*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 13:21:40 -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/t1260563103ujr501x1taqyizb.htm/, Retrieved Fri, 11 Dec 2009 21:25:06 +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/t1260563103ujr501x1taqyizb.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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17823.2 17872 17420.4 16704.4 15991.2 15583.6 19123.5 17838.7 17209.4 18586.5 16258.1 15141.6 19202.1 17746.5 19090.1 18040.3 17515.5 17751.8 21072.4 17170 19439.5 19795.4 17574.9 16165.4 19464.6 19932.1 19961.2 17343.4 18924.2 18574.1 21350.6 18594.6 19832.1 20844.4 19640.2 17735.4 19813.6 22160 20664.3 17877.4 20906.5 21164.1 21374.4 22952.3 21343.5 23899.3 22392.9 18274.1 22786.7 22321.5 17842.2 16373.5 15933.8 16446.1 17729 16643 16196.7 18252.1 17570.4 15836.8

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 17170 - - - - - - - 21 19439.5 - - - - - - - 22 19795.4 - - - - - - - 23 17574.9 - - - - - - - 24 16165.4 - - - - - - - 25 19464.6 - - - - - - - 26 19932.1 - - - - - - - 27 19961.2 - - - - - - - 28 17343.4 - - - - - - - 29 18924.2 - - - - - - - 30 18574.1 - - - - - - - 31 21350.6 - - - - - - - 32 18594.6 - - - - - - - 33 19832.1 20145.4351 18538.2547 21752.6156 0.3512 0.9707 0.8054 0.9707 34 20844.4 20430.2354 18795.6762 22064.7946 0.3097 0.7634 0.7767 0.9861 35 19640.2 18566.0121 16930.7955 20201.2288 0.099 0.0032 0.8826 0.4863 36 17735.4 16927.165 15170.6745 18683.6555 0.1836 0.0012 0.8023 0.0314 37 19813.6 20249.8099 18492.165 22007.4547 0.3133 0.9975 0.8094 0.9675 38 22160 20794.4543 19023.5628 22565.3457 0.0653 0.8612 0.8301 0.9925 39 20664.3 20757.4061 18953.3412 22561.471 0.4597 0.0638 0.8065 0.9906 40 17877.4 18156.6022 16342.679 19970.5255 0.3814 0.0034 0.8102 0.318 41 20906.5 19752.048 17920.8541 21583.2418 0.1083 0.9776 0.8122 0.8923 42 21164.1 19384.2296 17533.3527 21235.1065 0.0297 0.0535 0.8045 0.7985 43 21374.4 22167.74 20302.581 24032.899 0.2022 0.8542 0.8047 0.9999 44 22952.3 19413.8549 17531.8286 21295.8813 1e-04 0.0206 0.8032 0.8032 45 21343.5 20960.2634 18314.8622 23605.6646 0.3882 0.07 0.7984 0.9602 46 23899.3 21247.4478 18601.4749 23893.4206 0.0247 0.4716 0.6174 0.9753 47 22392.9 19383.2881 16729.5441 22037.0322 0.0131 4e-04 0.4248 0.7199 48 18274.1 17743.417 14944.5227 20542.3113 0.3551 6e-04 0.5022 0.2756 49 22786.7 21066.7878 18250.7664 23882.8092 0.1156 0.974 0.8085 0.9573 50 22321.5 21611.3188 18757.2605 24465.3772 0.3129 0.2098 0.3532 0.9809 51 17842.2 21574.0564 18659.2401 24488.8726 0.006 0.3076 0.7296 0.9774 52 16373.5 18973.4564 16026.1843 21920.7284 0.0419 0.7741 0.767 0.5995 53 15933.8 20568.8402 17579.6737 23558.0067 0.0012 0.997 0.4124 0.9023 54 16446.1 20200.9837 17167.4712 23234.4963 0.0076 0.9971 0.2669 0.8503 55 17729 22984.5475 19913.6176 26055.4775 4e-04 1 0.8479 0.9975 56 16643 20230.6389 17119.4202 23341.8576 0.0119 0.9425 0.0432 0.8487 57 16196.7 21777.0428 18019.6894 25534.3962 0.0018 0.9963 0.5895 0.9516 58 18252.1 22064.2402 18301.9541 25826.5262 0.0235 0.9989 0.1695 0.9647 59 17570.4 20200.0728 16410.9033 23989.2424 0.0869 0.8432 0.1283 0.7969 60 15836.8 18560.202 14604.0521 22516.3519 0.0886 0.6881 0.5564 0.4932 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0407 -0.0156 0 98178.9005 0 0 34 0.0408 0.0203 0.0179 171532.2999 134855.6002 367.2269 35 0.0449 0.0579 0.0312 1153879.6324 474530.2776 688.8616 36 0.0529 0.0477 0.0354 653243.8603 519208.6733 720.5614 37 0.0443 -0.0215 0.0326 190279.0362 453422.7459 673.3667 38 0.0434 0.0657 0.0381 1864715.1503 688638.1466 829.8422 39 0.0443 -0.0045 0.0333 8668.7459 591499.6608 769.0902 40 0.051 -0.0154 0.0311 77953.8931 527306.4398 726.1587 41 0.0473 0.0584 0.0341 1332759.5169 616801.2262 785.3669 42 0.0487 0.0918 0.0399 3167938.6277 871914.9663 933.7639 43 0.0429 -0.0358 0.0395 629388.394 849867.0961 921.8824 44 0.0495 0.1823 0.0514 12520593.3737 1822427.6192 1349.9732 45 0.0644 0.0183 0.0489 146870.2907 1693538.594 1301.3603 46 0.0635 0.1248 0.0543 7032320.2146 2074880.1383 1440.4444 47 0.0699 0.1553 0.061 9057763.5466 2540405.6989 1593.865 48 0.0805 0.0299 0.0591 281624.4539 2399231.8711 1548.9454 49 0.0682 0.0816 0.0604 2958097.9376 2432106.3456 1559.5212 50 0.0674 0.0329 0.0589 504357.2686 2325009.1746 1524.7981 51 0.0689 -0.173 0.0649 13926752.0253 2935627.2194 1713.3672 52 0.0793 -0.137 0.0685 6759773.1817 3126834.5175 1768.2858 53 0.0741 -0.2253 0.0759 21483597.8926 4000966.1068 2000.2415 54 0.0766 -0.1859 0.0809 14099151.9339 4459974.5535 2111.8652 55 0.0682 -0.2287 0.0874 27620779.797 5466966.0858 2338.1544 56 0.0785 -0.1773 0.0911 12871152.816 5775473.8662 2403.2216 57 0.088 -0.2562 0.0977 31140225.4554 6790063.9298 2605.7751 58 0.087 -0.1728 0.1006 14532412.6135 7087846.5715 2662.301 59 0.0957 -0.1302 0.1017 6915179.2528 7081451.4856 2661.0997 60 0.1088 -0.1467 0.1033 7416918.4685 7093432.4493 2663.3499

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260563103ujr501x1taqyizb/141741260562898.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260563103ujr501x1taqyizb/141741260562898.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260563103ujr501x1taqyizb/2jpzr1260562898.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260563103ujr501x1taqyizb/2jpzr1260562898.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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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