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R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Sat, 08 Dec 2007 06:56:55 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/08/t1197121424pyqi1w15iuar61t.htm/, Retrieved Sat, 08 Dec 2007 14:43:44 +0100

User-defined keywords:

Dataseries X:

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96,9 98,0 97,9 100,9 103,9 103,1 102,5 104,3 102,6 101,7 102,8 105,4 110,9 113,5 116,3 124,0 128,8 133,5 132,6 128,4 127,3 126,7 123,3 123,2 124,4 128,2 128,7 135,7 139,0 145,4 142,4 137,7 137,0 137,1 139,3 139,6 140,4 142,3 148,3 157,7 161,6 161,7 171,8 185,1 176,7 184,4 183,0 180,9 187,0 189,9 193,8 194,5 198,7 204,7 213,2 214,7 211,0 213,2 206,3 210,8

Text written by user:

lambda -0,6 d=1 D=1 ARIMA maximum

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 9 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 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[24]) 12 105.4 - - - - - - - 13 110.9 - - - - - - - 14 113.5 - - - - - - - 15 116.3 - - - - - - - 16 124 - - - - - - - 17 128.8 - - - - - - - 18 133.5 - - - - - - - 19 132.6 - - - - - - - 20 128.4 - - - - - - - 21 127.3 - - - - - - - 22 126.7 - - - - - - - 23 123.3 - - - - - - - 24 123.2 - - - - - - - 25 124.4 126.4379 126.5954 126.2807 1 0 0 0 26 128.2 128.8175 129.1137 128.5223 1 0 0 0 27 128.7 133.3834 133.7607 133.0078 1 0 0 0 28 135.7 140.4807 140.9889 139.9754 1 0 0 0 29 139 142.7823 143.3946 142.1742 1 0 0 0 30 145.4 151.3793 152.119 150.6455 1 0 0 0 31 142.4 151.0837 151.9086 150.266 1 0 0 0 32 137.7 141.5255 142.3251 140.733 1 0.9847 0 0 33 137 142.6896 143.5574 141.8302 1 0 0 0 34 137.1 143.3059 144.2409 142.3805 1 0 0 0 35 139.3 136.3101 137.2183 135.4114 1 0.9575 0 0 36 139.6 132.2582 133.1729 131.3535 1 1 0 0 37 140.4 129.2523 130.2672 128.2501 1 1 0 0 38 142.3 129.0884 130.2824 127.9119 1 1 0.0694 0 39 148.3 131.4279 132.7997 130.0786 1 1 0 0 40 157.7 131.0131 132.5302 129.5236 1 1 1 0 41 161.6 128.5581 130.1776 126.9706 1 1 1 0 42 161.7 132.9635 134.7962 131.1703 1 1 1 0 43 171.8 133.5578 135.5417 131.6199 1 1 1 0 44 185.1 127.5994 129.554 125.6916 1 1 1 0 45 176.7 129.9793 132.1002 127.9124 1 1 1 0 46 184.4 131.2864 133.5552 129.0787 1 1 1 0 47 183 127.011 129.2565 124.8273 1 1 1 3e-04 48 180.9 122.5221 124.7336 120.3727 1 1 1 0.7318 49 187 116.2005 118.3426 114.1198 1 1 1 1 50 189.9 114.0105 116.2095 111.8773 1 1 1 1 51 193.8 112.7801 115.0534 110.5778 1 1 1 1 52 194.5 107.3781 109.581 105.2452 1 1 1 1 53 198.7 103.6944 105.8745 101.5852 1 1 1 1 54 204.7 102.6627 104.8952 100.5052 1 1 1 1 55 213.2 103.324 105.669 101.0611 1 1 1 1 56 214.7 103.5814 106.0214 101.23 1 1 1 1 57 211 105.0367 107.6154 102.5555 1 1 1 1 58 213.2 105.8409 108.5363 103.251 1 1 1 1 59 206.3 106.3606 109.1583 103.6759 1 1 1 1 60 210.8 104.7373 107.5446 102.0455 1 1 1 1 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 25 -6e-04 -0.0161 4e-04 4.153 0.1154 0.3396 26 -0.0012 -0.0048 1e-04 0.3813 0.0106 0.1029 27 -0.0014 -0.0351 0.001 21.9345 0.6093 0.7806 28 -0.0018 -0.034 9e-04 22.8552 0.6349 0.7968 29 -0.0022 -0.0265 7e-04 14.306 0.3974 0.6304 30 -0.0025 -0.0395 0.0011 35.7526 0.9931 0.9966 31 -0.0028 -0.0575 0.0016 75.4075 2.0947 1.4473 32 -0.0029 -0.027 8e-04 14.6342 0.4065 0.6376 33 -0.0031 -0.0399 0.0011 32.3718 0.8992 0.9483 34 -0.0033 -0.0433 0.0012 38.5129 1.0698 1.0343 35 -0.0034 0.0219 6e-04 8.9398 0.2483 0.4983 36 -0.0035 0.0555 0.0015 53.9021 1.4973 1.2236 37 -0.004 0.0862 0.0024 124.2702 3.452 1.8579 38 -0.0047 0.1023 0.0028 174.5462 4.8485 2.2019 39 -0.0052 0.1284 0.0036 284.6686 7.9075 2.812 40 -0.0058 0.2037 0.0057 712.1917 19.7831 4.4478 41 -0.0063 0.257 0.0071 1091.7698 30.3269 5.507 42 -0.0069 0.2161 0.006 825.7873 22.9385 4.7894 43 -0.0074 0.2863 0.008 1462.4678 40.6241 6.3737 44 -0.0076 0.4506 0.0125 3306.3157 91.8421 9.5834 45 -0.0081 0.3594 0.01 2182.8232 60.634 7.7868 46 -0.0086 0.4046 0.0112 2821.0519 78.3626 8.8523 47 -0.0088 0.4408 0.0122 3134.7686 87.0769 9.3315 48 -0.009 0.4765 0.0132 3407.9805 94.6661 9.7297 49 -0.0091 0.6093 0.0169 5012.5695 139.238 11.7999 50 -0.0095 0.6656 0.0185 5759.2191 159.9783 12.6483 51 -0.01 0.7184 0.02 6564.2246 182.3396 13.5033 52 -0.0101 0.8114 0.0225 7590.2276 210.8397 14.5203 53 -0.0104 0.9162 0.0255 9026.0713 250.7242 15.8343 54 -0.0107 0.9939 0.0276 10411.6185 289.2116 17.0062 55 -0.0112 1.0634 0.0295 12072.7412 335.3539 18.3127 56 -0.0116 1.0728 0.0298 12347.3472 342.9819 18.5198 57 -0.0121 1.0088 0.028 11228.2115 311.8948 17.6605 58 -0.0125 1.0143 0.0282 11525.9757 320.166 17.8932 59 -0.0129 0.9396 0.0261 9987.8843 277.4412 16.6566 60 -0.0131 1.0127 0.0281 11249.2867 312.4802 17.6771

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121424pyqi1w15iuar61t/1o71r1197122204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121424pyqi1w15iuar61t/1o71r1197122204.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121424pyqi1w15iuar61t/2xolj1197122204.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/08/t1197121424pyqi1w15iuar61t/2xolj1197122204.ps (open in new window)

Parameters:

par1 = 36 ; par2 = -0.6 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 2 ; 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,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) } (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')

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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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