
andlag,aregiven,onlythespecificationfrom
lag
isused.
coef
IfgiventhisnumericvectorisusedastheinitialestimateoftheARMAcoefficients.ThepreliminaryestimatorsuggestedinHannanandRissanen(1982)isusedforthedefaultinitialization.
include.intercept
Shouldthemodelcontainanintercept?
namefortheseries.Defaultsto
deparse(substitute(x)).
qr.tol
the
tol
argumentfor
qr
whencomputingtheasymptoticstandarderrorsof
coef.
Examples
data(tcm)
-diff(tcm10y)
summary(r.arma<
-arma(r,order=c(1,0)))
-arma(r,order=c(2,0)))
-arma(r,order=c(0,1)))
-arma(r,order=c(0,2)))
-arma(r,order=c(1,1)))
plot(r.arma)
data(nino)
s<
-nino3.4
summary(s.arma<
-arma(s,order=c(20,0)))
summary(s.arma
<
-arma(s,lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL)))
acf(residuals(s.arma),na.action=na.remove)
pacf(residuals(s.arma),na.action=na.remove)
-arma(s,lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=12)))
-arma(s,lag=list(ar=c(1,3,7,10,12,13,16,17),ma=12)))
plot(s.arma)
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