forecasting voor Appelensoort Jonagold

*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, 19 Dec 2009 05:03:00 -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/19/t1261224267vb5f8khnihb8eh6.htm/, Retrieved Sat, 19 Dec 2009 13:04:29 +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/19/t1261224267vb5f8khnihb8eh6.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:

» Textbox « » Textfile « » CSV «

1.19 1.18 1.18 1.33 1.3 1.25 1.22 1.17 1.18 1.19 1.21 1.21 1.2 1.2 1.29 1.83 1.85 1.54 1.52 1.43 1.4 1.4 1.39 1.37 1.33 1.36 1.34 1.75 1.84 1.73 1.63 1.5 1.45 1.38 1.38 1.27 1.31 1.29 1.32 1.48 1.39 1.45 1.44 1.44 1.42 1.39 1.4 1.39 1.3 1.32 1.35 1.51 1.37 1.25 1.15 1.09 1.09 1.06 1.02 1.01 1 1 1.05 1.3 1.34 1.24 1.22 1.06 1 1 1 1.01

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 1 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 1.5 - - - - - - - 33 1.45 - - - - - - - 34 1.38 - - - - - - - 35 1.38 - - - - - - - 36 1.27 - - - - - - - 37 1.31 - - - - - - - 38 1.29 - - - - - - - 39 1.32 - - - - - - - 40 1.48 - - - - - - - 41 1.39 - - - - - - - 42 1.45 - - - - - - - 43 1.44 - - - - - - - 44 1.44 - - - - - - - 45 1.42 1.4667 1.2429 1.6904 0.3414 0.5923 0.558 0.5923 46 1.39 1.4362 1.1033 1.769 0.3929 0.5379 0.6296 0.491 47 1.4 1.4389 1.0698 1.8079 0.4182 0.6024 0.6227 0.4976 48 1.39 1.4234 1.032 1.8149 0.4336 0.5467 0.7788 0.4669 49 1.3 1.4232 1.0242 1.8222 0.2726 0.5648 0.7109 0.4671 50 1.32 1.418 1.0145 1.8215 0.317 0.7167 0.7329 0.4574 51 1.35 1.4195 1.0136 1.8254 0.3686 0.6845 0.6845 0.4606 52 1.51 1.4193 1.011 1.8277 0.3317 0.6304 0.3855 0.4605 53 1.37 1.4215 1.0103 1.8327 0.4031 0.3365 0.5596 0.4648 54 1.25 1.4225 1.0074 1.8377 0.2076 0.598 0.4484 0.4672 55 1.15 1.424 1.004 1.844 0.1005 0.7916 0.4702 0.4702 56 1.09 1.4246 0.9988 1.8504 0.0618 0.8969 0.4717 0.4717 57 1.09 1.425 0.9929 1.8572 0.0643 0.9357 0.5091 0.4729 58 1.06 1.425 0.9863 1.8638 0.0515 0.9328 0.5622 0.4734 59 1.02 1.4249 0.9796 1.8703 0.0374 0.9459 0.5437 0.4736 60 1.01 1.4247 0.973 1.8764 0.036 0.9605 0.5598 0.4735 61 1 1.4245 0.9668 1.8822 0.0346 0.962 0.703 0.4735 62 1 1.4243 0.9608 1.8878 0.0364 0.9636 0.6704 0.4736 63 1.05 1.4242 0.9551 1.8933 0.059 0.9618 0.6217 0.4737 64 1.3 1.4241 0.9496 1.8987 0.3041 0.9389 0.3614 0.4739 65 1.34 1.4241 0.9442 1.904 0.3656 0.6939 0.5875 0.4742 66 1.24 1.4241 0.939 1.9093 0.2285 0.633 0.7591 0.4745 67 1.22 1.4242 0.9338 1.9146 0.2072 0.7692 0.8634 0.4748 68 1.06 1.4242 0.9286 1.9198 0.0749 0.7904 0.9069 0.4751 69 1 1.4242 0.9235 1.925 0.0484 0.923 0.9046 0.4754 70 1 1.4243 0.9184 1.9301 0.0501 0.9499 0.9209 0.4757 71 1 1.4243 0.9133 1.9352 0.0518 0.9482 0.9395 0.4759 72 1.01 1.4243 0.9083 1.9403 0.0578 0.9465 0.9422 0.4762 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 45 0.0778 -0.0318 0 0.0022 0 0 46 0.1182 -0.0321 0.032 0.0021 0.0022 0.0464 47 0.1309 -0.027 0.0303 0.0015 0.0019 0.044 48 0.1403 -0.0235 0.0286 0.0011 0.0017 0.0416 49 0.143 -0.0866 0.0402 0.0152 0.0044 0.0665 50 0.1452 -0.0691 0.045 0.0096 0.0053 0.0727 51 0.1459 -0.049 0.0456 0.0048 0.0052 0.0723 52 0.1468 0.0639 0.0479 0.0082 0.0056 0.0748 53 0.1476 -0.0362 0.0466 0.0027 0.0053 0.0726 54 0.1489 -0.1213 0.054 0.0298 0.0077 0.0879 55 0.1505 -0.1924 0.0666 0.0751 0.0138 0.1176 56 0.1525 -0.2349 0.0806 0.1119 0.022 0.1484 57 0.1547 -0.2351 0.0925 0.1122 0.029 0.1702 58 0.1571 -0.2562 0.1042 0.1333 0.0364 0.1908 59 0.1594 -0.2842 0.1162 0.164 0.0449 0.2119 60 0.1617 -0.2911 0.1271 0.172 0.0529 0.2299 61 0.1639 -0.298 0.1372 0.1802 0.0603 0.2456 62 0.166 -0.2979 0.1461 0.18 0.067 0.2588 63 0.1681 -0.2627 0.1523 0.14 0.0708 0.2662 64 0.17 -0.0872 0.149 0.0154 0.0681 0.2609 65 0.1719 -0.0591 0.1447 0.0071 0.0652 0.2553 66 0.1738 -0.1293 0.144 0.0339 0.0637 0.2525 67 0.1757 -0.1434 0.144 0.0417 0.0628 0.2506 68 0.1775 -0.2557 0.1486 0.1326 0.0657 0.2563 69 0.1794 -0.2979 0.1546 0.18 0.0703 0.2651 70 0.1812 -0.2979 0.1601 0.18 0.0745 0.2729 71 0.183 -0.2979 0.1652 0.18 0.0784 0.28 72 0.1848 -0.2909 0.1697 0.1716 0.0817 0.2859

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/19/t1261224267vb5f8khnihb8eh6/1wyaq1261224178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261224267vb5f8khnihb8eh6/1wyaq1261224178.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261224267vb5f8khnihb8eh6/22cjy1261224178.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/19/t1261224267vb5f8khnihb8eh6/22cjy1261224178.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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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