WS 10

*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: Tue, 15 Dec 2009 01:18:50 -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/15/t1260865212ny14yg1sp7rjcyx.htm/, Retrieved Tue, 15 Dec 2009 09:20:15 +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/15/t1260865212ny14yg1sp7rjcyx.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:

WS 10

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

15.89 16.93 20.28 22.52 23.51 22.59 23.51 24.76 26.08 25.29 23.38 25.29 28.42 31.85 30.1 25.45 24.95 26.84 27.52 27.94 25.23 26.53 27.21 28.53 30.35 31.21 32.86 33.2 35.73 34.53 36.54 40.1 40.56 46.14 42.85 38.22 40.18 42.19 47.56 47.26 44.03 49.83 53.35 58.9 59.64 56.99 53.2 53.24 57.85 55.69 55.64 62.52 64.4 64.65 67.71 67.21 59.37 53.26 52.42 55.03

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[32]) 20 27.94 - - - - - - - 21 25.23 - - - - - - - 22 26.53 - - - - - - - 23 27.21 - - - - - - - 24 28.53 - - - - - - - 25 30.35 - - - - - - - 26 31.21 - - - - - - - 27 32.86 - - - - - - - 28 33.2 - - - - - - - 29 35.73 - - - - - - - 30 34.53 - - - - - - - 31 36.54 - - - - - - - 32 40.1 - - - - - - - 33 40.56 43.5653 40.4782 46.6525 0.0282 0.9861 1 0.9861 34 46.14 44.5196 38.8723 50.1668 0.2869 0.9153 1 0.9375 35 42.85 42.0266 33.9435 50.1097 0.4209 0.1593 0.9998 0.6798 36 38.22 41.0451 31.8484 50.2418 0.2736 0.3502 0.9962 0.5798 37 40.18 42.1495 32.2693 52.0298 0.348 0.7822 0.9904 0.6578 38 42.19 42.7953 32.0384 53.5522 0.4561 0.6832 0.9826 0.6883 39 47.56 42.1447 30.3778 53.9116 0.1835 0.497 0.939 0.6333 40 47.26 41.6495 29.0522 54.2467 0.1913 0.1789 0.9057 0.5953 41 44.03 41.7314 28.4595 55.0033 0.3671 0.2071 0.8123 0.5952 42 49.83 42.0877 28.1436 56.0318 0.1382 0.3924 0.856 0.61 43 53.35 41.894 27.2522 56.5359 0.0626 0.144 0.7632 0.5949 44 58.9 41.5316 26.2314 56.8318 0.013 0.065 0.5728 0.5728 45 59.64 41.3391 25.4839 57.1944 0.0118 0.015 0.5384 0.5609 46 56.99 41.3844 25.0166 57.7522 0.0308 0.0144 0.2845 0.5611 47 53.2 41.5332 24.669 58.3974 0.0876 0.0362 0.4392 0.5661 48 53.24 41.5463 24.179 58.9136 0.0935 0.0942 0.6463 0.5648 49 57.85 41.4841 23.6245 59.3436 0.0362 0.0985 0.5569 0.5604 50 55.69 41.4759 23.1476 59.8041 0.0643 0.04 0.4696 0.5585 51 55.64 41.5322 22.7502 60.3143 0.0705 0.0698 0.2647 0.5594 52 62.52 41.5529 22.3228 60.7829 0.0163 0.0755 0.2804 0.5589 53 64.4 41.5572 21.887 61.2275 0.0114 0.0184 0.4027 0.5577 54 64.65 41.5345 21.436 61.633 0.0121 0.0129 0.2093 0.5556 55 67.71 41.5614 21.045 62.0778 0.0062 0.0137 0.13 0.5555 56 67.21 41.6004 20.6736 62.5272 0.0082 0.0072 0.0526 0.5559 57 59.37 41.631 20.2953 62.9667 0.0516 0.0094 0.049 0.5559 58 53.26 41.6342 19.8947 63.3737 0.1473 0.0549 0.0831 0.555 59 52.42 41.612 19.4748 63.7492 0.1693 0.1512 0.1524 0.5532 60 55.03 41.6044 19.0788 64.1301 0.1214 0.1733 0.1557 0.5521 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0362 -0.069 0 9.032 0 0 34 0.0647 0.0364 0.0527 2.6258 5.8289 2.4143 35 0.0981 0.0196 0.0417 0.678 4.1119 2.0278 36 0.1143 -0.0688 0.0485 7.9814 5.0793 2.2537 37 0.1196 -0.0467 0.0481 3.8791 4.8393 2.1998 38 0.1282 -0.0141 0.0424 0.3664 4.0938 2.0233 39 0.1425 0.1285 0.0547 29.3252 7.6983 2.7746 40 0.1543 0.1347 0.0647 31.4781 10.6708 3.2666 41 0.1623 0.0551 0.0637 5.2836 10.0722 3.1737 42 0.169 0.184 0.0757 59.9432 15.0593 3.8806 43 0.1783 0.2735 0.0937 131.2388 25.6211 5.0617 44 0.188 0.4182 0.1207 301.662 48.6245 6.9731 45 0.1957 0.4427 0.1455 334.9217 70.6473 8.4052 46 0.2018 0.3771 0.162 243.5338 82.9964 9.1102 47 0.2072 0.2809 0.17 136.1145 86.5376 9.3026 48 0.2133 0.2815 0.1769 136.7422 89.6754 9.4697 49 0.2197 0.3945 0.1897 267.844 100.1559 10.0078 50 0.2255 0.3427 0.1982 202.0414 105.8162 10.2867 51 0.2307 0.3397 0.2057 199.0287 110.7221 10.5225 52 0.2361 0.5046 0.2206 439.6207 127.167 11.2768 53 0.2415 0.5497 0.2363 521.7919 145.9587 12.0813 54 0.2469 0.5565 0.2508 534.3261 163.6118 12.7911 55 0.2519 0.6292 0.2673 683.7487 186.2264 13.6465 56 0.2567 0.6156 0.2818 655.8506 205.7941 14.3455 57 0.2615 0.4261 0.2876 314.673 210.1492 14.4965 58 0.2664 0.2792 0.2873 135.1597 207.265 14.3967 59 0.2714 0.2597 0.2862 116.8129 203.9149 14.2799 60 0.2762 0.3227 0.2875 180.2455 203.0696 14.2502

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260865212ny14yg1sp7rjcyx/1fz621260865127.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260865212ny14yg1sp7rjcyx/1fz621260865127.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260865212ny14yg1sp7rjcyx/2ztij1260865127.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260865212ny14yg1sp7rjcyx/2ztij1260865127.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; 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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