Workshop 6: Q1
| Summary of compuational transaction | |
| Raw Input | view raw input (R code) |
| Raw Output | view raw output of R engine |
| Computing time | 1 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 | 3862 | - | - | - | - | - | - | - |
| 37 | 3608 | - | - | - | - | - | - | - |
| 38 | 3301 | - | - | - | - | - | - | - |
| 39 | 3882 | - | - | - | - | - | - | - |
| 40 | 3605 | - | - | - | - | - | - | - |
| 41 | 4305 | - | - | - | - | - | - | - |
| 42 | 4216 | - | - | - | - | - | - | - |
| 43 | 3971 | - | - | - | - | - | - | - |
| 44 | 3988 | - | - | - | - | - | - | - |
| 45 | 4317 | - | - | - | - | - | - | - |
| 46 | 4484 | - | - | - | - | - | - | - |
| 47 | 4247 | - | - | - | - | - | - | - |
| 48 | 3520 | - | - | - | - | - | - | - |
| 49 | 3687 | 3488.7259 | 2999.3003 | 3978.1514 | 0.2136 | 0.4502 | 0.3164 | 0.4502 |
| 50 | 3405 | 3249.6126 | 2743.4335 | 3755.7917 | 0.2737 | 0.0452 | 0.4211 | 0.1476 |
| 51 | 3990 | 3717.7724 | 3204.7582 | 4230.7866 | 0.1492 | 0.8839 | 0.2652 | 0.7751 |
| 52 | 4047 | 3753.8915 | 3235.0611 | 4272.7219 | 0.1341 | 0.1862 | 0.7131 | 0.8115 |
| 53 | 4549 | 4380.4388 | 3855.9694 | 4904.9082 | 0.2644 | 0.8936 | 0.611 | 0.9993 |
| 54 | 4559 | 4301.445 | 3771.4107 | 4831.4793 | 0.1704 | 0.18 | 0.624 | 0.9981 |
| 55 | 3926 | 3625.1975 | 3089.658 | 4160.7371 | 0.1355 | 3e-04 | 0.1028 | 0.6499 |
| 56 | 4206 | 3688.1971 | 3147.2083 | 4229.1859 | 0.0303 | 0.1945 | 0.1387 | 0.7289 |
| 57 | 4517 | 4217.1958 | 3670.8111 | 4763.5805 | 0.1411 | 0.516 | 0.3602 | 0.9938 |
| 58 | 4387 | 4422.6866 | 3870.9501 | 4974.4231 | 0.4496 | 0.3688 | 0.4138 | 0.9993 |
| 59 | 3219 | 3859.8662 | 3302.7633 | 4416.969 | 0.0121 | 0.0318 | 0.0866 | 0.8841 |
| 60 | 3129 | 3575.7994 | 3012.9436 | 4138.6552 | 0.0599 | 0.893 | 0.577 | 0.577 |
| Univariate ARIMA Extrapolation Forecast Performance | ||||||
| time | % S.E. | PE | MAPE | Sq.E | MSE | RMSE |
| 49 | 0.0716 | 0.0568 | 0.0047 | 39312.6376 | 3276.0531 | 57.2368 |
| 50 | 0.0795 | 0.0478 | 0.004 | 24145.2425 | 2012.1035 | 44.8565 |
| 51 | 0.0704 | 0.0732 | 0.0061 | 74107.8684 | 6175.6557 | 78.5853 |
| 52 | 0.0705 | 0.0781 | 0.0065 | 85912.5872 | 7159.3823 | 84.6131 |
| 53 | 0.0611 | 0.0385 | 0.0032 | 28412.8761 | 2367.7397 | 48.6594 |
| 54 | 0.0629 | 0.0599 | 0.005 | 66334.5638 | 5527.8803 | 74.3497 |
| 55 | 0.0754 | 0.083 | 0.0069 | 90482.1151 | 7540.1763 | 86.8342 |
| 56 | 0.0748 | 0.1404 | 0.0117 | 268119.8401 | 22343.32 | 149.4768 |
| 57 | 0.0661 | 0.0711 | 0.0059 | 89882.5709 | 7490.2142 | 86.546 |
| 58 | 0.0636 | -0.0081 | 7e-04 | 1273.532 | 106.1277 | 10.3018 |
| 59 | 0.0736 | -0.166 | 0.0138 | 410709.4295 | 34225.7858 | 185.0021 |
| 60 | 0.0803 | -0.125 | 0.0104 | 199629.7011 | 16635.8084 | 128.9799 |
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| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/07/t1197047771wei5o3kmwy1efnz/2mb9p1197048341.png (open in new window) |
| http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/07/t1197047771wei5o3kmwy1efnz/2mb9p1197048341.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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