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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Type 'contributors()' for more information and
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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(897262
+ ,1133132
+ ,1384548
+ ,2324057
+ ,2502808
+ ,2516762
+ ,5579822
+ ,4945991
+ ,2019915
+ ,1830905
+ ,1251016
+ ,949902
+ ,923000
+ ,1215747
+ ,1479112
+ ,2371781
+ ,2521576
+ ,2350559
+ ,5673323
+ ,4414295
+ ,2016902
+ ,1958302
+ ,1284086
+ ,1186305
+ ,957833
+ ,1255719
+ ,1482709
+ ,2361136
+ ,2508100
+ ,2254488
+ ,5669953
+ ,4227480
+ ,2067790
+ ,1958419
+ ,1318158
+ ,1287921
+ ,1076982
+ ,1293669
+ ,1582053
+ ,2393005
+ ,2310531
+ ,2597899
+ ,5507587
+ ,4194133
+ ,2185092
+ ,2122018
+ ,1413348
+ ,1338342
+ ,1052655
+ ,1370046
+ ,1887027
+ ,2448017
+ ,2550796
+ ,2655837
+ ,5269499
+ ,4247405
+ ,2109722
+ ,2143145
+ ,1582013
+ ,1413221
+ ,1118520
+ ,1478655
+ ,2000108
+ ,2085234
+ ,2651805
+ ,2522176
+ ,5170142
+ ,4150129
+ ,2104254
+ ,2211398
+ ,1505900
+ ,1524305
+ ,1093144
+ ,1449647
+ ,1771197
+ ,2445932
+ ,2678945
+ ,2400737
+ ,4796880
+ ,4118001
+ ,2125714
+ ,2125515
+ ,1508760
+ ,1508765
+ ,1091075
+ ,1514814
+ ,1748997
+ ,2424406
+ ,2747942
+ ,2377332
+ ,5210706
+ ,3882821
+ ,2197469
+ ,2271155
+ ,1618917
+ ,1391579
+ ,1143249
+ ,1445785
+ ,1870242
+ ,2597788
+ ,2436231
+ ,2684184
+ ,4705109
+ ,4331347
+ ,2369192
+ ,2283947
+ ,1749607
+ ,1598601
+ ,1221234
+ ,1497778
+ ,1823567
+ ,2489908
+ ,2532837
+ ,2456065
+ ,4627018
+ ,4276894
+ ,2314950
+ ,2238987
+ ,1652753
+ ,1561968
+ ,1115878
+ ,1596714
+ ,1910242
+ ,2286450
+ ,2772441
+ ,2394538
+ ,4715128
+ ,4402420
+ ,2325392
+ ,2306683
+ ,1725282
+ ,1541370
+ ,1168142
+ ,1457835
+ ,1816380
+ ,2446552
+ ,2575774
+ ,2537852
+ ,4728097
+ ,4372685
+ ,2302672
+ ,2346402
+ ,1689915
+ ,1576183)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> 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      ar2     ar3     ma1    sar1    sar2     sma1
      -1.1454  -0.0736  0.1910  0.9675  0.6418  0.2069  -0.7644
s.e.   0.0979   0.1413  0.0929  0.0369  0.2207  0.0985   0.2261

sigma^2 estimated as 2.030e+10:  log likelihood = -1595.57,  aic = 3207.14
Warning messages:
1: In log(s2) : NaNs produced
2: In log(s2) : NaNs produced
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 1155189 1596926 1898360 2334315 2723740 2410808 4632235 4399550 2330966
[10] 2316220 1724642 1566609

$se
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 142491.7 144733.0 145920.8 146129.0 146911.7 148310.6 149744.5 150981.9
 [9] 151901.9 152523.1 152907.6 153127.9

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1]  875905.7 1313249.4 1612355.0 2047902.6 2435792.9 2120118.9 4338735.6
 [8] 4103625.6 2033238.4 2017274.8 1424943.2 1266478.6
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 1434473 1880603 2184365 2620728 3011687 2701496 4925734 4695475 2628694
[10] 2615166 2024341 1866740
> 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$pred))
  [1]  897262 1133132 1384548 2324057 2502808 2516762 5579822 4945991 2019915
 [10] 1830905 1251016  949902  923000 1215747 1479112 2371781 2521576 2350559
 [19] 5673323 4414295 2016902 1958302 1284086 1186305  957833 1255719 1482709
 [28] 2361136 2508100 2254488 5669953 4227480 2067790 1958419 1318158 1287921
 [37] 1076982 1293669 1582053 2393005 2310531 2597899 5507587 4194133 2185092
 [46] 2122018 1413348 1338342 1052655 1370046 1887027 2448017 2550796 2655837
 [55] 5269499 4247405 2109722 2143145 1582013 1413221 1118520 1478655 2000108
 [64] 2085234 2651805 2522176 5170142 4150129 2104254 2211398 1505900 1524305
 [73] 1093144 1449647 1771197 2445932 2678945 2400737 4796880 4118001 2125714
 [82] 2125515 1508760 1508765 1091075 1514814 1748997 2424406 2747942 2377332
 [91] 5210706 3882821 2197469 2271155 1618917 1391579 1143249 1445785 1870242
[100] 2597788 2436231 2684184 4705109 4331347 2369192 2283947 1749607 1598601
[109] 1221234 1497778 1823567 2489908 2532837 2456065 4627018 4276894 2314950
[118] 2238987 1652753 1561968 1115878 1596714 1910242 2286450 2772441 2394538
[127] 4715128 4402420 2325392 2306683 1725282 1541370 1155189 1596926 1898360
[136] 2334315 2723740 2410808 4632235 4399550 2330966 2316220 1724642 1566609
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 133 
End = 144 
Frequency = 1 
 [1] 0.12334917 0.09063224 0.07686678 0.06260036 0.05393749 0.06151905
 [7] 0.03232661 0.03431758 0.06516692 0.06585001 0.08866048 0.09774478
> postscript(file="/var/www/html/rcomp/tmp/1v6wo1229982034.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/rcomp/tmp/2j4mf1229982035.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/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/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/rcomp/tmp/3s5q81229982035.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/rcomp/tmp/4ludy1229982035.tab") 
> 
> system("convert tmp/1v6wo1229982034.ps tmp/1v6wo1229982034.png")
> system("convert tmp/2j4mf1229982035.ps tmp/2j4mf1229982035.png")
> 
> 
> proc.time()
   user  system elapsed 
  4.263   0.537   4.643