cs.shw.ws10.r3.2

*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: Fri, 18 Dec 2009 02:08:00 -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/18/t1261127581p8pr6syekxhih79.htm/, Retrieved Fri, 18 Dec 2009 10:13:03 +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/18/t1261127581p8pr6syekxhih79.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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7.1 6.9 6.8 7.5 7.6 7.8 8.0 8.1 8.2 8.3 8.2 8.0 7.9 7.6 7.6 8.3 8.4 8.4 8.4 8.4 8.6 8.9 8.8 8.3 7.5 7.2 7.4 8.8 9.3 9.3 8.7 8.2 8.3 8.5 8.6 8.5 8.2 8.1 7.9 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 8.5 8.3 8.0 8.2 8.1 8.1 8.0 7.9 7.9 8.0 8.0 7.9 8.0 7.7 7.2 7.5 7.3 7.0 7.0 7.0 7.2 7.3 7.1 6.8 6.4 6.1 6.5 7.7 7.9 7.5 6.9 6.6 6.9 7.7 8.0 8.0 7.7 7.3 7.4 8.1 8.3 8.2

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[62]) 50 8.3 - - - - - - - 51 8 - - - - - - - 52 8.2 - - - - - - - 53 8.1 - - - - - - - 54 8.1 - - - - - - - 55 8 - - - - - - - 56 7.9 - - - - - - - 57 7.9 - - - - - - - 58 8 - - - - - - - 59 8 - - - - - - - 60 7.9 - - - - - - - 61 8 - - - - - - - 62 7.7 - - - - - - - 63 7.2 7.3891 7.0826 7.6956 0.1133 0.0234 0 0.0234 64 7.5 7.6022 7.0331 8.1713 0.3624 0.917 0.0198 0.3681 65 7.3 7.5592 6.7677 8.3507 0.2605 0.5583 0.0903 0.3637 66 7 7.6678 6.7882 8.5475 0.0684 0.7938 0.1678 0.4714 67 7 7.6904 6.7929 8.5878 0.0658 0.9342 0.2494 0.4916 68 7 7.6575 6.757 8.5581 0.0762 0.9238 0.2989 0.4632 69 7.2 7.6741 6.7644 8.5838 0.1535 0.9268 0.3132 0.4777 70 7.3 7.7324 6.7904 8.6744 0.1841 0.866 0.2889 0.5269 71 7.1 7.6636 6.6636 8.6636 0.1347 0.7619 0.2548 0.4715 72 6.8 7.5173 6.4576 8.5769 0.0923 0.7799 0.2395 0.3677 73 6.4 7.5293 6.4285 8.6301 0.0222 0.903 0.201 0.3806 74 6.1 7.2902 6.1662 8.4142 0.019 0.9397 0.2374 0.2374 75 6.5 7.0684 5.8713 8.2656 0.176 0.9436 0.4147 0.1506 76 7.7 7.442 6.1269 8.7571 0.3503 0.9198 0.4655 0.3503 77 7.9 7.4363 5.9791 8.8935 0.2664 0.3614 0.5727 0.3614 78 7.5 7.5193 5.9651 9.0735 0.4903 0.3156 0.7437 0.4098 79 6.9 7.5117 5.9067 9.1168 0.2275 0.5057 0.734 0.4091 80 6.6 7.4757 5.8403 9.1111 0.147 0.7549 0.7157 0.394 81 6.9 7.5292 5.8609 9.1975 0.2299 0.8625 0.6505 0.4205 82 7.7 7.6228 5.906 9.3396 0.4649 0.7954 0.6438 0.4649 83 8 7.5571 5.7758 9.3384 0.313 0.4375 0.6925 0.4375 84 8 7.3866 5.5372 9.2361 0.2578 0.2578 0.7329 0.3699 85 7.7 7.3215 5.4137 9.2293 0.3487 0.2429 0.8281 0.3487 86 7.3 7.0856 5.1339 9.0373 0.4148 0.2686 0.8389 0.2686 87 7.4 6.9014 4.8744 8.9284 0.3149 0.35 0.651 0.22 88 8.1 7.3737 5.2483 9.4991 0.2515 0.4903 0.3817 0.3817 89 8.3 7.4073 5.1711 9.6435 0.217 0.2719 0.3329 0.3988 90 8.2 7.4888 5.1662 9.8115 0.2742 0.2468 0.4962 0.4293 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 63 0.0212 -0.0256 0 0.0357 0 0 64 0.0382 -0.0134 0.0195 0.0104 0.0231 0.152 65 0.0534 -0.0343 0.0244 0.0672 0.0378 0.1944 66 0.0585 -0.0871 0.0401 0.446 0.1398 0.374 67 0.0595 -0.0898 0.05 0.4766 0.2072 0.4552 68 0.06 -0.0859 0.056 0.4324 0.2447 0.4947 69 0.0605 -0.0618 0.0568 0.2248 0.2419 0.4918 70 0.0622 -0.0559 0.0567 0.187 0.235 0.4848 71 0.0666 -0.0735 0.0586 0.3176 0.2442 0.4942 72 0.0719 -0.0954 0.0623 0.5145 0.2712 0.5208 73 0.0746 -0.15 0.0702 1.2754 0.3625 0.6021 74 0.0787 -0.1633 0.078 1.4166 0.4503 0.6711 75 0.0864 -0.0804 0.0782 0.3231 0.4406 0.6637 76 0.0902 0.0347 0.0751 0.0666 0.4138 0.6433 77 0.1 0.0624 0.0742 0.215 0.4006 0.6329 78 0.1055 -0.0026 0.0697 4e-04 0.3756 0.6128 79 0.109 -0.0814 0.0704 0.3742 0.3755 0.6128 80 0.1116 -0.1171 0.073 0.7668 0.3972 0.6303 81 0.113 -0.0836 0.0736 0.3959 0.3972 0.6302 82 0.1149 0.0101 0.0704 0.006 0.3776 0.6145 83 0.1203 0.0586 0.0699 0.1962 0.369 0.6074 84 0.1277 0.083 0.0704 0.3762 0.3693 0.6077 85 0.1329 0.0517 0.0696 0.1432 0.3595 0.5996 86 0.1405 0.0303 0.068 0.046 0.3464 0.5886 87 0.1499 0.0722 0.0682 0.2486 0.3425 0.5852 88 0.1471 0.0985 0.0693 0.5275 0.3496 0.5913 89 0.154 0.1205 0.0712 0.7969 0.3662 0.6051 90 0.1582 0.095 0.0721 0.5058 0.3712 0.6092

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/18/t1261127581p8pr6syekxhih79/1xwd91261127277.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t1261127581p8pr6syekxhih79/1xwd91261127277.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t1261127581p8pr6syekxhih79/2jtdr1261127277.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/18/t1261127581p8pr6syekxhih79/2jtdr1261127277.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

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