Foorcasting
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 2 seconds |
| R Server | 'Gwilym Jenkins' @ 72.249.127.135 |
| 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 | 102.6 | - | - | - | - | - | - | - |
| 37 | 89 | - | - | - | - | - | - | - |
| 38 | 93.8 | - | - | - | - | - | - | - |
| 39 | 116.7 | - | - | - | - | - | - | - |
| 40 | 106.8 | - | - | - | - | - | - | - |
| 41 | 98.5 | - | - | - | - | - | - | - |
| 42 | 118.7 | - | - | - | - | - | - | - |
| 43 | 90 | - | - | - | - | - | - | - |
| 44 | 91.9 | - | - | - | - | - | - | - |
| 45 | 113.3 | - | - | - | - | - | - | - |
| 46 | 113.1 | - | - | - | - | - | - | - |
| 47 | 104.1 | - | - | - | - | - | - | - |
| 48 | 108.7 | - | - | - | - | - | - | - |
| 49 | 96.7 | 94.5454 | 84.3994 | 104.6914 | 0.3386 | 0.0031 | 0.858 | 0.0031 |
| 50 | 101 | 99.9008 | 89.2962 | 110.5054 | 0.4195 | 0.7229 | 0.8703 | 0.0519 |
| 51 | 116.9 | 117.5819 | 105.6706 | 129.4932 | 0.4553 | 0.9968 | 0.5577 | 0.9281 |
| 52 | 105.8 | 106.233 | 90.9727 | 121.4933 | 0.4778 | 0.0853 | 0.471 | 0.3757 |
| 53 | 99 | 104.1078 | 87.6913 | 120.5243 | 0.271 | 0.4199 | 0.7484 | 0.2918 |
| 54 | 129.4 | 117.4655 | 99.0576 | 135.8733 | 0.1019 | 0.9754 | 0.4477 | 0.8247 |
| 55 | 83 | 89.9542 | 69.0764 | 110.8321 | 0.2569 | 1e-04 | 0.4983 | 0.0392 |
| 56 | 88.9 | 88.6508 | 66.1565 | 111.1451 | 0.4913 | 0.6888 | 0.3885 | 0.0403 |
| 57 | 115.9 | 113.0562 | 88.4331 | 137.6793 | 0.4105 | 0.9727 | 0.4923 | 0.6356 |
| 58 | 104.2 | 114.4115 | 87.6324 | 141.1906 | 0.2274 | 0.4566 | 0.5382 | 0.662 |
| 59 | 113.4 | 106.0904 | 77.4853 | 134.6955 | 0.3082 | 0.5515 | 0.5542 | 0.429 |
| 60 | 112.2 | 107.9465 | 77.2624 | 138.6306 | 0.3929 | 0.3638 | 0.4808 | 0.4808 |
| Univariate ARIMA Extrapolation Forecast Performance | ||||||
| time | % S.E. | PE | MAPE | Sq.E | MSE | RMSE |
| 49 | 0.0548 | 0.0228 | 0.0019 | 4.6424 | 0.3869 | 0.622 |
| 50 | 0.0542 | 0.011 | 9e-04 | 1.2083 | 0.1007 | 0.3173 |
| 51 | 0.0517 | -0.0058 | 5e-04 | 0.465 | 0.0387 | 0.1968 |
| 52 | 0.0733 | -0.0041 | 3e-04 | 0.1875 | 0.0156 | 0.125 |
| 53 | 0.0805 | -0.0491 | 0.0041 | 26.0895 | 2.1741 | 1.4745 |
| 54 | 0.08 | 0.1016 | 0.0085 | 142.4329 | 11.8694 | 3.4452 |
| 55 | 0.1184 | -0.0773 | 0.0064 | 48.3612 | 4.0301 | 2.0075 |
| 56 | 0.1295 | 0.0028 | 2e-04 | 0.0621 | 0.0052 | 0.0719 |
| 57 | 0.1111 | 0.0252 | 0.0021 | 8.0871 | 0.6739 | 0.8209 |
| 58 | 0.1194 | -0.0893 | 0.0074 | 104.274 | 8.6895 | 2.9478 |
| 59 | 0.1376 | 0.0689 | 0.0057 | 53.4302 | 4.4525 | 2.1101 |
| 60 | 0.145 | 0.0394 | 0.0033 | 18.0921 | 1.5077 | 1.2279 |
 |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/11/t1197385944h2hd99g5su7naa9/10d2u1197381655.png (open in new window) |
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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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