ws 10 forcasting

*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 11:58:40 -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/t12604715990exg65epzo23e1l.htm/, Retrieved Thu, 10 Dec 2009 20:00:01 +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/t12604715990exg65epzo23e1l.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:

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No (this computation is public)

User-defined keywords:

ws 10 forcasting

Dataseries X:

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8.2 8.0 7.5 6.8 6.5 6.6 7.6 8.0 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7.0 7.1 7.2 7.1 6.9 7.0 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8.0 8.1

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[40]) 28 8.2 - - - - - - - 29 7.9 - - - - - - - 30 7.3 - - - - - - - 31 6.9 - - - - - - - 32 6.6 - - - - - - - 33 6.7 - - - - - - - 34 6.9 - - - - - - - 35 7 - - - - - - - 36 7.1 - - - - - - - 37 7.2 - - - - - - - 38 7.1 - - - - - - - 39 6.9 - - - - - - - 40 7 - - - - - - - 41 6.8 6.9682 6.6547 7.2816 0.1465 0.4211 0 0.4211 42 6.4 7.0459 6.4654 7.6264 0.0146 0.7968 0.1955 0.5616 43 6.7 6.8677 5.9884 7.747 0.3542 0.8514 0.4713 0.3841 44 6.6 6.7018 5.6774 7.7263 0.4228 0.5014 0.5772 0.2842 45 6.4 6.7015 5.6271 7.7759 0.2912 0.5734 0.5011 0.293 46 6.3 6.6609 5.5709 7.7508 0.2582 0.6805 0.3336 0.271 47 6.2 6.6443 5.5495 7.7391 0.2132 0.7312 0.2621 0.2621 48 6.5 6.6092 5.5077 7.7107 0.4229 0.7667 0.1913 0.2434 49 6.8 6.6183 5.5086 7.728 0.3742 0.5828 0.1521 0.2501 50 6.8 6.5181 5.4002 7.636 0.3106 0.3106 0.1538 0.1991 51 6.4 6.4579 5.3322 7.5836 0.4598 0.2757 0.2207 0.1726 52 6.1 6.5581 5.4249 7.6913 0.2141 0.6078 0.2223 0.2223 53 5.8 6.7732 5.5777 7.9688 0.0553 0.8651 0.4825 0.355 54 6.1 7.0164 5.7123 8.3204 0.0842 0.9662 0.8229 0.5098 55 7.2 7.0754 5.6149 8.5358 0.4336 0.9047 0.6928 0.5403 56 7.3 7.0463 5.4857 8.6069 0.375 0.4235 0.7124 0.5232 57 6.9 7.0157 5.4066 8.6248 0.444 0.3645 0.7734 0.5076 58 6.1 7.0044 5.3684 8.6403 0.1393 0.5497 0.8006 0.5021 59 5.8 7.0038 5.3477 8.6599 0.0771 0.8576 0.8293 0.5018 60 6.2 7.0052 5.3307 8.6796 0.173 0.9208 0.7228 0.5024 61 7.1 7.0056 5.3135 8.6976 0.4565 0.8246 0.5941 0.5026 62 7.7 7.0053 5.2963 8.7143 0.2128 0.4568 0.5931 0.5024 63 7.9 7.005 5.2796 8.7304 0.1546 0.2149 0.754 0.5023 64 7.7 7.0048 5.2634 8.7463 0.217 0.1568 0.8457 0.5022 65 7.4 7.0048 5.2475 8.762 0.3297 0.219 0.9105 0.5021 66 7.5 7.0048 5.2319 8.7776 0.292 0.3311 0.8414 0.5021 67 8 7.0048 5.2164 8.7931 0.1377 0.2936 0.4153 0.5021 68 8.1 7.0048 5.2011 8.8084 0.117 0.1397 0.3742 0.5021 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 41 0.023 -0.0241 0 0.0283 0 0 42 0.042 -0.0917 0.0579 0.4172 0.2227 0.4719 43 0.0653 -0.0244 0.0467 0.0281 0.1579 0.3973 44 0.078 -0.0152 0.0389 0.0104 0.121 0.3478 45 0.0818 -0.045 0.0401 0.0909 0.115 0.3391 46 0.0835 -0.0542 0.0424 0.1302 0.1175 0.3428 47 0.0841 -0.0669 0.0459 0.1974 0.1289 0.3591 48 0.085 -0.0165 0.0422 0.0119 0.1143 0.3381 49 0.0855 0.0274 0.0406 0.033 0.1053 0.3245 50 0.0875 0.0432 0.0409 0.0795 0.1027 0.3205 51 0.0889 -0.009 0.038 0.0034 0.0937 0.306 52 0.0882 -0.0699 0.0406 0.2099 0.1033 0.3215 53 0.0901 -0.1437 0.0486 0.9472 0.1683 0.4102 54 0.0948 -0.1306 0.0544 0.8397 0.2162 0.465 55 0.1053 0.0176 0.052 0.0155 0.2028 0.4504 56 0.113 0.036 0.051 0.0644 0.1942 0.4407 57 0.117 -0.0165 0.0489 0.0134 0.1835 0.4284 58 0.1192 -0.1291 0.0534 0.8179 0.2188 0.4677 59 0.1206 -0.1719 0.0596 1.4492 0.2835 0.5325 60 0.122 -0.1149 0.0624 0.6483 0.3018 0.5493 61 0.1232 0.0135 0.0601 0.0089 0.2878 0.5365 62 0.1245 0.0992 0.0618 0.4826 0.2967 0.5447 63 0.1257 0.1278 0.0647 0.8011 0.3186 0.5645 64 0.1268 0.0992 0.0661 0.4833 0.3255 0.5705 65 0.128 0.0564 0.0658 0.1562 0.3187 0.5645 66 0.1291 0.0707 0.0659 0.2452 0.3159 0.562 67 0.1303 0.1421 0.0688 0.9905 0.3409 0.5838 68 0.1314 0.1564 0.0719 1.1995 0.3715 0.6095

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t12604715990exg65epzo23e1l/1febd1260471517.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604715990exg65epzo23e1l/1febd1260471517.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604715990exg65epzo23e1l/2d5l91260471517.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t12604715990exg65epzo23e1l/2d5l91260471517.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; 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 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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