*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: Mon, 14 Dec 2009 06:19:12 -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/14/t1260796833p09odpm9r709tfk.htm/, Retrieved Mon, 14 Dec 2009 14:20:36 +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/2009/Dec/14/t1260796833p09odpm9r709tfk.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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95.1 97.0 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99.0 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102.0 106.0 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100.0 110.7 112.8 109.8 117.3 109.1 115.9 96.0 99.8 116.8 115.7 99.4 94.3

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 4 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 95.7 - - - - - - - 21 113.2 - - - - - - - 22 105.9 - - - - - - - 23 108.8 - - - - - - - 24 102.3 - - - - - - - 25 99 - - - - - - - 26 100.7 - - - - - - - 27 115.5 - - - - - - - 28 100.7 - - - - - - - 29 109.9 - - - - - - - 30 114.6 - - - - - - - 31 85.4 - - - - - - - 32 100.5 - - - - - - - 33 114.8 114.8675 107.793 121.5308 0.4921 1 0.6881 1 34 116.5 108.9491 101.4329 115.9792 0.0176 0.0514 0.8024 0.9908 35 112.9 107.8555 99.7502 115.3929 0.0948 0.0123 0.403 0.9721 36 102 103.148 94.4401 111.1759 0.3896 0.0086 0.582 0.741 37 106 97.3684 88.2741 105.683 0.0209 0.1375 0.3503 0.2302 38 105.3 98.8697 89.8758 107.111 0.0631 0.045 0.3317 0.3491 39 118.8 112.561 104.717 119.893 0.0477 0.9739 0.216 0.9994 40 106.1 101.9986 93.2575 110.0476 0.159 0 0.6241 0.6424 41 109.3 103.8109 95.227 111.7373 0.0873 0.2857 0.0661 0.7935 42 117.2 113.5615 105.7689 120.8527 0.164 0.874 0.3901 0.9998 43 92.5 85.1164 74.3988 94.6278 0.0641 0 0.4767 8e-04 44 104.2 98.3857 89.2747 106.7218 0.0858 0.9168 0.3096 0.3096 45 112.5 114.2972 105.7752 122.2264 0.3284 0.9937 0.4505 0.9997 46 122.4 108.714 99.7124 117.0253 6e-04 0.186 0.0332 0.9736 47 113.3 106.904 97.6257 115.439 0.0709 2e-04 0.0843 0.9293 48 100 102.5058 92.7441 111.4154 0.2907 0.0088 0.5443 0.6705 49 110.7 96.9162 86.5614 106.2667 0.0019 0.259 0.0284 0.2263 50 112.8 98.3999 88.208 107.631 0.0011 0.0045 0.0715 0.3278 51 109.8 110.9203 101.9802 119.1918 0.3953 0.328 0.0309 0.9932 52 117.3 101.9588 92.1504 110.903 4e-04 0.0429 0.1821 0.6254 53 109.1 103.5232 93.8763 112.3447 0.1077 0.0011 0.0997 0.7491 54 115.9 113.8959 105.2039 121.9701 0.3133 0.8778 0.2113 0.9994 55 96 83.93 71.6919 94.5979 0.0133 0 0.0577 0.0012 56 99.8 98.059 87.8123 107.3318 0.3564 0.6683 0.0971 0.3029 57 116.8 114.0942 104.7982 122.688 0.2686 0.9994 0.6419 0.999 58 115.7 107.9244 98.0412 116.9755 0.0461 0.0273 9e-04 0.9461 59 99.4 107.6911 97.6975 116.833 0.0377 0.043 0.1146 0.9384 60 94.3 102.5865 92.0048 112.1745 0.0451 0.7426 0.7015 0.6651 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0296 -6e-04 0 0.0046 0 0 34 0.0329 0.0693 0.0349 57.0159 28.5102 5.3395 35 0.0357 0.0468 0.0389 25.447 27.4891 5.243 36 0.0397 -0.0111 0.0319 1.3179 20.9463 4.5767 37 0.0436 0.0886 0.0433 74.5051 31.6581 5.6266 38 0.0425 0.065 0.0469 41.349 33.2732 5.7683 39 0.0332 0.0554 0.0481 38.9246 34.0806 5.8379 40 0.0403 0.0402 0.0471 16.8214 31.9232 5.6501 41 0.039 0.0529 0.0478 30.1297 31.7239 5.6324 42 0.0328 0.032 0.0462 13.2385 29.8754 5.4658 43 0.057 0.0867 0.0499 54.5174 32.1156 5.6671 44 0.0432 0.0591 0.0507 33.8059 32.2564 5.6795 45 0.0354 -0.0157 0.048 3.2298 30.0236 5.4794 46 0.039 0.1259 0.0535 187.3063 41.2581 6.4232 47 0.0407 0.0598 0.054 40.9088 41.2348 6.4214 48 0.0443 -0.0244 0.0521 6.2788 39.05 6.249 49 0.0492 0.1422 0.0574 189.9934 47.9291 6.9231 50 0.0479 0.1463 0.0624 207.3626 56.7865 7.5357 51 0.038 -0.0101 0.0596 1.2551 53.8638 7.3392 52 0.0448 0.1505 0.0641 235.3532 62.9383 7.9334 53 0.0435 0.0539 0.0637 31.1011 61.4222 7.8372 54 0.0362 0.0176 0.0616 4.0163 58.8128 7.669 55 0.0648 0.1438 0.0651 145.6852 62.5899 7.9114 56 0.0482 0.0178 0.0632 3.0311 60.1083 7.753 57 0.0384 0.0237 0.0616 7.3211 57.9968 7.6156 58 0.0428 0.072 0.062 60.4601 58.0915 7.6218 59 0.0433 -0.077 0.0625 68.7422 58.486 7.6476 60 0.0477 -0.0808 0.0632 68.6668 58.8496 7.6713

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t1260796833p09odpm9r709tfk/1k1wh1260796748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260796833p09odpm9r709tfk/1k1wh1260796748.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260796833p09odpm9r709tfk/26ht51260796748.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t1260796833p09odpm9r709tfk/26ht51260796748.ps (open in new window)

Parameters (Session):

par1 = colombia ; par2 = www.ico.org ; par3 = Prices paid to growers in exporting Member countries in US cents per lb (Arabica, 1977/1 - 2006/12) ; par4 = usa ; par5 = www.ico.org ; par6 = Retail prices in importing Member countries in US cents per lb (Arabica, 1977/1 - 2006/12) ;

Parameters (R input):

par1 = 12 ; par2 = 2.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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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