R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(274,291,280,258,252,251,224,225,234,233,229,208,224,226,223,205,201,202,183,188,200,206,211,201,299,244,251,241,244,252,234,246,265,277,287,275,320,338,342,322,323,343,315,334,359,362,378,345,422,430,443,431,425,432,387,396,411,421,424,410,464,486,490,459,454,446,406,412,428,429,425,396,429,439,424,379,370,353,322,322,338,348,350,312,358,378,352,312,310,292,276,269,286,292,288,255,304,299,293,275,272,264,234,231,263,264,264,245,297,317,318,315,312,310,306,313,350,354,371,357,419,425,424,399,393,378,371,364,384,377,383,352)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '1'
> par1 = '12'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> par1 <- as.numeric(par1) #cut off periods
> par2 <- as.numeric(par2) #lambda
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #p
> par7 <- as.numeric(par7) #q
> par8 <- as.numeric(par8) #P
> par9 <- as.numeric(par9) #Q
> if (par10 == 'TRUE') par10 <- TRUE
> if (par10 == 'FALSE') par10 <- FALSE
> if (par2 == 0) x <- log(x)
> if (par2 != 0) x <- x^par2
> lx <- length(x)
> first <- lx - 2*par1
> nx <- lx - par1
> nx1 <- nx + 1
> fx <- lx - nx
> if (fx < 1) {
+ fx <- par5
+ nx1 <- lx + fx - 1
+ first <- lx - 2*fx
+ }
> first <- 1
> if (fx < 3) fx <- round(lx/10,0)
> (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))

Call:
arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, 
    par4, par9), period = par5), include.mean = par10, method = "ML")

Coefficients:
         ar1     ar2      ma1     sma1
      0.6367  0.3144  -0.8033  -0.9682
s.e.  0.1112  0.0963   0.0690   0.7595

sigma^2 estimated as 146.8:  log likelihood = -430.44,  aic = 870.88
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 415.0036 427.7061 430.8238 415.1120 417.6073 421.3812 401.0607 411.0991
 [9] 435.9534 445.8974 454.4945 436.6277

$se
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 12.56959 16.32140 20.86635 25.11845 29.47197 33.84095 38.26023 42.71936
 [9] 47.21763 51.74893 56.30907 60.88947

