Paper_ARIMAest_output11
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 4 seconds |
| R Server | 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 |
| Univariate ARIMA Extrapolation Forecast | ||||||||
| time | Y[t] | F[t] | 95% LB | 95% UB | p-value (H0: Y[t] = F[t]) | P(F[t]>Y[t-1]) | P(F[t]>Y[t-s]) | P(F[t]>Y[84]) |
| 72 | 26451 | - | - | - | - | - | - | - |
| 73 | 47460 | - | - | - | - | - | - | - |
| 74 | 50104 | - | - | - | - | - | - | - |
| 75 | 61465 | - | - | - | - | - | - | - |
| 76 | 53726 | - | - | - | - | - | - | - |
| 77 | 39477 | - | - | - | - | - | - | - |
| 78 | 43895 | - | - | - | - | - | - | - |
| 79 | 31481 | - | - | - | - | - | - | - |
| 80 | 29896 | - | - | - | - | - | - | - |
| 81 | 33842 | - | - | - | - | - | - | - |
| 82 | 39120 | - | - | - | - | - | - | - |
| 83 | 33702 | - | - | - | - | - | - | - |
| 84 | 25094 | - | - | - | - | - | - | - |
| 85 | 51442 | 55267.8897 | 48041.6017 | 62494.1777 | 0.1497 | 1 | 0.9829 | 1 |
| 86 | 45594 | 50897.4969 | 43387.4797 | 58407.514 | 0.0832 | 0.4435 | 0.582 | 1 |
| 87 | 52518 | 55958.9065 | 48044.8486 | 63872.9645 | 0.1971 | 0.9949 | 0.0863 | 1 |
| 88 | 48564 | 50627.4979 | 42286.259 | 58968.7368 | 0.3139 | 0.3284 | 0.2333 | 1 |
| 89 | 41745 | 43104.3311 | 34673.2148 | 51535.4474 | 0.376 | 0.1022 | 0.8005 | 1 |
| 90 | 49585 | 43885.3973 | 35302.2767 | 52468.518 | 0.0965 | 0.6875 | 0.4991 | 1 |
| 91 | 32747 | 36717.6746 | 28070.2086 | 45365.1407 | 0.1841 | 0.0018 | 0.8824 | 0.9958 |
| 92 | 33379 | 30587.7479 | 21899.6553 | 39275.8404 | 0.2644 | 0.3131 | 0.562 | 0.8924 |
| 93 | 35645 | 33363.6809 | 24641.4951 | 42085.8667 | 0.3041 | 0.4986 | 0.4572 | 0.9684 |
| 94 | 37034 | 40239.3847 | 31503.8166 | 48974.9528 | 0.236 | 0.8487 | 0.5992 | 0.9997 |
| 95 | 35681 | 31867.8814 | 23122.3069 | 40613.4558 | 0.1964 | 0.1235 | 0.3405 | 0.9355 |
| 96 | 20972 | 22456.1244 | 13704.9811 | 31207.2676 | 0.3698 | 0.0015 | 0.2773 | 0.2773 |
| Univariate ARIMA Extrapolation Forecast Performance | ||||||
| time | % S.E. | PE | MAPE | Sq.E | MSE | RMSE |
| 85 | 0.0667 | -0.0692 | 0.0058 | 14637432.221 | 1219786.0184 | 1104.4392 |
| 86 | 0.0753 | -0.1042 | 0.0087 | 28127079.2645 | 2343923.272 | 1530.9877 |
| 87 | 0.0722 | -0.0615 | 0.0051 | 11839837.8667 | 986653.1556 | 993.3042 |
| 88 | 0.0841 | -0.0408 | 0.0034 | 4258023.6291 | 354835.3024 | 595.6805 |
| 89 | 0.0998 | -0.0315 | 0.0026 | 1847781.1042 | 153981.7587 | 392.4051 |
| 90 | 0.0998 | 0.1299 | 0.0108 | 32485470.6045 | 2707122.5504 | 1645.3336 |
| 91 | 0.1202 | -0.1081 | 0.009 | 15766257.0609 | 1313854.7551 | 1146.235 |
| 92 | 0.1449 | 0.0913 | 0.0076 | 7791088.4695 | 649257.3725 | 805.7651 |
| 93 | 0.1334 | 0.0684 | 0.0057 | 5204416.8476 | 433701.404 | 658.5601 |
| 94 | 0.1108 | -0.0797 | 0.0066 | 10274491.2286 | 856207.6024 | 925.3149 |
| 95 | 0.14 | 0.1197 | 0.01 | 14539873.8288 | 1211656.1524 | 1100.7525 |
| 96 | 0.1988 | -0.0661 | 0.0055 | 2202625.0887 | 183552.0907 | 428.4298 |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197542283oogjp3db4htin2o/1ah9z1197543163.png (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197542283oogjp3db4htin2o/2da4p1197543163.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/13/t1197542283oogjp3db4htin2o/2da4p1197543163.ps (open in new window) |
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'))
(forecast <- predict(arima.out,fx))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
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)
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
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)
bitmap(file='test2.png')
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()
load(file='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='mytable.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='mytable1.tab')
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