loïqueverhasselt

*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: Sat, 13 Dec 2008 10:45:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/13/t1229190371c7r615rts8irknw.htm/, Retrieved Sat, 13 Dec 2008 18:46:11 +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/2008/Dec/13/t1229190371c7r615rts8irknw.htm/}, year = {2008}, } @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 = {2008}, 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:

workshop arima forecast step 1

Dataseries X:

» Textbox « » Textfile « » CSV «

99.4 97.5 94.6 92.6 92.5 89.8 88.8 87.4 85.2 83.1 84.7 84.8 85.8 86.3 89 89 89.3 91.9 94.9 94.4 96.8 96.9 98 97.9 100.9 103.9 103.1 102.5 104.3 102.6 101.7 102.8 105.4 110.9 113.5 116.3 124 128.8 133.5 132.6 128.4 127.3 126.7 123.3 123.2 124.4 128.2 128.7 135.7 139 145.4 142.4 137.7 137 137.1 139.3 139.6 140.4 142.3 148.3

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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[20]) 8 87.4 - - - - - - - 9 85.2 - - - - - - - 10 83.1 - - - - - - - 11 84.7 - - - - - - - 12 84.8 - - - - - - - 13 85.8 - - - - - - - 14 86.3 - - - - - - - 15 89 - - - - - - - 16 89 - - - - - - - 17 89.3 - - - - - - - 18 91.9 - - - - - - - 19 94.9 - - - - - - - 20 94.4 - - - - - - - 21 96.8 94.1634 91.0451 97.2816 0.0487 0.4409 1 0.4409 22 96.9 94.0514 88.499 99.6037 0.1573 0.166 0.9999 0.451 23 98 93.9984 86.3277 101.669 0.1533 0.2292 0.9912 0.4591 24 97.9 93.9733 84.4624 103.4842 0.2092 0.2033 0.9706 0.465 25 100.9 93.9614 82.8322 105.0906 0.1109 0.244 0.9247 0.4692 26 103.9 93.9558 81.3811 106.5304 0.0606 0.1395 0.8836 0.4724 27 103.1 93.9531 80.068 107.8383 0.0983 0.0801 0.7578 0.4749 28 102.5 93.9519 78.8632 109.0405 0.1334 0.1174 0.74 0.4768 29 104.3 93.9513 77.7454 110.1571 0.1054 0.1506 0.7131 0.4784 30 102.6 93.951 76.6988 111.2032 0.1629 0.1198 0.5921 0.4797 31 101.7 93.9509 75.7118 112.19 0.2025 0.1763 0.4594 0.4808 32 102.8 93.9508 74.7752 113.1264 0.1829 0.2142 0.4817 0.4817 33 105.4 93.9508 73.8823 114.0193 0.1317 0.1937 0.3904 0.4825 34 110.9 93.9508 73.0273 114.8742 0.0562 0.1417 0.3912 0.4832 35 113.5 93.9508 72.206 115.6955 0.039 0.0633 0.3576 0.4838 36 116.3 93.9507 71.4145 116.487 0.026 0.0445 0.3656 0.4844 37 124 93.9507 70.65 117.2515 0.0057 0.0301 0.2794 0.4849 38 128.8 93.9507 69.9097 117.9918 0.0022 0.0071 0.2086 0.4854 39 133.5 93.9507 69.1915 118.71 9e-04 0.0029 0.2344 0.4858 40 132.6 93.9507 68.4936 119.4079 0.0015 0.0012 0.2552 0.4862 41 128.4 93.9507 67.8143 120.0872 0.0049 0.0019 0.2188 0.4866 42 127.3 93.9507 67.1523 120.7492 0.0074 0.0059 0.2635 0.4869 43 126.7 93.9507 66.5062 121.3953 0.0097 0.0086 0.29 0.4872 44 123.3 93.9507 65.8749 122.0266 0.0202 0.0111 0.2684 0.4875 45 123.2 93.9507 65.2576 122.6439 0.0229 0.0225 0.2171 0.4878 46 124.4 93.9507 64.6532 123.2483 0.0208 0.0252 0.1284 0.488 47 128.2 93.9507 64.0611 123.8404 0.0124 0.0229 0.0999 0.4882 48 128.7 93.9507 63.4805 124.421 0.0127 0.0138 0.0753 0.4885 49 135.7 93.9507 62.9107 124.9908 0.0042 0.0141 0.0289 0.4887 50 139 93.9507 62.3512 125.5503 0.0026 0.0048 0.0153 0.4889 51 145.4 93.9507 61.8014 126.1 9e-04 0.003 0.008 0.4891 52 142.4 93.9507 61.2609 126.6406 0.0018 0.001 0.0102 0.4893 53 137.7 93.9507 60.7292 