WS 10 Forecast Werkzoekenden Mannen

*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: Thu, 17 Dec 2009 14:00:37 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/17/t1261083915j7l9v71bc9vibnh.htm/, Retrieved Thu, 17 Dec 2009 22:05:17 +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/2009/Dec/17/t1261083915j7l9v71bc9vibnh.htm/}, year = {2009}, } @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 = {2009}, 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:

kvn WS10 review

Dataseries X:

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267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710

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 3 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[39]) 27 276836 - - - - - - - 28 275216 - - - - - - - 29 274352 - - - - - - - 30 271311 - - - - - - - 31 289802 - - - - - - - 32 290726 - - - - - - - 33 292300 - - - - - - - 34 278506 - - - - - - - 35 269826 - - - - - - - 36 265861 - - - - - - - 37 269034 - - - - - - - 38 264176 - - - - - - - 39 255198 - - - - - - - 40 253353 248783.779 243725.2332 253842.3248 0.0383 0.0065 0 0.0065 41 246057 245467.3851 237009.7179 253925.0522 0.4457 0.0338 0 0.0121 42 235372 242584.4337 229872.0152 255296.8522 0.1331 0.2962 0 0.0259 43 258556 258678.5158 243717.2594 273639.7722 0.4936 0.9989 0 0.6758 44 260993 258552.7059 240927.253 276178.1588 0.3931 0.4999 2e-04 0.6454 45 254663 258794.5413 238753.9924 278835.0903 0.3431 0.4149 5e-04 0.6375 46 250643 243598.934 221265.2711 265932.5969 0.2682 0.1658 0.0011 0.1544 47 243422 233716.1506 209080.0014 258352.2998 0.22 0.089 0.002 0.0437 48 247105 228482.1872 201614.1431 255350.2313 0.0871 0.1379 0.0032 0.0257 49 248541 230450.7837 201367.8689 259533.6985 0.1114 0.1308 0.0047 0.0477 50 245039 224421.1713 193142.6495 255699.693 0.0982 0.0653 0.0064 0.0269 51 237080 214292.2975 180836.6013 247747.9937 0.0909 0.0358 0.0083 0.0083 52 237085 206764.0414 169101.1237 244426.9592 0.0573 0.0573 0.0077 0.0059 53 225554 202359.6743 160007.6124 244711.7361 0.1415 0.054 0.0216 0.0072 54 226839 198417.2638 150499.3503 246335.1774 0.1225 0.1335 0.0653 0.0101 55 247934 213479.8703 161103.6466 265856.0941 0.0986 0.3086 0.0458 0.0592 56 248333 212348.849 155187.1416 269510.5564 0.1086 0.1112 0.0477 0.0709 57 246969 211611.7657 149835.063 273388.4684 0.131 0.122 0.086 0.0834 58 245098 195462.5692 129168.1813 261756.9571 0.0711 0.0639 0.0514 0.0387 59 246263 184650.8971 113837.0103 255464.7838 0.0441 0.0472 0.0519 0.0254 60 255765 178512.1588 103245.2741 253779.0434 0.0221 0.0388 0.037 0.0229 61 264319 179599.4203 99903.6499 259295.1907 0.0186 0.0305 0.045 0.0315 62 268347 172711.3283 88613.3536 256809.3029 0.0129 0.0164 0.0459 0.0273 63 273046 161746.2329 73272.4837 250219.9821 0.0068 0.0091 0.0476 0.0192 64 273963 153403.4337 58916.3126 247890.5548 0.0062 0.0065 0.0413 0.0174 65 267430 148205.6429 47270.0537 249141.2321 0.0103 0.0073 0.0666 0.0189 66 271993 143490.3791 35358.4712 251622.287 0.0099 0.0123 0.0654 0.0214 67 292710 157800.1697 43264.8217 272335.5176 0.0105 0.0253 0.0615 0.0478 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 40 0.0104 0.0184 0 20877780.3572 0 0 41 0.0176 0.0024 0.0104 347645.7774 10612713.0673 3257.7159 42 0.0267 -0.0297 0.0168 52019199.5387 24414875.2244 4941.1411 43 0.0295 -5e-04 0.0127 15010.1208 18314908.9485 4279.5921 44 0.0348 0.0094 0.0121 5955035.404 15842934.2396 3980.3184 45 0.0395 -0.016 0.0127 17069633.838 16047384.1727 4005.9186 46 0.0468 0.0289 0.015 49618865.5608 20843310.0853 4565.4474 47 0.0538 0.0415 0.0184 94203512.3569 30013335.3692 5478.4428 48 0.06 0.0815 0.0254 346809156.9088 65212871.0958 8075.4487 49 0.0644 0.0785 0.0307 327255926.8886 91417176.6751 9561.233 50 0.0711 0.0919 0.0362 425094862.0605 121751511.7101 11034.1067 51 0.0797 0.1063 0.0421 519279386.9456 154878834.6464 12445.0325 52 0.0929 0.1466 0.0501 919360527.8144 213685118.7363 14617.9725 53 0.1068 0.1146 0.0547 537976746.6267 236848806.4427 15389.893 54 0.1232 0.1432 0.0606 807795085.9793 274911891.7452 16580.4672 55 0.1252 0.1614 0.0669 1187087051.6443 331922839.2389 18218.7497 56 0.1373 0.1695 0.073 1294859121.0971 388566149.9364 19712.0813 57 0.1489 0.1671 0.0782 1250134020.0337 436431031.6085 20890.9318 58 0.173 0.2539 0.0874 2463675994.0394 543128134.8943 23305.1096 59 0.1957 0.3337 0.0998 3796051227.0185 705774289.5005 26566.4128 60 0.2151 0.4328 0.1156 5968001479.6556 956356536.6508 30925.0147 61 0.2264 0.4717 0.1318 7177407187.801 1239131566.2485 35201.3006 62 0.2484 0.5537 0.1501 9146181704.0072 1582916354.8467 39785.8814 63 0.2791 0.6881 0.1726 12387638164.0962 2033113096.8988 45090.0554 64 0.3143 0.7859 0.1971 14534609031.9268 2533172934.2999 50330.6361 65 0.3475 0.8045 0.2205 14214447327.1261 2982452718.6394 54611.8368 66 0.3845 0.8955 0.2455 16512923574.7699 3483581268.8664 59021.8711 67 0.3703 0.8549 0.2672 18200662320.2718 4009191306.4166 63318.1752

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/17/t1261083915j7l9v71bc9vibnh/18kkq1261083633.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261083915j7l9v71bc9vibnh/18kkq1261083633.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261083915j7l9v71bc9vibnh/222uw1261083633.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/17/t1261083915j7l9v71bc9vibnh/222uw1261083633.ps (open in new window)

Parameters (Session):

par1 = 6 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 2 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 6 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 2 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

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

par1 <- as.numeric(par1) #cut off periods par1 <- 28 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 par6 <- 3 par7 <- as.numeric(par7) #q par7 <- 3 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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