R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(1375.06,1334.38,1335.61,1307.24,1183.2,1187.79,1270.81,1238.67,1204.45,1178.5,1044.64,1076.59,1129.68,1144.93,1140.21,1100.29,1153.79,1114.2,1079.27,1014.05,903.69,912.55,867.81,854.54,911.17,899.26,895.87,837.61,846.62,890.19,935.96,988,992.55,989.53,1019.44,1038.73,1049.9,1080.64,1132.52,1143.37,1123.98,1133.07,1102.78,1132.76,1105.85,1088.93,1117.66,1118.07,1168.94,1199.21,1181.4,1199.63,1194.9,1164.42,1178.28,1202.25,1222.24,1224.27,1225.91,1191.96,1237.37,1262.07,1278.72,1276.65,1293.83,1302.18,1290,1253.12,1260.24,1287.15,1317.81,1363.38,1388.63,1416.42,1424.16,1444.65,1406.95,1463.65,1511.14,1514.49,1520.98,1454.62,1497.12,1539.66,1463.39,1479.23,1378.76,1354.87,1316.94,1370.47,1403.22,1341.25,1257.33,1281.47,1216.93,969.13,883.04)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '0'
> 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: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> 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     ma1
      -0.6875  0.9619
s.e.   0.1006  0.0450

sigma^2 estimated as 1422:  log likelihood = -424.65,  aic = 855.3
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 1453.726 1460.370 1455.802 1458.943 1456.784 1458.268 1457.248 1457.949
 [9] 1457.467 1457.799 1457.571 1457.727

$se
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1]  37.71597  61.09279  73.54659  86.66174  96.51165 106.39760 114.83280
 [8] 123.07838 130.55276 137.78607 144.55040 151.08286

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 1379.803 1340.629 1311.651 1289.086 1267.621 1249.729 1232.175 1216.716
 [9] 1201.584 1187.738 1174.252 1161.605
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 1527.650 1580.112 1599.954 1628.800 1645.947 1666.808 1682.320 1699.183
 [9] 1713.350 1727.859 1740.889 1753.850
> 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$pred))
 [1] 1375.060 1334.380 1335.610 1307.240 1183.200 1187.790 1270.810 1238.670
 [9] 1204.450 1178.500 1044.640 1076.590 1129.680 1144.930 1140.210 1100.290
[17] 1153.790 1114.200 1079.270 1014.050  903.690  912.550  867.810  854.540
[25]  911.170  899.260  895.870  837.610  846.620  890.190  935.960  988.000
[33]  992.550  989.530 1019.440 1038.730 1049.900 1080.640 1132.520 1143.370
[41] 1123.980 1133.070 1102.780 1132.760 1105.850 1088.930 1117.660 1118.070
[49] 1168.940 1199.210 1181.400 1199.630 1194.900 1164.420 1178.280 1202.250
[57] 1222.240 1224.270 1225.910 1191.960 1237.370 1262.070 1278.720 1276.650
[65] 1293.830 1302.180 1290.000 1253.120 1260.240 1287.150 1317.810 1363.380
[73] 1388.630 1416.420 1424.160 1444.650 1406.950 1463.650 1511.140 1514.490
[81] 1520.980 1454.620 1497.120 1539.660 1463.390 1453.726 1460.370 1455.802
[89] 1458.943 1456.784 1458.268 1457.248 1457.949 1457.467 1457.799 1457.571
[97] 1457.727
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 86 
End = 97 
Frequency = 1 
 [1] 0.02594434 0.04183376 0.05051962 0.05940036 0.06624981 0.07296161
 [7] 0.07880115 0.08441883 0.08957511 0.09451653 0.09917214 0.10364274
> postscript(file="/var/www/html/freestat/rcomp/tmp/1xd2m1229019949.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/freestat/rcomp/tmp/2jjk41229019949.ps",horizontal=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[1:12] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/html/freestat/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/freestat/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/www/html/freestat/rcomp/tmp/3u7pm1229019950.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/www/html/freestat/rcomp/tmp/4fr971229019950.tab") 
> 
> system("convert tmp/1xd2m1229019949.ps tmp/1xd2m1229019949.png")
> system("convert tmp/2jjk41229019949.ps tmp/2jjk41229019949.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.849   0.450   1.019