Faillissementen Brussel

*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: Mon, 20 Dec 2010 18:08:43 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/20/t1292868418k9lli3of02g9qi0.htm/, Retrieved Mon, 20 Dec 2010 19:07:01 +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/2010/Dec/20/t1292868418k9lli3of02g9qi0.htm/}, year = {2010}, } @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 = {2010}, 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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89 97 154 81 110 116 73 73 174 103 130 91 136 106 136 122 131 135 75 68 143 115 93 128 152 125 107 116 220 137 34 51 153 145 116 145 98 118 139 140 113 149 79 47 166 180 122 134 114 125 181 142 143 187 137 62 239 157 139 187 99 146 175 148 130 183 115 80 223 131 201 157

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 2 seconds R Server 'George Udny Yule' @ 72.249.76.132 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]) 36 145 - - - - - - - 37 98 - - - - - - - 38 118 - - - - - - - 39 139 - - - - - - - 40 140 - - - - - - - 41 113 - - - - - - - 42 149 - - - - - - - 43 79 - - - - - - - 44 47 - - - - - - - 45 166 - - - - - - - 46 180 - - - - - - - 47 122 - - - - - - - 48 134 - - - - - - - 49 114 93.982 33.7847 154.1793 0.2573 0.0963 0.448 0.0963 50 125 123.7793 63.2137 184.3449 0.4842 0.6242 0.5742 0.3704 51 181 140.5798 75.7845 205.3751 0.1107 0.6813 0.5191 0.5789 52 142 137.6187 72.8083 202.4292 0.4473 0.0948 0.4713 0.5436 53 143 111.9645 45.7094 178.2196 0.1793 0.1871 0.4878 0.2572 54 187 150.2702 84.0069 216.5335 0.1386 0.5851 0.515 0.6848 55 137 79.4049 12.944 145.8658 0.0447 8e-04 0.5048 0.0537 56 62 46.4884 -19.9756 112.9523 0.3237 0.0038 0.494 0.0049 57 239 165.7379 99.2 232.2758 0.0155 0.9989 0.4969 0.8251 58 157 180.278 113.74 246.8161 0.2465 0.0418 0.5033 0.9136 59 139 122.1016 55.554 188.6493 0.3093 0.152 0.5012 0.363 60 187 133.891 67.343 200.439 0.0589 0.4402 0.4987 0.4987 61 99 93.9166 3.7019 184.1314 0.456 0.0216 0.3313 0.1919 62 146 123.8399 33.3784 214.3015 0.3156 0.7048 0.49 0.4129 63 175 140.6049 47.1971 234.0126 0.2352 0.4549 0.1983 0.5551 64 148 137.5957 44.1765 231.015 0.4136 0.2163 0.4632 0.5301 65 130 111.9484 17.4974 206.3993 0.354 0.2272 0.2597 0.3236 66 183 150.2834 55.8267 244.7401 0.2486 0.6631 0.2231 0.6323 67 115 79.411 -15.1873 174.0093 0.2304 0.0159 0.1164 0.129 68 80 46.4836 -48.117 141.0842 0.2437 0.0779 0.3739 0.0349 69 223 165.734 71.0802 260.3878 0.1178 0.9621 0.0646 0.7444 70 131 180.2809 85.627 274.9348 0.1538 0.1882 0.6851 0.8311 71 201 122.1031 27.4423 216.7639 0.0512 0.4269 0.3632 0.4027 72 157 133.89 39.229 228.5511 0.3161 0.0823 0.1357 0.4991 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 49 0.3268 0.213 0 400.7199 0 0 50 0.2496 0.0099 0.1114 1.49 201.105 14.1811 51 0.2352 0.2875 0.1701 1633.7924 678.6674 26.0512 52 0.2403 0.0318 0.1356 19.1955 513.7995 22.6671 53 0.3019 0.2772 0.1639 963.203 603.6802 24.5699 54 0.225 0.2444 0.1773 1349.0773 727.913 26.9799 55 0.427 0.7253 0.2556 3317.1995 1097.8111 33.1332 56 0.7294 0.3337 0.2654 240.6106 990.661 31.4748 57 0.2048 0.442 0.285 5367.3302 1476.9576 38.4312 58 0.1883 -0.1291 0.2694 541.8669 1383.4485 37.1947 59 0.2781 0.1384 0.2575 285.5552 1283.6401 35.8279 60 0.2536 0.3967 0.2691 2820.5655 1411.7172 37.5728 61 0.4901 0.0541 0.2526 25.8406 1305.1113 36.1263 62 0.3727 0.1789 0.2473 491.068 1246.9653 35.3124 63 0.3389 0.2446 0.2471 1183.0239 1242.7026 35.252 64 0.3464 0.0756 0.2364 108.2488 1171.7992 34.2316 65 0.4305 0.1612 0.232 325.8613 1122.0382 33.4968 66 0.3207 0.2177 0.2312 1070.3781 1119.1681 33.454 67 0.6078 0.4482 0.2426 1266.5789 1126.9266 33.5697 68 1.0383 0.721 0.2665 1123.3507 1126.7478 33.5671 69 0.2914 0.3455 0.2703 3279.3949 1229.2548 35.0607 70 0.2679 -0.2734 0.2704 2428.605 1283.7707 35.8297 71 0.3955 0.6461 0.2868 6224.7224 1498.5947 38.7117 72 0.3607 0.1726 0.282 534.0713 1458.4062 38.1891

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292868418k9lli3of02g9qi0/1h7201292868520.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292868418k9lli3of02g9qi0/1h7201292868520.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292868418k9lli3of02g9qi0/2o8ic1292868520.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/20/t1292868418k9lli3of02g9qi0/2o8ic1292868520.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; 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,par1)) (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.mape1 <- array(0, dim=fx) perf.se <- array(0, dim=fx) perf.mse <- array(0, dim=fx) perf.mse1 <- 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$pred[i] perf.se[i] = (x[nx+i] - forecast$pred[i])^2 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[1] = abs(perf.pe[1]) perf.mse[1] = abs(perf.se[1]) for (i in 2:fx) { perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i]) perf.mape1[i] = perf.mape[i] / i perf.mse[i] = perf.mse[i-1] + perf.se[i] perf.mse1[i] = perf.mse[i] / i } perf.rmse = sqrt(perf.mse1) 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:par1] <- 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.mape1[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse1[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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