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 390.3672 395.7161 389.9257 365.8798 359.8422 355.0529 326.0706 327.3692
 [9] 343.4068 344.4695 344.1287 317.2844
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 439.6401 459.6960 471.7218 464.3441 475.3724 487.7094 476.0507 494.8291
 [9] 528.4999 547.3253 564.8602 555.9711
> if (par2 == 0) {
+ x <- exp(x)
+ forecast$pred <- exp(forecast$pred)
+ lb <- exp(lb)
+ ub <- exp(ub)
+ }
> if (par2 != 0) {
+ x <- x^(1/par2)
+ forecast$pred <- forecast$pred^(1/par2)
+ lb <- lb^(1/par2)
+ ub <- ub^(1/par2)
+ }
> if (par2 < 0) {
+ olb <- lb
+ lb <- ub
+ ub <- olb
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
  [1] 274.0000 291.0000 280.0000 258.0000 252.0000 251.0000 224.0000 225.0000
  [9] 234.0000 233.0000 229.0000 208.0000 224.0000 226.0000 223.0000 205.0000
 [17] 201.0000 202.0000 183.0000 188.0000 200.0000 206.0000 211.0000 201.0000
 [25] 299.0000 244.0000 251.0000 241.0000 244.0000 252.0000 234.0000 246.0000
 [33] 265.0000 277.0000 287.0000 275.0000 320.0000 338.0000 342.0000 322.0000
 [41] 323.0000 343.0000 315.0000 334.0000 359.0000 362.0000 378.0000 345.0000
 [49] 422.0000 430.0000 443.0000 431.0000 425.0000 432.0000 387.0000 396.0000
 [57] 411.0000 421.0000 424.0000 410.0000 464.0000 486.0000 490.0000 459.0000
 [65] 454.0000 446.0000 406.0000 412.0000 428.0000 429.0000 425.0000 396.0000
 [73] 429.0000 439.0000 424.0000 379.0000 370.0000 353.0000 322.0000 322.0000
 [81] 338.0000 348.0000 350.0000 312.0000 358.0000 378.0000 352.0000 312.0000
 [89] 310.0000 292.0000 276.0000 269.0000 286.0000 292.0000 288.0000 255.0000
 [97] 304.0000 299.0000 293.0000 275.0000 272.0000 264.0000 234.0000 231.0000
[105] 263.0000 264.0000 264.0000 245.0000 297.0000 317.0000 318.0000 315.0000
[113] 312.0000 310.0000 306.0000 313.0000 350.0000 354.0000 371.0000 357.0000
[121] 415.0036 427.7061 430.8238 415.1120 417.6073 421.3812 401.0607 411.0991
[129] 435.9534 445.8974 454.4945 436.6277
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 121 
End = 132 
Frequency = 1 
 [1] 0.03028791 0.03816031 0.04843362 0.06051005 0.07057340 0.08030959
 [7] 0.09539760 0.10391499 0.10830890 0.11605569 0.12389385 0.13945396
> postscript(file="/var/wessaorg/rcomp/tmp/1r33x1323160001.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
> box()
> par(opar)
> dev.off()
null device 
          1 
> prob.dec <- array(NA, dim=fx)
> prob.sdec <- array(NA, dim=fx)
> prob.ldec <- array(NA, dim=fx)
> prob.pval <- array(NA, dim=fx)
> perf.pe <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- array(0, dim=fx)
> perf.rmse <- array(0, dim=fx)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
+ prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
+ prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
+ prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
+ }
> perf.mape[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/wessaorg/rcomp/tmp/2ml3y1323160001.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
> dum <- forecast$pred
> dum[1:par1] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'Y[t]',1,header=TRUE)
> a<-table.element(a,'F[t]',1,header=TRUE)
> a<-table.element(a,'95% LB',1,header=TRUE)
> a<-table.element(a,'95% UB',1,header=TRUE)
> a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
> mylab <- paste('P(F[t]>Y[',nx,sep='')
> mylab <- paste(mylab,'])',sep='')
> a<-table.element(a,mylab,1,header=TRUE)
> a<-table.row.end(a)
> for (i in (nx-par5):nx) {
+ a<-table.row.start(a)
+ a<-table.element(a,i,header=TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.row.end(a)
+ }
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(x[nx+i],4))
+ a<-table.element(a,round(forecast$pred[i],4))
+ a<-table.element(a,round(lb[i],4))
+ a<-table.element(a,round(ub[i],4))
+ a<-table.element(a,round((1-prob.pval[i]),4))
+ a<-table.element(a,round((1-prob.dec[i]),4))
+ a<-table.element(a,round((1-prob.sdec[i]),4))
+ a<-table.element(a,round((1-prob.ldec[i]),4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/37wi51323160001.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'% S.E.',1,header=TRUE)
> a<-table.element(a,'PE',1,header=TRUE)
> a<-table.element(a,'MAPE',1,header=TRUE)
> a<-table.element(a,'Sq.E',1,header=TRUE)
> a<-table.element(a,'MSE',1,header=TRUE)
> a<-table.element(a,'RMSE',1,header=TRUE)
> a<-table.row.end(a)
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(perc.se[i],4))
+ a<-table.element(a,round(perf.pe[i],4))
+ a<-table.element(a,round(perf.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[i],4))
+ a<-table.element(a,round(perf.rmse[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/4pdgz1323160001.tab") 
> 
> try(system("convert tmp/1r33x1323160001.ps tmp/1r33x1323160001.png",intern=TRUE))
character(0)
> try(system("convert tmp/2ml3y1323160001.ps tmp/2ml3y1323160001.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.412   0.118   1.546