*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 06:22:54 -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/t1260537849log5c8huwx8mgzw.htm/, Retrieved Fri, 11 Dec 2009 14:24:12 +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/t1260537849log5c8huwx8mgzw.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 «

153.3 154.5 155.2 156.9 157 157.4 157.2 157.5 158 158.5 159 159.3 160 160.8 161.9 162.5 162.7 162.8 162.9 163 164 164.7 164.8 164.9 165 165.8 166.1 167.2 167.7 168.3 168.6 168.9 169.1 169.5 169.6 169.7 169.8 170.4 170.9 171.9 171.9 172 172 172.4 173 173.7 173.8 173.8 173.9 174.6 175 175.9 176 175.1 175.6 175.9 176.7 176.1 176.1 176.2 176.3 177.8 178.5 179.4 179.5 179.6 179.7 179.7 179.8 179.9 180.2 180.4 180.4 181.3 181.9 182.5 182.7 183.1 183.6 183.7 183.8 183.9 184.1 184.4 184.5 185.9 186.6 187.6 187.8 187.9 188 188.3 188.4 188.5 188.5 188.6 188.6 189.4 190 191.9 192.5 193 193.5 193.9 194.2 194.9 194.9 194.9 194.9 195.5 196 196.2 196.2 196.2 196.2 197 197.7 198 198.2 198.5 198.6 199.5 200 201.3 202.2 202.9 203.5 203.5 204 204.1 204.3 204.5 204.8 205.1 205.7 206.5 206.9 207.1 207.8 208 208.5 208.6 209 209.1 209.7 209.8 209.9 210 210.8 211.4 211.7 212 212.2 2 etc...

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[212]) 200 230 - - - - - - - 201 230.2 - - - - - - - 202 230.8 - - - - - - - 203 231 - - - - - - - 204 231.7 - - - - - - - 205 231.9 - - - - - - - 206 233 - - - - - - - 207 235.1 - - - - - - - 208 236 - - - - - - - 209 236.9 - - - - - - - 210 237.1 - - - - - - - 211 237.5 - - - - - - - 212 238.2 - - - - - - - 213 238.9 238.5618 237.9173 239.2064 0.1519 0.8644 1 0.8644 214 239.1 238.9931 238.0141 239.9721 0.4153 0.5739 1 0.9438 215 240 239.2994 238.0072 240.5917 0.144 0.6189 1 0.9523 216 240.2 239.6442 238.0852 241.2032 0.2423 0.3273 1 0.9653 217 240.5 239.8947 238.0987 241.6906 0.2544 0.3695 1 0.9678 218 240.7 240.5078 238.4997 242.5159 0.4256 0.503 1 0.9879 219 241.1 241.3397 239.1382 243.5412 0.4155 0.7155 1 0.9974 220 241.4 241.9953 239.6155 244.3752 0.312 0.7695 1 0.9991 221 242.2 242.4786 239.9326 245.0245 0.4151 0.7968 1 0.9995 222 242.9 242.8067 240.1047 245.5088 0.473 0.6701 1 0.9996 223 243.2 243.2021 240.3525 246.0517 0.4994 0.5823 1 0.9997 224 243.9 243.5786 240.5887 246.5686 0.4166 0.598 0.9998 0.9998 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 213 0.0014 0.0014 1e-04 0.1144 0.0095 0.0976 214 0.0021 4e-04 0 0.0114 0.001 0.0309 215 0.0028 0.0029 2e-04 0.4908 0.0409 0.2022 216 0.0033 0.0023 2e-04 0.3089 0.0257 0.1604 217 0.0038 0.0025 2e-04 0.3664 0.0305 0.1747 218 0.0043 8e-04 1e-04 0.0369 0.0031 0.0555 219 0.0047 -0.001 1e-04 0.0575 0.0048 0.0692 220 0.005 -0.0025 2e-04 0.3544 0.0295 0.1719 221 0.0054 -0.0011 1e-04 0.0776 0.0065 0.0804 222 0.0057 4e-04 0 0.0087 7e-04 0.0269 223 0.006 0 0 0 0 6e-04 224 0.0063 0.0013 1e-04 0.1033 0.0086 0.0928

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260537849log5c8huwx8mgzw/1zj051260537772.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260537849log5c8huwx8mgzw/1zj051260537772.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260537849log5c8huwx8mgzw/28fir1260537772.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260537849log5c8huwx8mgzw/28fir1260537772.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 2 ; 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 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 par7 <- as.numeric(par7) #q 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,fx)) (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.se <- array(0, dim=fx) perf.mse <- 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$pred[i] perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 perf.mse[i] = perf.mse[i] + perf.se[i] 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 = perf.mape / fx perf.mse = perf.mse / fx perf.rmse = sqrt(perf.mse) 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[1:12] <- 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.mape[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse[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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