werkloosheid

*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: Sun, 14 Dec 2008 11:02:13 -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/14/t1229277829fh0qq3ovyx25pzq.htm/, Retrieved Sun, 14 Dec 2008 19:03:51 +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/14/t1229277829fh0qq3ovyx25pzq.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:

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Dataseries X:

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180144 173666 165688 161570 156145 153730 182698 200765 176512 166618 158644 159585 163095 159044 155511 153745 150569 150605 179612 194690 189917 184128 175335 179566 181140 177876 175041 169292 166070 166972 206348 215706 202108 195411 193111 195198 198770 194163 190420 189733 186029 191531 232571 243477 227247 217859 208679 213188 216234 213586 209465 204045 200237 203666 241476 260307 243324 244460 233575 237217 235243 230354 227184 221678 217142 219452 256446 265845 248624 241114 229245 231805 219277 219313 212610 214771 211142 211457 240048 240636 230580 208795 197922 194596

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[48]) 36 195198 - - - - - - - 37 198770 - - - - - - - 38 194163 - - - - - - - 39 190420 - - - - - - - 40 189733 - - - - - - - 41 186029 - - - - - - - 42 191531 - - - - - - - 43 232571 - - - - - - - 44 243477 - - - - - - - 45 227247 - - - - - - - 46 217859 - - - - - - - 47 208679 - - - - - - - 48 213188 - - - - - - - 49 216234 216831.5318 207050.9225 226612.1411 0.4523 0.7674 0.9999 0.7674 50 213586 212226.6444 198189.0316 226264.2573 0.4247 0.2879 0.9942 0.4466 51 209465 208483.7068 191203.0611 225764.3525 0.4557 0.2814 0.9798 0.2968 52 204045 207796.7086 187791.9108 227801.5065 0.3566 0.4351 0.9616 0.2987 53 200237 204092.7087 181692.6349 226492.7825 0.3679 0.5017 0.943 0.2131 54 203666 209594.7087 185031.8367 234157.5807 0.3181 0.7724 0.9253 0.3872 55 241476 250634.7087 224084.6418 277184.7756 0.2495 0.9997 0.9088 0.9971 56 260307 261540.7087 233142.1625 289939.2549 0.4661 0.9169 0.8937 0.9996 57 243324 245310.7087 215176.8606 275444.5568 0.4486 0.1647 0.88 0.9817 58 244460 235922.7087 204148.1878 267697.2296 0.2992 0.324 0.8674 0.9196 59 233575 226742.7087 193408.1688 260077.2486 0.3439 0.1488 0.8559 0.7873 60 237217 231251.7087 196426.9628 266076.4546 0.3685 0.448 0.8453 0.8453 61 235243 234895.2405 194806.1184 274984.3626 0.4932 0.4548 0.8192 0.8557 62 230354 230290.3531 185423.1168 275157.5895 0.4989 0.4144 0.7672 0.7725 63 227184 226547.4155 177360.5887 275734.2423 0.4899 0.4397 0.752 0.7028 64 221678 225860.4173 172703.7704 279017.0643 0.4387 0.4805 0.7894 0.6798 65 217142 222156.4174 165306.4868 279006.348 0.4314 0.5066 0.7751 0.6214 66 219452 227658.4174 167340.9232 287975.9116 0.3949 0.6337 0.7822 0.6809 67 256446 268698.4174 205102.1471 332294.6877 0.3529 0.9355 0.7993 0.9564 68 265845 279604.4174 212890.3177 346318.5171 0.343 0.7519 0.7146 0.9745 69 248624 263374.4174 193681.831 333067.0038 0.3391 0.4723 0.7136 0.9209 70 241114 253986.4174 181437.5229 326535.3119 0.364 0.5576 0.6016 0.8648 71 229245 244806.4174 169509.4879 320103.3469 0.3427 0.5383 0.615 0.7948 72 231805 249315.4174 171367.2738 327263.561 0.3299 0.6931 0.6195 0.8182 73 219277 252958.9492 169459.5774 336458.321 0.2146 0.6902 0.6612 0.8247 74 219313 248354.0618 159552.2828 337155.8408 0.2608 0.7395 0.6544 0.7812 75 212610 244611.1242 150803.4346 338418.8138 0.2519 0.7014 