werkloosheid/invoer

*The author of this computation has been verified*

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

Title produced by software: ARIMA Forecasting

Date of computation: Wed, 17 Dec 2008 16:06:44 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c.htm/, Retrieved Thu, 18 Dec 2008 00:08:02 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c.htm/}, year = {2008}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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15.59 13.17 11.20 13.30 10.78 11.60 15.18 15.87 12.58 11.43 10.30 11.17 11.26 11.20 9.99 11.17 10.29 10.47 14.36 16.06 14.47 13.24 13.03 14.43 13.98 13.62 12.20 12.24 12.07 12.30 16.12 18.38 14.59 12.96 14.14 13.92 14.24 14.10 12.91 13.69 14.11 13.99 17.93 21.37 16.25 14.53 15.36 14.95 15.95 15.25 12.67 13.86 14.65 12.41 17.46 18.95 15.33 15.31 14.84 14.75 15.83 14.83 13.00 13.92 13.94 12.54 18.12 17.83 14.41 15.18 12.99 13.06 12.81 12.95 10.48 13.23 11.80 11.69 15.33 14.89 12.92 11.27 10.68 11.55

Output produced by software:

Summary of computational 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[64]) 52 13.86 - - - - - - - 53 14.65 - - - - - - - 54 12.41 - - - - - - - 55 17.46 - - - - - - - 56 18.95 - - - - - - - 57 15.33 - - - - - - - 58 15.31 - - - - - - - 59 14.84 - - - - - - - 60 14.75 - - - - - - - 61 15.83 - - - - - - - 62 14.83 - - - - - - - 63 13 - - - - - - - 64 13.92 - - - - - - - 65 13.94 14.6675 12.892 16.4429 0.211 0.7954 0.5077 0.7954 66 12.54 12.7102 10.5413 14.8791 0.4389 0.1332 0.6069 0.1371 67 18.12 17.5819 15.0207 20.1431 0.3402 0.9999 0.5372 0.9975 68 17.83 19.1035 15.8759 22.3311 0.2197 0.7248 0.5371 0.9992 69 14.41 15.5777 11.9772 19.1782 0.2625 0.1101 0.5536 0.8166 70 15.18 15.4662 11.4706 19.4617 0.4442 0.6978 0.5305 0.7759 71 12.99 15.0324 10.6029 19.4618 0.1831 0.474 0.5339 0.6887 72 13.06 14.9668 10.2132 19.7205 0.2159 0.7925 0.5356 0.667 73 12.81 16.0065 10.9146 21.0984 0.1093 0.8716 0.5271 0.7891 74 12.95 15.0307 9.6087 20.4527 0.226 0.7889 0.5289 0.656 75 10.48 13.203 7.4952 18.9108 0.1749 0.5346 0.5278 0.4028 76 13.23 14.1076 8.1101 20.1051 0.3871 0.8821 0.5244 0.5244 77 11.8 14.8681 7.8655 21.8707 0.1952 0.6767 0.6025 0.6046 78 11.69 12.9081 5.2675 20.5487 0.3773 0.6119 0.5376 0.3976 79 15.33 17.7749 9.4906 26.0592 0.2815 0.925 0.4675 0.8191 80 14.89 19.3026 10.1904 28.4149 0.1713 0.8036 0.6243 0.8765 81 12.92 15.7741 6.0418 25.5065 0.2827 0.5707 0.6082 0.6456 82 11.27 15.6615 5.2958 26.0272 0.2032 0.6979 0.5363 0.629 83 10.68 15.2303 4.2102 26.2503 0.2092 0.7594 0.6549 0.5921 84 11.55 15.1631 3.5843 26.7418 0.2704 0.776 0.6391 0.5833 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 65 0.0618 -0.0496 0.0025 0.5292 0.0265 0.1627 66 0.0871 -0.0134 7e-04 0.029 0.0014 0.0381 67 0.0743 0.0306 0.0015 0.2895 0.0145 0.1203 68 0.0862 -0.0667 0.0033 1.6218 0.0811 0.2848 69 0.1179 -0.075 0.0037 1.3635 0.0682 0.2611 70 0.1318 -0.0185 9e-04 0.0819 0.0041 0.064 71 0.1503 -0.1359 0.0068 4.1712 0.2086 0.4567 72 0.162 -0.1274 0.0064 3.636 0.1818 0.4264 73 0.1623 -0.1997 0.01 10.2176 0.5109 0.7148 74 0.184 -0.1384 0.0069 4.3292 0.2165 0.4653 75 0.2206 -0.2062 0.0103 7.4148 0.3707 0.6089 76 0.2169 -0.0622 0.0031 0.7701 0.0385 0.1962 77 0.2403 -0.2064 0.0103 9.4131 0.4707 0.686 78 0.302 -0.0944 0.0047 1.4838 0.0742 0.2724 79 0.2378 -0.1375 0.0069 5.9775 0.2989 0.5467 80 0.2409 -0.2286 0.0114 19.4712 0.9736 0.9867 81 0.3148 -0.1809 0.009 8.1461 0.4073 0.6382 82 0.3377 -0.2804 0.014 19.2855 0.9643 0.982 83 0.3692 -0.2988 0.0149 20.7049 1.0352 1.0175 84 0.3896 -0.2383 0.0119 13.0543 0.6527 0.8079

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c/1lzop1229555202.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c/1lzop1229555202.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c/2svz31229555202.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229555280k5y8zch67njod3c/2svz31229555202.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

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) } 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')

Copyright

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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