数学建模算法（六）：时间序列

1.R（世博会

x<-c(1.37,1.46,1.65,1.53,1.66,1.81,2.38,2.73);
pri<-ts(data=x,frequency =10)
library(forecast)
pri.arima<-auto.arima(pri,ic=c('bic'))
fore<-forecast.Arima(pri.arima,h=12)
fore
1、境外游客数：
> pri.arima
Series: pri
ARIMA(0,1,0) with drift

Coefficients:
       drift
      0.1943
s.e.  0.0758

sigma^2 estimated as 0.04017:  log likelihood=1.32
AIC=1.36   AICc=4.36   BIC=1.25
> fore
   Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
 9       2.924286 2.667440 3.181132 2.531474 3.317098
10       3.118571 2.755336 3.481806 2.563051 3.674091
11       3.312857 2.867987 3.757727 2.632487 3.993227
12       3.507143 2.993451 4.020835 2.721519 4.292767
13       3.701429 3.127104 4.275753 2.823074 4.579783
14       3.895714 3.266573 4.524856 2.933526 4.857903
15       4.090000 3.410450 4.769550 3.050717 5.129283
16       4.284286 3.557816 5.010756 3.173246 5.395326
17       4.478571 3.708034 5.249109 3.300136 5.657007
18       4.672857 3.860639 5.485075 3.430677 5.915038
19       4.867143 4.015281 5.719004 3.564333 6.169953
20       5.061429 4.171688 5.951169 3.700688 6.422169

 2.（2014D研究生

library(zoo)
x<-c(0.489945984,0.528481066,2.600427657,2.918029633,2.589649436,1.438194248,1.257541996,1.361928647

  )
#y<-log(x);
pri<-ts(data=x,frequency =1,start=c(2005))
plot(pri)
acf(pri)
pacf(pri)
p<-shapiro.test(pri)  #p-vaule 大于0.05即可认为服从残差服从正p态分布
library(forecast)
pri.arima<-auto.arima(pri)
pri2<-arima(pri,c(0,2,0),method = "ML")
r<-pri.arima$residuals
p2<-Box.test(r,type="Ljung-Box",lag=3, fitdf=1)
p3<-Box.test(pri2$residuals,type="Ljung-Box",lag=3, fitdf=1)
tsdiag(pri2)
fore<-forecast.Arima(pri.arima,h=8,level = c(99.5))
fore2<-predict(pri2,8,se.fit=TRUE,level=99.5)
fore