*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: Thu, 10 Dec 2009 16:55:31 -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/t1260489371gxe3uezzc95x97v.htm/, Retrieved Fri, 11 Dec 2009 00:56:13 +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/t1260489371gxe3uezzc95x97v.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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149 139 135 130 127 122 117 112 113 149 157 157 147 137 132 125 123 117 114 111 112 144 150 149 134 123 116 117 111 105 102 95 93 124 130 124 115 106 105 105 101 95 93 84 87 116 120 117 109 105 107 109 109 108 107 99 103 131 137 135

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]) 20 111 - - - - - - - 21 112 - - - - - - - 22 144 - - - - - - - 23 150 - - - - - - - 24 149 - - - - - - - 25 134 - - - - - - - 26 123 - - - - - - - 27 116 - - - - - - - 28 117 - - - - - - - 29 111 - - - - - - - 30 105 - - - - - - - 31 102 - - - - - - - 32 95 - - - - - - - 33 93 98.4931 80.6683 116.3178 0.2729 0.6495 0.0687 0.6495 34 124 104.093 75.5378 132.6482 0.0859 0.7768 0.0031 0.7337 35 130 110.9558 74.7715 147.1401 0.1511 0.2399 0.0172 0.8063 36 124 115.3678 75.904 154.8316 0.3341 0.2337 0.0474 0.8441 37 115 117.0042 76.3871 157.6213 0.4615 0.3678 0.2061 0.8558 38 106 116.8463 75.7773 157.9154 0.3024 0.5351 0.3845 0.8514 39 105 116.0226 74.6456 157.3996 0.3008 0.6825 0.5004 0.8403 40 105 115.2622 73.5294 156.9951 0.3149 0.6851 0.4675 0.8294 41 101 114.8362 72.6364 157.036 0.2602 0.6761 0.5707 0.8216 42 95 114.7191 71.9556 157.4827 0.1831 0.7353 0.672 0.8169 43 93 114.7752 71.4019 158.1486 0.1626 0.8142 0.7181 0.8142 44 84 114.8791 70.8948 158.8633 0.0844 0.8352 0.8121 0.8121 45 87 114.9601 70.3854 159.5349 0.1095 0.9133 0.8329 0.8099 46 116 114.9991 69.8573 160.1409 0.4827 0.8879 0.348 0.8074 47 120 115.0051 69.3139 160.6963 0.4152 0.483 0.26 0.8046 48 117 114.9952 68.7654 161.2251 0.4661 0.416 0.3513 0.8017 49 109 114.9829 68.2207 161.7451 0.401 0.4663 0.4997 0.7989 50 105 114.9746 67.6844 162.2648 0.3397 0.5978 0.645 0.7961 51 107 114.9713 67.1573 162.7853 0.3719 0.6586 0.6586 0.7935 52 109 114.9714 66.6383 163.3045 0.4043 0.6267 0.657 0.791 53 109 114.9728 66.1258 163.8198 0.4053 0.5947 0.7125 0.7886 54 108 114.9742 65.6187 164.3297 0.3909 0.5938 0.7862 0.7862 55 107 114.975 65.1164 164.8336 0.3769 0.608 0.8062 0.7838 56 99 114.9752 64.6187 165.3318 0.267 0.6219 0.886 0.7816 57 103 114.9752 64.1257 165.8246 0.3222 0.731 0.8596 0.7793 58 131 114.975 63.6373 166.3126 0.2703 0.6762 0.4844 0.7772 59 137 114.9748 63.1536 166.7961 0.2024 0.2722 0.4246 0.775 60 135 114.9748 62.6744 167.2752 0.2265 0.2046 0.4698 0.7729 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0923 -0.0558 0 30.1739 0 0 34 0.14 0.1912 0.1235 396.2885 213.2312 14.6024 35 0.1664 0.1716 0.1396 362.6811 263.0479 16.2188 36 0.1745 0.0748 0.1234 74.5149 215.9146 14.694 37 0.1771 -0.0171 0.1021 4.0167 173.535 13.1733 38 0.1793 -0.0928 0.1006 117.643 164.2197 12.8148 39 0.182 -0.095 0.0998 121.4978 158.1166 12.5744 40 0.1847 -0.089 0.0984 105.3133 151.5162 12.3092 41 0.1875 -0.1205 0.1009 191.4406 155.9522 12.4881 42 0.1902 -0.1719 0.108 388.8434 179.2413 13.3881 43 0.1928 -0.1897 0.1154 474.1608 206.0522 14.3545 44 0.1953 -0.2688 0.1282 953.516 268.3408 16.3811 45 0.1978 -0.2432 0.137 781.77 307.8354 17.5452 46 0.2003 0.0087 0.1279 1.0018 285.9187 16.9091 47 0.2027 0.0434 0.1222 24.9493 268.5208 16.3866 48 0.2051 0.0174 0.1157 4.0191 251.9894 15.8742 49 0.2075 -0.052 0.112 35.7954 239.2721 15.4684 50 0.2099 -0.0868 0.1106 99.4931 231.5066 15.2153 51 0.2122 -0.0693 0.1084 63.5418 222.6664 14.922 52 0.2145 -0.0519 0.1056 35.6574 213.3159 14.6053 53 0.2168 -0.0519 0.103 35.6743 204.8568 14.3128 54 0.219 -0.0607 0.1011 48.6392 197.756 14.0626 55 0.2212 -0.0694 0.0997 63.6005 191.9231 13.8536 56 0.2235 -0.1389 0.1013 255.2084 194.56 13.9485 57 0.2256 -0.1042 0.1015 143.4046 192.5138 13.8749 58 0.2278 0.1394 0.1029 256.8012 194.9864 13.9638 59 0.23 0.1916 0.1062 485.108 205.7316 14.3433 60 0.2321 0.1742 0.1086 401.0104 212.7059 14.5844

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260489371gxe3uezzc95x97v/1ntg41260489330.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260489371gxe3uezzc95x97v/1ntg41260489330.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260489371gxe3uezzc95x97v/2md2i1260489330.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260489371gxe3uezzc95x97v/2md2i1260489330.ps (open in new window)

Parameters (Session):

par1 = 13 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 13 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; 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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