Paper Forecasting ARIMA 24m

*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: Sat, 11 Dec 2010 12:59:41 +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/11/t12920722547mq6pwoiudghf9o.htm/, Retrieved Sat, 11 Dec 2010 13:57:36 +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/11/t12920722547mq6pwoiudghf9o.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:

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17848 19592 21092 20899 25890 24965 22225 20977 22897 22785 22769 19637 20203 20450 23083 21738 26766 25280 22574 22729 21378 22902 24989 21116 15169 15846 20927 18273 22538 15596 14034 11366 14861 15149 13577 13026 13190 13196 15826 14733 16307 15703 14589 12043 15057 14053 12698 10888 10045 11549 13767 12434 13116 14211 12266 12602 15714 13742 12745 10491 10057 10900 11771 11992 11933 14504 11727 11477 13578 11555 11846 11397 10066 10269 14279 13870 13695 14420 11424 9704 12464 14301 13464 9893 11572 12380 16692 16052 16459 14761 13654 13480 18068 16560 14530 10650 11651 13735 13360 17818 20613 16231 13862 12004 17734 15034 12609 12320 10833 11350 13648 14890 16325 18045 15616 11926 16855 15083 12520 12355

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 '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[96]) 84 9893 - - - - - - - 85 11572 - - - - - - - 86 12380 - - - - - - - 87 16692 - - - - - - - 88 16052 - - - - - - - 89 16459 - - - - - - - 90 14761 - - - - - - - 91 13654 - - - - - - - 92 13480 - - - - - - - 93 18068 - - - - - - - 94 16560 - - - - - - - 95 14530 - - - - - - - 96 10650 - - - - - - - 97 11651 10547.6976 6980.6036 14114.7915 0.2722 0.4776 0.2868 0.4776 98 13735 11238.2191 6194.4144 16282.0238 0.166 0.4363 0.3286 0.5904 99 13360 14571.782 8394.7461 20748.8179 0.3503 0.6047 0.2506 0.8933 100 17818 13922.6163 6790.1849 21055.0478 0.1422 0.5614 0.2792 0.8158 101 20613 14648.8933 6674.7234 22623.0632 0.0713 0.218 0.3282 0.8372 102 16231 14286.4203 5551.2505 23021.5902 0.3313 0.0779 0.4576 0.7927 103 13862 12302.4413 2867.4533 21737.4293 0.373 0.2072 0.3894 0.6343 104 12004 11535.8736 1449.5063 21622.2409 0.4638 0.3256 0.3528 0.5683 105 17734 14792.7228 4094.5635 25490.882 0.295 0.6953 0.2742 0.7761 106 15034 14175.9909 2899.182 25452.7997 0.4407 0.2682 0.3393 0.73 107 12609 13106.5993 1279.4178 24933.7809 0.4671 0.3747 0.4068 0.658 108 12320 10254.0909 -2098.9666 22607.1484 0.3715 0.3543 0.475 0.475 109 10833 10151.7884 -3122.416 23425.9928 0.4599 0.3744 0.4124 0.4707 110 11350 10842.31 -3292.2547 24976.8747 0.4719 0.5005 0.3442 0.5106 111 13648 14175.8728 -769.6059 29121.3516 0.4724 0.6445 0.5426 0.6781 112 14890 13526.7072 -2187.8959 29241.3103 0.4325 0.494 0.2962 0.6401 113 16325 14252.9842 -2194.8172 30700.7855 0.4025 0.4697 0.2243 0.6662 114 18045 13890.5112 -3259.1705 31040.1929 0.3175 0.3904 0.3945 0.6444 115 15616 11906.5322 -5917.4124 29730.4767 0.3417 0.2498 0.4149 0.5549 116 11926 11139.9645 -7333.6496 29613.5785 0.4668 0.3174 0.4635 0.5207 117 16855 14396.8136 -4704.3861 33498.0134 0.4004 0.6001 0.366 0.6497 118 15083 13780.0817 -5928.7297 33488.8931 0.4485 0.3799 0.4504 0.6222 119 12520 12710.6902 -7587.5526 33008.9331 0.4927 0.4094 0.5039 0.5789 120 12355 9858.1817 -11012.8527 30729.2162 0.4073 0.4013 0.4086 0.4704 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 97 0.1725 0.1046 0 1217276.2452 0 0 98 0.229 0.2222 0.1634 6233914.806 3725595.5256 1930.1802 99 0.2163 -0.0832 0.1366 1468415.5518 2973202.201 1724.2976 100 0.2614 0.2798 0.1724 15174013.8185 6023405.1053 2454.2626 101 0.2777 0.4071 0.2194 35570568.9192 11932837.8681 3454.394 102 0.312 0.1361 0.2055 3781390.0437 10574263.2307 3251.8092 103 0.3913 0.1268 0.1942 2432223.277 9411114.6659 3067.754 104 0.4461 0.0406 0.175 219142.3281 8262118.1237 2874.39 105 0.369 0.1988 0.1777 8651111.7291 8305339.6354 2881.8986 106 0.4059 0.0605 0.166 736179.6704 7548423.6389 2747.4395 107 0.4604 -0.038 0.1543 247605.1129 6884712.8638 2623.8736 108 0.6146 0.2015 0.1583 4267980.5466 6666651.8374 2581.986 109 0.6671 0.0671 0.1512 464049.1896 6189528.5568 2487.8763 110 0.6651 0.0468 0.1438 257749.1583 5765830.0283 2401.2143 111 0.5379 -0.0372 0.1367 278649.7357 5400018.0088 2323.7939 112 0.5927 0.1008 0.1344 1858567.2259 5178677.3349 2275.6707 113 0.5888 0.1454 0.1351 4293249.6791 5126593.3551 2264.1982 114 0.6299 0.2991 0.1442 17259777.1105 5800659.1193 2408.4558 115 0.7638 0.3115 0.153 13760151.4586 6219579.7687 2493.9085 116 0.8461 0.0706 0.1489 617851.8623 5939493.3734 2437.1076 117 0.6769 0.1707 0.1499 6042680.184 5944407.0311 2438.1155 118 0.7297 0.0946 0.1474 1697596.0055 5751370.1663 2398.2014 119 0.8148 -0.015 0.1416 36362.7587 5502891.5833 2345.8243 120 1.0802 0.2533 0.1463 6234101.4554 5533358.6613 2352.3092

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/11/t12920722547mq6pwoiudghf9o/14c3j1292072378.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920722547mq6pwoiudghf9o/14c3j1292072378.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920722547mq6pwoiudghf9o/2tv0c1292072378.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/11/t12920722547mq6pwoiudghf9o/2tv0c1292072378.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; 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')

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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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