[读者文库]Introduction to Time Series Analysis and Forecasting(using R)

Example 4.8
The liquor store sales data are in the second column of the array called liqsales.data in which the first column is the month of the year. We will first fit additive and multiplicative seasonal models to the entire data to see the difference in the fits. Then we will use the data up to December 2003 to fit the multiplicative model and make forecasts for the coming year (2004). We will once again use Holt–Winters function given in stats package. In all cases we set all parameters to 0.2.

1. y.ts<- ts(liqsales.data[,2], start = c(1992,1), freq = 12)
   
2. liq.hw.add<-HoltWinters(y.ts,alpha=0.2,beta=0.2,gamma=0.2,
   
3. seasonal="additive")
   
4. plot(y.ts,type="p", pch=16,cex=.5,xlab='Date',ylab='Sales',
   
5. main="Additive Model")
   
6. lines(liq.hw.add$fitted[,1])
   
7. liq.hw.mult<-HoltWinters(y.ts,alpha=0.2,beta=0.2,gamma=0.2,
   
8. seasonal="multiplicative")
   
9. plot(y.ts,type="p", pch=16,cex=.5,xlab='Date',ylab='Sales',
   
10. main="Multiplicative Model")
    
11. lines(liq.hw.mult$fitted[,1])
    
12. y1<-liqsales.data[1:144,]
    
13. y1.ts<-ts(y1[,2], start = c(1992,1), freq = 12)
    
14. liq.hw1<-HoltWinters(y1.ts,alpha=0.2,beta=0.2,gamma=0.2,
    
15. seasonal="multiplicative")
    
16. y2<-liqsales.data[145:156,]
    
17. y2.ts<-ts(y2[,2],start=c(2004,1),freq=12)
    
18. y2.forecast<-predict(liq.hw1, n.ahead=12, prediction.interval =
    
19. TRUE)
    
20. plot(y1.ts,type="p", pch=16,cex=.5,xlab='Date',ylab='Sales',
    
21. xlim=c(1992,2005))
    
22. points(y2.ts)
    
23. lines(y2.forecast[,1])
    
24. lines(y2.forecast[,2])
    
25. lines(y2.forecast[,3])

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Example 5.1
The loan applications data are in the second column of the
array called loan.data in which the first column is the number of weeks.
We first plot the data as well as the ACF and PACF.

1. plot(loan.data[,2],type="o",pch=16,cex=.5,xlab='Week',ylab='Loan
   
2. Applications')
   
3. 
   
4. par(mfrow=c(1,2),oma=c(0,0,0,0))
   
5. acf(loan.data[,2],lag.max=25,type="correlation",main="ACF for the
   
6. Number \nof Loan Applications")
   
7. acf(loan.data[,2], lag.max=25,type="partial",main="PACF for the
   
8. Number \nof Loan Applications")
   
9. 
   
10. #Fit an ARIMA(2,0,0) model to the data using arima function in the stats
    
11. package.
    
12. loan.fit.ar2<-arima(loan.data[,2],order=c(2, 0, 0))
    
13. loan.fit.ar2
    
14. 
    
15. res.loan.ar2<-as.vector(residuals(loan.fit.ar2))
    
16. #to obtain the fitted values we use the function fitted() from
    
17. #the forecast package
    
18. library(forecast)
    
19. fit.loan.ar2<-as.vector(fitted(loan.fit.ar2))
    
20. Box.test(res.loan.ar2,lag=48,fitdf=3,type="Ljung")
    
21. #ACF and PACF of the Residuals
    
22. par(mfrow=c(1,2),oma=c(0,0,0,0))
    
23. acf(res.loan.ar2,lag.max=25,type="correlation",main="ACF of the
    
24. Residuals \nof AR(2) Model")
    
25. acf(res.loan.ar2, lag.max=25,type="partial",main="PACF of the
    
26. Residuals \nof AR(2) Model")
    
27. 
    
28. #4-in-1 plot of the residuals
    
29. par(mfrow=c(2,2),oma=c(0,0,0,0))
    
30. qqnorm(res.loan.ar2,datax=TRUE,pch=16,xlab='Residual',main='')
    
31. qqline(res.loan.ar2,datax=TRUE)
    
32. plot(fit.loan.ar2,res.loan.ar2,pch=16, xlab='Fitted Value',
    
33. ylab='Residual')
    
34. abline(h=0)
    
35. hist(res.loan.ar2,col="gray",xlab='Residual',main='')
    
36. plot(res.loan.ar2,type="l",xlab='Observation Order',
    
37. ylab='Residual')
    
38. points(res.loan.ar2,pch=16,cex=.5)
    
39. abline(h=0)
    
40. 
    
41. Plot fitted values
    
42. plot(loan.data[,2],type="p",pch=16,cex=.5,xlab='Week',ylab='Loan
    
43. Applications')
    
44. lines(fit.loan.ar2)
    
45. legend(95,88,c("y(t)","yhat(t)"), pch=c(16, NA),lwd=c(NA,.5),
    
46. cex=.55)

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Example 6.2
The data for this example are in the array called vistemp. data of which the two columns represent the viscosity and the temperature respectively. Below we first start with the prewhitening step.

1. xt<-vistemp.data[,1]
   
2. yt<-vistemp.data[,2]
   
3. par(mfrow=c(2,1),oma=c(0,0,0,0))
   
4. plot(xt,type="o",pch=16,cex=.5,xlab='Time',ylab=expression
   
5. (italic(x[italic(t)])))
   
6. plot(yt,type="o",pch=16,cex=.5,xlab='Time',ylab= expression
   
7. (italic(y[italic(t)])))

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