Forecast - Serie 1 - Paper
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 7 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[48]) |
| 36 | 50556 | - | - | - | - | - | - | - |
| 37 | 18387 | - | - | - | - | - | - | - |
| 38 | 27534 | - | - | - | - | - | - | - |
| 39 | 38030 | - | - | - | - | - | - | - |
| 40 | 31917 | - | - | - | - | - | - | - |
| 41 | 26414 | - | - | - | - | - | - | - |
| 42 | 35306 | - | - | - | - | - | - | - |
| 43 | 38271 | - | - | - | - | - | - | - |
| 44 | 41454 | - | - | - | - | - | - | - |
| 45 | 52408 | - | - | - | - | - | - | - |
| 46 | 53536 | - | - | - | - | - | - | - |
| 47 | 53152 | - | - | - | - | - | - | - |
| 48 | 56421 | - | - | - | - | - | - | - |
| 49 | 21538 | 26451.4889 | 18169.0787 | 34733.8991 | 0.1225 | 0 | 0.9718 | 0 |
| 50 | 33625 | 33245.7405 | 24363.7911 | 42127.6899 | 0.4667 | 0.9951 | 0.8962 | 0 |
| 51 | 42625 | 44672.0891 | 35228.587 | 54115.5913 | 0.3355 | 0.9891 | 0.916 | 0.0074 |
| 52 | 31295 | 37645.7811 | 27672.2942 | 47619.2679 | 0.106 | 0.1639 | 0.8699 | 1e-04 |
| 53 | 33795 | 32125.7005 | 21649.0051 | 42602.3959 | 0.3774 | 0.5618 | 0.8574 | 0 |
| 54 | 41227 | 40110.5713 | 29153.7536 | 51067.389 | 0.4209 | 0.8707 | 0.805 | 0.0018 |
| 55 | 45382 | 43694.5915 | 32277.8248 | 55111.3581 | 0.386 | 0.6641 | 0.8241 | 0.0145 |
| 56 | 47206 | 44369.4112 | 32510.5214 | 56228.301 | 0.3196 | 0.4335 | 0.685 | 0.0232 |
| 57 | 46235 | 53167.1948 | 40882.0829 | 65452.3068 | 0.1344 | 0.8292 | 0.5482 | 0.3018 |
| 58 | 51378 | 55711.2856 | 43014.2512 | 68408.32 | 0.2518 | 0.9282 | 0.6315 | 0.4564 |
| 59 | 46865 | 53691.131 | 40595.1244 | 66787.1377 | 0.1535 | 0.6354 | 0.5322 | 0.3414 |
| 60 | 58608 | 58645.9535 | 45162.7752 | 72129.1317 | 0.4978 | 0.9566 | 0.6268 | 0.6268 |
| Univariate ARIMA Extrapolation Forecast Performance | ||||||
| time | % S.E. | PE | MAPE | Sq.E | MSE | RMSE |
| 49 | 0.1598 | -0.1858 | 0.0155 | 24142373.0419 | 2011864.4202 | 1418.4021 |
| 50 | 0.1363 | 0.0114 | 0.001 | 143837.772 | 11986.481 | 109.4828 |
| 51 | 0.1079 | -0.0458 | 0.0038 | 4190573.8582 | 349214.4882 | 590.9437 |
| 52 | 0.1352 | -0.1687 | 0.0141 | 40332420.265 | 3361035.0221 | 1833.3126 |
| 53 | 0.1664 | 0.052 | 0.0043 | 2786560.8058 | 232213.4005 | 481.8853 |
| 54 | 0.1394 | 0.0278 | 0.0023 | 1246413.0826 | 103867.7569 | 322.2852 |
| 55 | 0.1333 | 0.0386 | 0.0032 | 2847347.5547 | 237278.9629 | 487.1129 |
| 56 | 0.1364 | 0.0639 | 0.0053 | 8046236.0077 | 670519.6673 | 818.8527 |
| 57 | 0.1179 | -0.1304 | 0.0109 | 48055325.3261 | 4004610.4438 | 2001.1523 |
| 58 | 0.1163 | -0.0778 | 0.0065 | 18777364.0373 | 1564780.3364 | 1250.9118 |
| 59 | 0.1244 | -0.1271 | 0.0106 | 46596065.0044 | 3883005.417 | 1970.5343 |
| 60 | 0.1173 | -6e-04 | 1e-04 | 1440.4647 | 120.0387 | 10.9562 |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198231179nzlvnkf00zy04vz/1t7bb1198232178.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198231179nzlvnkf00zy04vz/1t7bb1198232178.ps (open in new window) |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198231179nzlvnkf00zy04vz/28lo21198232178.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/21/t1198231179nzlvnkf00zy04vz/28lo21198232178.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)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(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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