WS 10 ARIMA forecasting

*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 08:13:13 -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/t1260545582nhduev6uj4creoi.htm/, Retrieved Fri, 11 Dec 2009 16:33:05 +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/t1260545582nhduev6uj4creoi.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)

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Dataseries X:

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98.8 100.5 110.4 96.4 101.9 106.2 81 94.7 101 109.4 102.3 90.7 96.2 96.1 106 103.1 102 104.7 86 92.1 106.9 112.6 101.7 92 97.4 97 105.4 102.7 98.1 104.5 87.4 89.9 109.8 111.7 98.6 96.9 95.1 97 112.7 102.9 97.4 111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3

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 3 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[72]) 60 102.3 - - - - - - - 61 99 - - - - - - - 62 100.7 - - - - - - - 63 115.5 - - - - - - - 64 100.7 - - - - - - - 65 109.9 - - - - - - - 66 114.6 - - - - - - - 67 85.4 - - - - - - - 68 100.5 - - - - - - - 69 114.8 - - - - - - - 70 116.5 - - - - - - - 71 112.9 - - - - - - - 72 102 - - - - - - - 73 106 104.6291 98.36 110.8981 0.3341 0.7945 0.9608 0.7945 74 105.3 104.889 98.6205 111.1576 0.4489 0.3642 0.9049 0.8168 75 118.8 116.5947 109.9978 123.1916 0.2562 0.9996 0.6275 1 76 106.1 106.3557 98.9623 113.7491 0.473 5e-04 0.9331 0.8759 77 109.3 109.0252 101.6015 116.4489 0.4711 0.78 0.4087 0.9682 78 117.2 114.2573 106.5109 122.0036 0.2283 0.8951 0.4654 0.999 79 92.5 90.191 82.1874 98.1946 0.2859 0 0.8797 0.0019 80 104.2 100.5248 92.451 108.5986 0.1861 0.9743 0.5024 0.3601 81 112.5 114.5878 106.3039 122.8716 0.3107 0.993 0.48 0.9986 82 122.4 117.5014 109.1064 125.8963 0.1264 0.8785 0.5924 0.9999 83 113.3 109.8448 101.371 118.3186 0.2121 0.0018 0.2399 0.9652 84 100 101.3831 92.7851 109.9812 0.3763 0.0033 0.4441 0.4441 85 110.7 102.8235 93.4662 112.1808 0.0495 0.7229 0.2529 0.5685 86 112.8 103.2284 93.8035 112.6532 0.0233 0.0601 0.3333 0.6008 87 109.8 113.8739 104.2336 123.5143 0.2038 0.5864 0.1583 0.9921 88 117.3 106.2349 96.3051 116.1647 0.0145 0.2408 0.5106 0.7984 89 109.1 105.2619 95.2544 115.2694 0.2261 0.0092 0.2145 0.7385 90 115.9 112.7793 102.5987 122.9598 0.274 0.7606 0.1974 0.981 91 96 89.0992 78.7847 99.4137 0.0949 0 0.2591 0.0071 92 99.8 98.4788 88.0921 108.8654 0.4016 0.68 0.1402 0.2532 93 116.8 113.0316 102.5303 123.5328 0.2409 0.9932 0.5395 0.9803 94 115.7 114.6121 104.0509 125.1734 0.42 0.3424 0.0742 0.9904 95 99.4 107.2338 96.6161 117.8514 0.0741 0.059 0.1314 0.833 96 94.3 100.1923 89.5025 110.882 0.14 0.5578 0.5141 0.3702 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 73 0.0306 0.0131 0 1.8795 0 0 74 0.0305 0.0039 0.0085 0.1689 1.0242 1.012 75 0.0289 0.0189 0.012 4.8633 2.3039 1.5179 76 0.0355 -0.0024 0.0096 0.0654 1.7443 1.3207 77 0.0347 0.0025 0.0082 0.0755 1.4105 1.1877 78 0.0346 0.0258 0.0111 8.6596 2.6187 1.6182 79 0.0453 0.0256 0.0132 5.3315 3.0062 1.7339 80 0.041 0.0366 0.0161 13.5072 4.3189 2.0782 81 0.0369 -0.0182 0.0163 4.3589 4.3233 2.0793 82 0.0365 0.0417 0.0189 23.9968 6.2906 2.5081 83 0.0394 0.0315 0.02 11.9383 6.8041 2.6085 84 0.0433 -0.0136 0.0195 1.913 6.3965 2.5291 85 0.0464 0.0766 0.0239 62.0399 10.6767 3.2675 86 0.0466 0.0927 0.0288 91.616 16.4581 4.0569 87 0.0432 -0.0358 0.0293 16.5971 16.4674 4.058 88 0.0477 0.1042 0.0339 122.437 23.0905 4.8053 89 0.0485 0.0365 0.0341 14.7308 22.5987 4.7538 90 0.0461 0.0277 0.0337 9.739 21.8843 4.6781 91 0.0591 0.0775 0.036 47.6209 23.2389 4.8207 92 0.0538 0.0134 0.0349 1.7457 22.1642 4.7079 93 0.0474 0.0333 0.0348 14.201 21.785 4.6674 94 0.047 0.0095 0.0337 1.1834 20.8486 4.566 95 0.0505 -0.0731 0.0354 61.3682 22.6103 4.755 96 0.0544 -0.0588 0.0364 34.719 23.1148 4.8078

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260545582nhduev6uj4creoi/1kc6e1260544390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260545582nhduev6uj4creoi/1kc6e1260544390.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260545582nhduev6uj4creoi/2piq61260544390.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260545582nhduev6uj4creoi/2piq61260544390.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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,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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