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WS5: Q1 inflatie

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Thu, 06 Dec 2007 09:15:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/06/t1196956947l4qe4kf508ryz8p.htm/, Retrieved Thu, 06 Dec 2007 17:02:30 +0100

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1,1 1,3 1,2 1,6 1,7 1,5 0,9 1,5 1,4 1,6 1,7 1,4 1,8 1,7 1,4 1,2 1 1,7 2,4 2 2,1 2 1,8 2,7 2,3 1,9 2 2,3 2,8 2,4 2,3 2,7 2,7 2,9 3 2,2 2,3 2,8 2,8 2,8 2,2 2,6 2,8 2,5 2,4 2,3 1,9 1,7 2 2,1 1,7 1,8 1,8 1,8 1,3 1,3 1,3 1,2 1,4 2,2

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Output produced by software:

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[24]) 12 1.4 - - - - - - - 13 1.8 - - - - - - - 14 1.7 - - - - - - - 15 1.4 - - - - - - - 16 1.2 - - - - - - - 17 1 - - - - - - - 18 1.7 - - - - - - - 19 2.4 - - - - - - - 20 2 - - - - - - - 21 2.1 - - - - - - - 22 2 - - - - - - - 23 1.8 - - - - - - - 24 2.7 - - - - - - - 25 2.3 0 -3.2648 3.2648 0.0837 0.0525 0.1399 0.0525 26 1.9 0 -3.2648 3.2648 0.127 0.0837 0.1537 0.0525 27 2 0 -3.2648 3.2648 0.1149 0.127 0.2003 0.0525 28 2.3 0 -3.2648 3.2648 0.0837 0.1149 0.2356 0.0525 29 2.8 0 -3.2648 3.2648 0.0464 0.0837 0.2741 0.0525 30 2.4 0 -3.2648 3.2648 0.0748 0.0464 0.1537 0.0525 31 2.3 0 -3.2648 3.2648 0.0837 0.0748 0.0748 0.0525 32 2.7 0 -3.2648 3.2648 0.0525 0.0837 0.1149 0.0525 33 2.7 0 -3.2648 3.2648 0.0525 0.0525 0.1037 0.0525 34 2.9 0 -3.2648 3.2648 0.0408 0.0525 0.1149 0.0525 35 3 0 -3.2648 3.2648 0.0358 0.0408 0.1399 0.0525 36 2.2 0 -3.2648 3.2648 0.0933 0.0358 0.0525 0.0525 37 2.3 0 -3.2648 3.2648 0.0837 0.0933 0.0837 0.0525 38 2.8 0 -3.2648 3.2648 0.0464 0.0837 0.127 0.0525 39 2.8 0 -3.2648 3.2648 0.0464 0.0464 0.1149 0.0525 40 2.8 0 -3.2648 3.2648 0.0464 0.0464 0.0837 0.0525 41 2.2 0 -3.2648 3.2648 0.0933 0.0464 0.0464 0.0525 42 2.6 0 -3.2648 3.2648 0.0593 0.0933 0.0748 0.0525 43 2.8 0 -3.2648 3.2648 0.0464 0.0593 0.0837 0.0525 44 2.5 0 -3.2648 3.2648 0.0667 0.0464 0.0525 0.0525 45 2.4 0 -3.2648 3.2648 0.0748 0.0667 0.0525 0.0525 46 2.3 0 -3.2648 3.2648 0.0837 0.0748 0.0408 0.0525 47 1.9 0 -3.2648 3.2648 0.127 0.0837 0.0358 0.0525 48 1.7 0 -3.2648 3.2648 0.1537 0.127 0.0933 0.0525 49 2 0 -3.2648 3.2648 0.1149 0.1537 0.0837 0.0525 50 2.1 0 -3.2648 3.2648 0.1037 0.1149 0.0464 0.0525 51 1.7 0 -3.2648 3.2648 0.1537 0.1037 0.0464 0.0525 52 1.8 0 -3.2648 3.2648 0.1399 0.1537 0.0464 0.0525 53 1.8 0 -3.2648 3.2648 0.1399 0.1399 0.0933 0.0525 54 1.8 0 -3.2648 3.2648 0.1399 0.1399 0.0593 0.0525 55 1.3 0 -3.2648 3.2648 0.2176 0.1399 0.0464 0.0525 56 1.3 0 -3.2648 3.2648 0.2176 0.2176 0.0667 0.0525 57 1.3 0 -3.2648 3.2648 0.2176 0.2176 0.0748 0.0525 58 1.2 0 -3.2648 3.2648 0.2356 0.2176 0.0837 0.0525 59 1.4 0 -3.2648 3.2648 0.2003 0.2356 0.127 0.0525 60 2.2 0 -3.2648 3.2648 0.0933 0.2003 0.1537 0.0525 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 25 Inf Inf Inf 5.29 0.1469 0.3833 26 Inf Inf Inf 3.61 0.1003 0.3167 27 Inf Inf Inf 4 0.1111 0.3333 28 Inf Inf Inf 5.29 0.1469 0.3833 29 Inf Inf Inf 7.84 0.2178 0.4667 30 Inf Inf Inf 5.76 0.16 0.4 31 Inf Inf Inf 5.29 0.1469 0.3833 32 Inf Inf Inf 7.29 0.2025 0.45 33 Inf Inf Inf 7.29 0.2025 0.45 34 Inf Inf Inf 8.41 0.2336 0.4833 35 Inf Inf Inf 9 0.25 0.5 36 Inf Inf Inf 4.84 0.1344 0.3667 37 Inf Inf Inf 5.29 0.1469 0.3833 38 Inf Inf Inf 7.84 0.2178 0.4667 39 Inf Inf Inf 7.84 0.2178 0.4667 40 Inf Inf Inf 7.84 0.2178 0.4667 41 Inf Inf Inf 4.84 0.1344 0.3667 42 Inf Inf Inf 6.76 0.1878 0.4333 43 Inf Inf Inf 7.84 0.2178 0.4667 44 Inf Inf Inf 6.25 0.1736 0.4167 45 Inf Inf Inf 5.76 0.16 0.4 46 Inf Inf Inf 5.29 0.1469 0.3833 47 Inf Inf Inf 3.61 0.1003 0.3167 48 Inf Inf Inf 2.89 0.0803 0.2833 49 Inf Inf Inf 4 0.1111 0.3333 50 Inf Inf Inf 4.41 0.1225 0.35 51 Inf Inf Inf 2.89 0.0803 0.2833 52 Inf Inf Inf 3.24 0.09 0.3 53 Inf Inf Inf 3.24 0.09 0.3 54 Inf Inf Inf 3.24 0.09 0.3 55 Inf Inf Inf 1.69 0.0469 0.2167 56 Inf Inf Inf 1.69 0.0469 0.2167 57 Inf Inf Inf 1.69 0.0469 0.2167 58 Inf Inf Inf 1.44 0.04 0.2 59 Inf Inf Inf 1.96 0.0544 0.2333 60 Inf Inf Inf 4.84 0.1344 0.3667

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/06/t1196956947l4qe4kf508ryz8p/1r1061196957735.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/06/t1196956947l4qe4kf508ryz8p/1r1061196957735.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/06/t1196956947l4qe4kf508ryz8p/2ijib1196957735.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/06/t1196956947l4qe4kf508ryz8p/2ijib1196957735.ps (open in new window)

Parameters:

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

R code (references can be found in the software module):

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')) (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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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