*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: Tue, 15 Dec 2009 10:36:52 -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/15/t1260898710j0cdzxwohjrgrcj.htm/, Retrieved Tue, 15 Dec 2009 18:38:33 +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/15/t1260898710j0cdzxwohjrgrcj.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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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 8.2 8.1 8.1 8 7.9 7.9 8 8 7.9 8 7.7 7.2 7.5 7.3 7 7 7 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 8 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 6 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 8.3 - - - - - - - 21 8 - - - - - - - 22 8.2 - - - - - - - 23 8.1 - - - - - - - 24 8.1 - - - - - - - 25 8 - - - - - - - 26 7.9 - - - - - - - 27 7.9 - - - - - - - 28 8 - - - - - - - 29 8 - - - - - - - 30 7.9 - - - - - - - 31 8 - - - - - - - 32 7.7 - - - - - - - 33 7.2 7.3377 7.154 7.5237 0.0735 1e-04 0 1e-04 34 7.5 7.1067 6.747 7.4758 0.0184 0.3102 0 8e-04 35 7.3 6.8839 6.2976 7.4962 0.0914 0.0243 0 0.0045 36 7 6.7367 6.0116 7.503 0.2503 0.0748 2e-04 0.0069 37 7 6.5699 5.7404 7.4553 0.1705 0.1705 8e-04 0.0062 38 7 6.2214 5.351 7.1574 0.0515 0.0515 2e-04 0.001 39 7.2 6.0964 5.1666 7.1032 0.0158 0.0393 2e-04 9e-04 40 7.3 6.0635 5.0655 7.151 0.0129 0.0203 2e-04 0.0016 41 7.1 6.1062 5.0296 7.2871 0.0495 0.0238 8e-04 0.0041 42 6.8 5.9981 4.8566 7.2601 0.1065 0.0435 0.0016 0.0041 43 6.4 6.1761 4.9394 7.5508 0.3748 0.1869 0.0047 0.0149 44 6.1 5.8342 4.5587 7.2667 0.358 0.2194 0.0053 0.0053 45 6.5 5.4776 4.0126 7.1702 0.1182 0.2355 0.023 0.005 46 7.7 5.0731 3.3607 7.1368 0.0063 0.0877 0.0106 0.0063 47 7.9 4.8347 2.7754 7.4619 0.0111 0.0163 0.0329 0.0163 48 7.5 4.54 2.2837 7.564 0.0275 0.0147 0.0554 0.0203 49 6.9 4.2634 1.8764 7.6163 0.0616 0.0292 0.0548 0.0223 50 6.6 3.7115 1.381 7.1711 0.0509 0.0354 0.0312 0.0119 51 6.9 3.5241 1.1392 7.221 0.0367 0.0515 0.0257 0.0134 52 7.7 3.4111 0.9554 7.3788 0.0171 0.0424 0.0274 0.0171 53 8 3.4734 0.8701 7.8101 0.0204 0.0281 0.0506 0.0281 54 8 3.3622 0.7069 7.9892 0.0247 0.0247 0.0727 0.0331 55 7.7 3.4836 0.6574 8.5385 0.051 0.04 0.1291 0.051 56 7.3 3.1881 0.4445 8.4353 0.0623 0.046 0.1384 0.046 57 7.4 2.9076 0.2273 8.6059 0.0611 0.0654 0.1083 0.0496 58 8.1 2.5887 0.0579 8.8641 0.0426 0.0665 0.0552 0.0552 59 8.3 2.416 0 9.6331 0.055 0.0613 0.0682 0.0756 60 8.2 2.1045 0.0647 9.9586 0.0641 0.061 0.0891 0.0813 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0129 -0.0188 0 0.019 0 0 34 0.0265 0.0553 0.037 0.1546 0.0868 0.2946 35 0.0454 0.0604 0.0448 0.1732 0.1156 0.34 36 0.058 0.0391 0.0434 0.0693 0.104 0.3225 37 0.0688 0.0655 0.0478 0.185 0.1202 0.3467 38 0.0768 0.1251 0.0607 0.6061 0.2012 0.4486 39 0.0843 0.181 0.0779 1.2178 0.3464 0.5886 40 0.0915 0.2039 0.0936 1.529 0.4943 0.703 41 0.0987 0.1628 0.1013 0.9877 0.5491 0.741 42 0.1073 0.1337 0.1046 0.643 0.5585 0.7473 43 0.1136 0.0363 0.0984 0.0501 0.5123 0.7157 44 0.1253 0.0456 0.094 0.0707 0.4755 0.6895 45 0.1576 0.1866 0.1011 1.0452 0.5193 0.7206 46 0.2076 0.5178 0.1309 6.9007 0.9751 0.9875 47 0.2772 0.634 0.1644 9.3959 1.5365 1.2396 48 0.3398 0.652 0.1949 8.7615 1.9881 1.41 49 0.4013 0.6184 0.2198 6.9519 2.28 1.51 50 0.4756 0.7783 0.2508 8.3435 2.6169 1.6177 51 0.5352 0.9579 0.288 11.3967 3.079 1.7547 52 0.5935 1.2573 0.3365 18.3947 3.8448 1.9608 53 0.637 1.3032 0.3825 20.49 4.6374 2.1535 54 0.7021 1.3794 0.4278 21.5092 5.4043 2.3247 55 0.7403 1.2103 0.4619 17.7779 5.9423 2.4377 56 0.8397 1.2898 0.4964 16.908 6.3992 2.5297 57 0.9999 1.5451 0.5383 20.1819 6.9505 2.6364 58 1.2368 2.1289 0.5995 30.3739 7.8514 2.802 59 1.5241 2.4354 0.6675 34.6211 8.8429 2.9737 60 1.9041 2.8964 0.7471 37.1553 9.854 3.1391

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260898710j0cdzxwohjrgrcj/1gbi11260898606.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260898710j0cdzxwohjrgrcj/1gbi11260898606.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260898710j0cdzxwohjrgrcj/241oa1260898606.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260898710j0cdzxwohjrgrcj/241oa1260898606.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 0.5 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; 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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