时间序列例子.docx
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时间序列例子.docx
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时间序列例子
yield<-c(15.2,16.9,15.3,14.9,15.7,15.1,16.7)
>yield<-ts(yield,start=1884)
>plot(yield)
plot(yield,type="p")
plot(yield,type="o")
plot(yield,type="h")
plot(yield,type="o",pch=17)
plot(yield,lty=2)
>plot(yield,lwd=2)
>plot(yield,main='1884-1890',xlab='年份',ylab='产量')
plot(yield)
>abline(v=1887,lty=2)
>plot(yield)
>abline(v=c(1885,1889),lty=2)
>plot(yield)
>abline(h=c(15.5,16.5),lty=2)
>library(TSA)
>data(oil.price)p88石油价格时间序列
>oil.price
JanFebMarAprMayJunJulAugSepOctNovDec
198622.9315.4512.6112.8415.3813.4311.5815.1014.8714.9015.2216.11
198718.6517.7518.3018.6819.4420.0721.3420.3119.5319.8618.8517.27
198817.1316.8016.2017.8617.4216.5315.5015.5214.5413.7714.1416.38
198918.0217.9419.4821.0720.1220.0519.7818.5819.5920.1019.8621.10
199022.8622.1120.3918.4318.2016.7018.4527.3133.5136.0432.3327.28
199125.2320.4819.9020.8321.2320.1921.4021.6921.8923.2322.4619.50
199218.7919.0118.9220.2320.9822.3821.7721.3421.8821.6820.3419.41
199319.0320.0920.3220.2519.9519.0917.8918.0117.5018.1516.6114.51
199415.0314.7814.6816.4217.8919.0619.6518.3817.4517.7218.0717.16
199518.0418.5718.5419.9019.7418.4517.3218.0218.2317.4317.9919.03
199618.8519.0921.3323.5021.1620.4221.3021.9023.9724.8823.7025.23
199725.1322.1820.9719.7020.8219.2619.6619.9519.8021.3220.1918.33
>head(oil.price)
[1]22.9315.4512.6112.8415.3813.43
>tail(oil.price)
[1]64.9865.5962.2658.3259.4165.48
>plot(oil.price)
as.vector(oil.price)
[1]22.9315.4512.6112.8415.3813.4311.5815.1014.8714.9015.2216.1118.6517.7518.3018.6819.4420.0721.34
[20]20.3119.5319.8618.8517.2717.1316.8016.2017.8617.4216.5315.5015.5214.5413.7714.1416.3818.0217.94
[39]19.4821.0720.1220.0519.7818.5819.5920.1019.8621.1022.8622.1120.3918.4318.2016.7018.4527.3133.51
[58]36.0432.3327.2825.2320.4819.9020.8321.2320.1921.4021.6921.8923.2322.4619.5018.7919.0118.9220.23
[77]20.9822.3821.7721.3421.8821.6820.3419.4119.0320.0920.3220.2519.9519.0917.8918.0117.5018.1516.61
[96]14.5115.0314.7814.6816.4217.8919.0619.6518.3817.4517.7218.0717.1618.0418.5718.5419.9019.7418.45
[115]17.3218.0218.2317.4317.9919.0318.8519.0921.3323.5021.1620.4221.3021.9023.9724.8823.7025.2325.13
[134]22.1820.9719.7020.8219.2619.6619.9519.8021.3220.1918.3316.7216.0615.1215.3514.9113.7214.1713.47
[153]15.0314.4613.0011.3512.5112.0114.6817.3117.7217.9220.1021.2823.8022.6925.0026.1027.2629.3729.84
[172]25.7228.7931.8229.7031.2633.8833.1134.4228.4429.5929.6127.2427.4928.6327.6026.4227.3726.2022.17
[191]19.6419.3919.7120.7224.5326.1827.0425.5226.9728.3929.6628.8426.3529.4632.9535.8333.5128.1728.11
[210]30.6630.7531.5728.3130.3431.1132.1334.3134.6836.7436.7540.2738.0240.7844.9045.9453.2848.4743.15
[229]46.8448.1554.1952.9849.8356.3558.9964.9865.5962.2658.3259.4165.48
>acf(as.vector(oil.price),main='SampleACFoftheOilPriceTimeSeries',xaxp=c(0,24,12))
acf(oil.price,main='SampleACFoftheOilPriceTimeSeries')
>pacf(as.vector(oil.price),main='SampleACFoftheOilPriceTimeSeries',xaxp=c(0,24,12))
plot(log(oil.price))
单位根检验
>adf.test(log(oil.price))
AugmentedDickey-FullerTest
data:
log(oil.price)
Dickey-Fuller=-1.1119,Lagorder=6,p-value=0.9189
alternativehypothesis:
stationary
>plot(diff(log(oil.price)))
白噪声检验
>for(iin1:
2)print(Box.test(diff(log(oil.price)),type='Ljung-Box',lag=6*i))
Box-Ljungtest
data:
diff(log(oil.price))
X-squared=18.5959,df=6,p-value=0.004903
Box-Ljungtest
data:
diff(log(oil.price))
X-squared=24.3938,df=12,p-value=0.01797
acf(diff(as.vector(log(oil.price))),main='SampleACFoftheDifferenceoftheOilPriceTimeSeries',xaxp=c(0,24,12))
>pacf(diff(as.vector(log(oil.price))),main='SamplePACFoftheDifferenceoftheOilPriceTimeSeries',xaxp=c(0,24,12))
>eacf(diff(log(oil.price)))
AR/MA
012345678910111213
0xooooooooooooo
1xxooooooooxooo
2oxoooooooooooo
3oxoooooooooooo
4oxxooooooooooo
5oxoxoooooooooo
6oxoxoooooooooo
7xxoxoooooooooo
>res=armasubsets(y=diff(log(oil.price)),nar=7,nma=7,
+y.name='test',ar.method='ols')
>plot(res)
>library(forecast)
>auto.arima(log(oil.price))
Series:
log(oil.price)
ARIMA(0,1,1)
Coefficients:
ma1
0.2956
s.e.0.0693
sigma^2estimatedas0.006717:
loglikelihood=260.29
AIC=-516.58AICc=-516.53BIC=-509.62
条件最小二乘估计
>arima(log(oil.price),order=c(0,1,1),method='CSS')
Call:
arima(x=log(oil.price),order=c(0,1,1),method="CSS")
Coefficients:
ma1
0.2731
s.e.0.0681
sigma^2estimatedas0.006731:
partloglikelihood=259.58
>arima(log(oil.price),order=c(0,1,1),method='ML')
极大似然估计
Call:
arima(x=log(oil.price),order=c(0,1,1),method="ML")
Coefficients:
ma1
0.2956
s.e.0.0693
sigma^2estimatedas0.006689:
loglikelihood=260.29,aic=-518.58
系数的置信区间
>m<-arima(log(oil.price),order=c(0,1,1),method='ML')
>confint(m)
2.5%97.5%
ma10.15968290.4315169
模型诊断
>tsdiag(m)
>tsdiag(m)
>predict(m)
$pred
Feb
20064.20755
$se
Feb
20060.08178378
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