127.1723 0.0049 0.0021 0.0211 0.4894 54 137 93.9507 60.2059 127.6956 0.0062 0.0055 0.0264 0.4896 55 137.1 93.9507 59.6905 128.211 0.0068 0.0069 0.0305 0.4897 56 139.3 93.9507 59.1828 128.7187 0.0053 0.0075 0.049 0.4899 57 139.6 93.9507 58.6824 129.2191 0.0056 0.0059 0.052 0.49 58 140.4 93.9507 58.189 129.7125 0.0055 0.0062 0.0476 0.4902 59 142.3 93.9507 57.7023 130.1992 0.0045 0.006 0.032 0.4903 60 148.3 93.9507 57.2221 130.6794 0.0019 0.0049 0.0318 0.4904 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 21 0.0169 0.028 7e-04 6.9518 0.1738 0.4169 22 0.0301 0.0303 8e-04 8.1147 0.2029 0.4504 23 0.0416 0.0426 0.0011 16.0131 0.4003 0.6327 24 0.0516 0.0418 0.001 15.4191 0.3855 0.6209 25 0.0604 0.0738 0.0018 48.144 1.2036 1.0971 26 0.0683 0.1058 0.0026 98.8872 2.4722 1.5723 27 0.0754 0.0974 0.0024 83.6651 2.0916 1.4462 28 0.0819 0.091 0.0023 73.0704 1.8268 1.3516 29 0.088 0.1101 0.0028 107.096 2.6774 1.6363 30 0.0937 0.0921 0.0023 74.8052 1.8701 1.3675 31 0.099 0.0825 0.0021 60.0491 1.5012 1.2252 32 0.1041 0.0942 0.0024 78.3083 1.9577 1.3992 33 0.109 0.1219 0.003 131.0848 3.2771 1.8103 34 0.1136 0.1804 0.0045 287.2768 7.1819 2.6799 35 0.1181 0.2081 0.0052 382.1731 9.5543 3.091 36 0.1224 0.2379 0.0059 499.489 12.4872 3.5337 37 0.1265 0.3198 0.008 902.9576 22.5739 4.7512 38 0.1306 0.3709 0.0093 1214.4705 30.3618 5.5102 39 0.1345 0.421 0.0105 1564.1435 39.1036 6.2533 40 0.1382 0.4114 0.0103 1493.7649 37.3441 6.111 41 0.1419 0.3667 0.0092 1186.7511 29.6688 5.4469 42 0.1455 0.355 0.0089 1112.1728 27.8043 5.273 43 0.149 0.3486 0.0087 1072.5137 26.8128 5.1781 44 0.1525 0.3124 0.0078 861.3787 21.5345 4.6405 45 0.1558 0.3113 0.0078 855.5189 21.388 4.6247 46 0.1591 0.3241 0.0081 927.1571 23.1789 4.8144 47 0.1623 0.3645 0.0091 1173.0114 29.3253 5.4153 48 0.1655 0.3699 0.0092 1207.5107 30.1878 5.4943 49 0.1686 0.4444 0.0111 1743.0003 43.575 6.6011 50 0.1716 0.4795 0.012 2029.4353 50.7359 7.1229 51 0.1746 0.5476 0.0137 2647.0258 66.1756 8.1348 52 0.1775 0.5157 0.0129 2347.3303 58.6833 7.6605 53 0.1804 0.4657 0.0116 1913.9973 47.8499 6.9174 54 0.1833 0.4582 0.0115 1853.2383 46.331 6.8067 55 0.1861 0.4593 0.0115 1861.8582 46.5465 6.8225 56 0.1888 0.4827 0.0121 2056.5549 51.4139 7.1703 57 0.1915 0.4859 0.0121 2083.8544 52.0964 7.2178 58 0.1942 0.4944 0.0124 2157.5332 53.9383 7.3443 59 0.1968 0.5146 0.0129 2337.6504 58.4413 7.6447 60 0.1995 0.5785 0.0145 2953.8415 73.846 8.5934

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229190371c7r615rts8irknw/1j1821229190303.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229190371c7r615rts8irknw/1j1821229190303.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229190371c7r615rts8irknw/249pq1229190303.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/13/t1229190371c7r615rts8irknw/249pq1229190303.ps (open in new window)

Parameters (Session):

par1 = 40 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 40 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; 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 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')

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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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