*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, 10 Dec 2009 08:30:09 -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/10/t1260459052zn8aq2jgyz4tvte.htm/, Retrieved Thu, 10 Dec 2009 16:30:55 +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/10/t1260459052zn8aq2jgyz4tvte.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:

Dataseries X:

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116222 110924 103753 99983 93302 91496 119321 139261 133739 123913 113438 109416 109406 105645 101328 97686 93093 91382 122257 139183 139887 131822 116805 113706 113012 110452 107005 102841 98173 98181 137277 147579 146571 138920 130340 128140 127059 122860 117702 113537 108366 111078 150739 159129 157928 147768 137507 136919 136151 133001 125554 119647 114158 116193 152803 161761 160942 149470 139208 134588 130322 126611 122401 117352 112135 112879 148729 157230 157221 146681 136524 132111

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 7 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[44]) 32 147579 - - - - - - - 33 146571 - - - - - - - 34 138920 - - - - - - - 35 130340 - - - - - - - 36 128140 - - - - - - - 37 127059 - - - - - - - 38 122860 - - - - - - - 39 117702 - - - - - - - 40 113537 - - - - - - - 41 108366 - - - - - - - 42 111078 - - - - - - - 43 150739 - - - - - - - 44 159129 - - - - - - - 45 157928 157749.1203 152651.8802 162846.3604 0.4726 0.2979 1 0.2979 46 147768 149948.3497 144019.8901 155876.8094 0.2355 0.0042 0.9999 0.0012 47 137507 141423.0497 135106.4576 147739.6417 0.1122 0.0245 0.9997 0 48 136919 139387.7381 132548.8934 146226.5828 0.2396 0.7051 0.9994 0 49 136151 138456.3676 130732.0562 146180.679 0.2793 0.6518 0.9981 0 50 133001 134327.6918 125403.4382 143251.9453 0.3854 0.3444 0.9941 0 51 125554 129153.0964 119002.9044 139303.2884 0.2435 0.2287 0.9865 0 52 119647 124925.9019 113732.7406 136119.0633 0.1776 0.4562 0.9769 0 53 114158 119692.9851 107689.4285 131696.5416 0.1831 0.503 0.9678 0 54 116193 122374.1763 109727.6063 135020.7462 0.169 0.8986 0.96 0 55 152803 162038.6452 148830.3472 175246.9432 0.0853 1 0.9532 0.667 56 161761 170452.5614 156695.8424 184209.2803 0.1078 0.994 0.9467 0.9467 57 160942 169097.6843 152610.3999 185584.9687 0.1661 0.8084 0.9079 0.882 58 149470 161310.5861 143331.3493 179289.8228 0.0984 0.516 0.9301 0.594 59 139208 152784.9734 133700.0193 171869.9275 0.0816 0.6332 0.9417 0.2574 60 134588 150740.6962 130471.1981 171010.1944 0.0592 0.8676 0.9093 0.2086 61 130322 149799.1761 128102.1681 171496.184 0.0392 0.9153 0.8912 0.1997 62 126611 145664.5863 122339.9723 168989.2003 0.0547 0.9013 0.8564 0.1289 63 122401 140489.6252 115527.036 165452.2144 0.0778 0.8621 0.8795 0.0717 64 117352 136265.788 109805.6639 162725.9122 0.0806 0.8478 0.8908 0.0452 65 112135 131036.9443 103271.3983 158802.4903 0.0911 0.833 0.8833 0.0237 66 112879 133720.6866 104802.5034 162638.8697 0.0789 0.9283 0.8826 0.0425 67 148729 173385.4892 143400.5172 203370.4611 0.0535 1 0.9108 0.8243 68 157230 181798.1715 150773.9512 212822.3918 0.0603 0.9817 0.8972 0.924 69 157221 180441.6631 146727.2446 214156.0816 0.0885 0.9114 0.8715 0.8923 70 146681 172653.4784 137104.5419 208202.4148 0.0761 0.8026 0.8994 0.7721 71 136524 164127.6539 127061.2539 201194.0538 0.0722 0.8219 0.9062 0.6042 72 132111 162083.8249 123442.1173 200725.5325 0.0642 0.9026 0.9184 0.5596 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 45 0.0165 0.0011 0 31997.9463 0 0 46 0.0202 -0.0145 0.0078 4753924.9539 2392961.4501 1546.92 47 0.0228 -0.0277 0.0145 15335444.8808 6707122.5937 2589.8113 48 0.025 -0.0177 0.0153 6094667.8063 6554008.8968 2560.0799 49 0.0285 -0.0167 0.0155 5314719.818 6306151.0811 2511.2051 50 0.0339 -0.0099 0.0146 1760111.0424 5548477.7413 2355.5207 51 0.0401 -0.0279 0.0165 12953494.6208 6606337.2955 2570.2796 52 0.0457 -0.0423 0.0197 27866805.7133 9263895.8477 3043.6649 53 0.0512 -0.0462 0.0227 30636059.9422 11638580.7471 3411.5364 54 0.0527 -0.0505 0.0254 38206939.9849 14295416.6709 3780.928 55 0.0416 -0.057 0.0283 85297142.2857 20750118.9995 4555.2299 56 0.0412 -0.051 0.0302 75543239.2225 25316212.3514 5031.5219 57 0.0497 -0.0482 0.0316 66515186.2952 28485364.1933 5337.1682 58 0.0569 -0.0734 0.0346 140199478.5396 36464943.7894 6038.621 59 0.0637 -0.0889 0.0382 184334207.7048 46322894.7171 6806.0925 60 0.0686 -0.1072 0.0425 260909594.8648 59734563.4763 7728.8138 61 0.0739 -0.13 0.0477 379360387.9611 78536082.5637 8862.0586 62 0.0817 -0.1308 0.0523 363039151.496 94341808.6155 9712.9712 63 0.0907 -0.1288 0.0563 327198361.7864 106597416.6771 10324.6025 64 0.0991 -0.1388 0.0604 357731377.7305 119154114.7298 10915.7737 65 0.1081 -0.1442 0.0644 357283499.4721 130493609.2413 11423.3799 66 0.1103 -0.1559 0.0686 434375899.1139 144306440.5992 12012.7616 67 0.0882 -0.1422 0.0718 607942458.449 164464528.3318 12824.3724 68 0.0871 -0.1351 0.0744 603595051.429 182761633.4608 13518.9361 69 0.0953 -0.1287 0.0766 539199193.3232 197019135.8553 14036.3505 70 0.105 -0.1504 0.0794 674569633.6668 215386462.6942 14676.0507 71 0.1152 -0.1682 0.0827 761961708.0377 235629990.2995 15350.244 72 0.1216 -0.1849 0.0864 898370232.0835 259299284.649 16102.7726

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459052zn8aq2jgyz4tvte/1d7w71260459002.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459052zn8aq2jgyz4tvte/1d7w71260459002.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459052zn8aq2jgyz4tvte/2saf31260459002.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260459052zn8aq2jgyz4tvte/2saf31260459002.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; 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 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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