0.6421 0.7443 76 214771 243924.1261 145364.375 342483.8771 0.281 0.7333 0.6709 0.7295 77 211142 240220.1261 137127.125 343313.1272 0.2902 0.6857 0.6696 0.6964 78 211457 245722.1261 138286.9864 353157.2659 0.2659 0.7359 0.6841 0.7236 79 240048 286762.1261 175153.6514 398370.6008 0.206 0.907 0.7028 0.9018 80 240636 297668.1261 182036.8415 413299.4108 0.1668 0.8356 0.7052 0.9239 81 230580 281438.1261 161919.3562 400956.896 0.2021 0.7483 0.7048 0.8685 82 208795 272050.1261 148766.3935 395333.8587 0.1573 0.7451 0.6886 0.8253 83 197922 262870.1261 135933.0508 389807.2015 0.158 0.7981 0.6982 0.7785 84 194596 267379.1261 136890.9524 397867.2998 0.1371 0.8516 0.7034 0.7922 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 49 0.023 -0.0028 1e-04 357044.2245 9917.8951 99.5886 50 0.0337 0.0064 2e-04 1847847.6223 51329.1006 226.5593 51 0.0423 0.0047 1e-04 962936.3365 26748.2316 163.5489 52 0.0491 -0.0181 5e-04 14075317.7705 390981.0492 625.2848 53 0.056 -0.0189 5e-04 14866489.5888 412958.0441 642.6181 54 0.0598 -0.0283 8e-04 35149586.8831 976377.4134 988.1181 55 0.054 -0.0365 0.001 83881945.1044 2330054.0307 1526.4515 56 0.0554 -0.0047 1e-04 1522037.1636 42278.8101 205.6181 57 0.0627 -0.0081 2e-04 3947011.4701 109639.2075 331.1181 58 0.0687 0.0362 0.001 72885342.6917 2024592.8525 1422.8819 59 0.075 0.0301 8e-04 46680204.3686 1296672.3436 1138.7152 60 0.0768 0.0258 7e-04 35584700.2594 988463.8961 994.2152 61 0.0871 0.0015 0 120936.6838 3359.3523 57.9599 62 0.0994 3e-04 0 4050.9263 112.5257 10.6078 63 0.1108 0.0028 1e-04 405239.8168 11256.6616 106.0974 64 0.1201 -0.0185 5e-04 17492614.8871 485905.9691 697.0696 65 0.1306 -0.0226 6e-04 25144381.9028 698455.0529 835.7362 66 0.1352 -0.036 0.001 67345286.6371 1870702.4066 1367.7362 67 0.1208 -0.0456 0.0013 150121732.2854 4170048.119 2042.0696 68 0.1217 -0.0492 0.0014 189321567.3465 5258932.4263 2293.2362 69 0.135 -0.056 0.0016 217574813.6447 6043744.8235 2458.4029 70 0.1457 -0.0507 0.0014 165699129.8686 4602753.6075 2145.4029 71 0.1569 -0.0636 0.0018 242157711.6769 6726603.1021 2593.5696 72 0.1595 -0.0702 0.002 306614717.7246 8517075.4924 2918.4029 73 0.1684 -0.1332 0.0037 1134473700.7515 31513158.3542 5613.6582 74 0.1824 -0.1169 0.0032 843383271.34 23427313.0928 4840.177 75 0.1957 -0.1308 0.0036 1024071950.6915 28446443.0748 5333.5207 76 0.2062 -0.1195 0.0033 849904758.6381 23608465.5177 4858.8543 77 0.219 -0.121 0.0034 845537417.8953 23487150.4971 4846.3544 78 0.2231 -0.1394 0.0039 1174098867.2396 32613857.4233 5710.8544 79 0.1986 -0.1629 0.0045 2182209578.0965 60616932.7249 7785.6877 80 0.1982 -0.1916 0.0053 3252663408.4751 90351761.3465 9505.3544 81 0.2167 -0.1807 0.005 2586548991.2852 71848583.0913 8476.3544 82 0.2312 -0.2325 0.0065 4001210979.0236 111144749.4173 10542.521 83 0.2464 -0.2471 0.0069 4218259085.0275 117173863.473 10824.6877 84 0.249 -0.2722 0.0076 5297383446.1504 147149540.1708 12130.521

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277829fh0qq3ovyx25pzq/1ew9z1229277731.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277829fh0qq3ovyx25pzq/1ew9z1229277731.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277829fh0qq3ovyx25pzq/240xg1229277731.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277829fh0qq3ovyx25pzq/240xg1229277731.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; 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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