*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, 11 Dec 2009 10:07:17 -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/11/t12605512657te5nppgkez4qjh.htm/, Retrieved Fri, 11 Dec 2009 18:07:47 +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/11/t12605512657te5nppgkez4qjh.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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1.71 0.81 0.71 1.01 0.01 0.71 1.51 2.41 2.31 3.61 3.81 4.41 4.91 6.51 7.21 7.11 7.61 7.51 6.81 5.81 6.11 5.31 5.21 4.81 4.61 3.91 3.11 2.91 3.01 3.01 3.01 3.51 3.51 3.51 3.41 3.81 3.71 3.41 3.61 4.01 4.11 4.21 4.51 4.31 3.91 4.51 4.51 4.51 4.01 3.91 4.71 4.61 4.41 4.41 4.01 4.11 4.51 4.01 3.71 3.61

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[32]) 20 5.81 - - - - - - - 21 6.11 - - - - - - - 22 5.31 - - - - - - - 23 5.21 - - - - - - - 24 4.81 - - - - - - - 25 4.61 - - - - - - - 26 3.91 - - - - - - - 27 3.11 - - - - - - - 28 2.91 - - - - - - - 29 3.01 - - - - - - - 30 3.01 - - - - - - - 31 3.01 - - - - - - - 32 3.51 - - - - - - - 33 3.51 3.7798 2.7484 4.8113 0.3041 0.6959 0 0.6959 34 3.51 3.8581 2.3498 5.3664 0.3255 0.6745 0.0296 0.6745 35 3.41 3.8496 1.7182 5.981 0.343 0.6226 0.1055 0.6226 36 3.81 3.8274 0.8823 6.7725 0.4954 0.6094 0.2566 0.5836 37 3.71 3.8195 0.086 7.553 0.4771 0.502 0.3391 0.5645 38 3.41 3.8231 -0.5593 8.2056 0.4267 0.5202 0.4845 0.5557 39 3.61 3.8282 -1.0803 8.7367 0.4653 0.5663 0.6129 0.5506 40 4.01 3.8301 -1.533 9.1933 0.4738 0.5321 0.6317 0.5466 41 4.11 3.8296 -1.9523 9.6115 0.4621 0.4756 0.6094 0.5431 42 4.21 3.8286 -2.3497 10.0068 0.4518 0.4644 0.6024 0.5402 43 4.51 3.8281 -2.7259 10.3822 0.4192 0.4545 0.5966 0.5379 44 4.31 3.8282 -3.0815 10.738 0.4457 0.4233 0.536 0.536 45 3.91 3.8284 -3.4185 11.0754 0.4912 0.4482 0.5343 0.5343 46 4.51 3.8285 -3.74 11.3971 0.43 0.4916 0.5329 0.5329 47 4.51 3.8285 -4.0484 11.7055 0.4327 0.4327 0.5415 0.5316 48 4.51 3.8285 -4.3454 12.0024 0.4351 0.4351 0.5018 0.5304 49 4.01 3.8285 -4.6321 12.289 0.4832 0.4373 0.5109 0.5294 50 3.91 3.8285 -4.9094 12.5663 0.4927 0.4838 0.5374 0.5285 51 4.71 3.8285 -5.1781 12.835 0.4239 0.4929 0.519 0.5276 52 4.61 3.8285 -5.439 13.0959 0.4344 0.4261 0.4847 0.5269 53 4.41 3.8285 -5.6927 13.3497 0.4524 0.4361 0.4769 0.5261 54 4.41 3.8285 -5.9399 13.5968 0.4536 0.4536 0.4695 0.5255 55 4.01 3.8285 -6.181 13.8379 0.4858 0.4547 0.4469 0.5249 56 4.11 3.8285 -6.4164 14.0733 0.4785 0.4861 0.4633 0.5243 57 4.51 3.8285 -6.6465 14.3034 0.4493 0.479 0.4939 0.5238 58 4.01 3.8285 -6.8716 14.5286 0.4867 0.4503 0.4503 0.5233 59 3.71 3.8285 -7.0921 14.7491 0.4915 0.487 0.4513 0.5228 60 3.61 3.8285 -7.3083 14.9652 0.4847 0.5083 0.4523 0.5223 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.1392 -0.0714 0 0.0728 0 0 34 0.1995 -0.0902 0.0808 0.1212 0.097 0.3114 35 0.2825 -0.1142 0.0919 0.1932 0.1291 0.3593 36 0.3926 -0.0045 0.0701 3e-04 0.0969 0.3113 37 0.4987 -0.0287 0.0618 0.012 0.0799 0.2827 38 0.5848 -0.1081 0.0695 0.1707 0.095 0.3083 39 0.6542 -0.057 0.0677 0.0476 0.0883 0.2971 40 0.7144 0.047 0.0651 0.0323 0.0813 0.2851 41 0.7703 0.0732 0.066 0.0786 0.081 0.2846 42 0.8233 0.0996 0.0694 0.1455 0.0874 0.2957 43 0.8735 0.1781 0.0793 0.4649 0.1218 0.3489 44 0.9209 0.1258 0.0832 0.2321 0.1309 0.3619 45 0.9658 0.0213 0.0784 0.0067 0.1214 0.3484 46 1.0086 0.178 0.0855 0.4644 0.1459 0.3819 47 1.0497 0.178 0.0917 0.4644 0.1671 0.4088 48 1.0893 0.178 0.0971 0.4645 0.1857 0.4309 49 1.1275 0.0474 0.0942 0.033 0.1767 0.4204 50 1.1645 0.0213 0.0901 0.0066 0.1673 0.409 51 1.2003 0.2303 0.0975 0.7771 0.1994 0.4465 52 1.235 0.2041 0.1028 0.6108 0.2199 0.469 53 1.2688 0.1519 0.1052 0.3382 0.2256 0.4749 54 1.3018 0.1519 0.1073 0.3382 0.2307 0.4803 55 1.3339 0.0474 0.1047 0.033 0.2221 0.4713 56 1.3653 0.0735 0.1034 0.0793 0.2161 0.4649 57 1.3959 0.178 0.1064 0.4645 0.2261 0.4755 58 1.426 0.0474 0.1041 0.033 0.2186 0.4676 59 1.4553 -0.0309 0.1014 0.014 0.2111 0.4594 60 1.4841 -0.0571 0.0998 0.0477 0.2052 0.453

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t12605512657te5nppgkez4qjh/1pl881260551235.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605512657te5nppgkez4qjh/1pl881260551235.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605512657te5nppgkez4qjh/2qey71260551235.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t12605512657te5nppgkez4qjh/2qey71260551235.ps (open in new window)

Parameters (Session):

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

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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