*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: Wed, 09 Dec 2009 13:34:31 -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/09/t1260390958ty0onizw526ohqy.htm/, Retrieved Wed, 09 Dec 2009 21:36:01 +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/09/t1260390958ty0onizw526ohqy.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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105.7 105.7 111.1 82.4 60 107.3 99.3 113.5 108.9 100.2 103.9 138.7 120.2 100.2 143.2 70.9 85.2 133 136.6 117.9 106.3 122.3 125.5 148.4 126.3 99.6 140.4 80.3 92.6 138.5 110.9 119.6 105 109 129.4 148.6 101.4 134.8 143.7 81.6 90.3 141.5 140.7 140.2 100.2 125.7 119.6 134.7 109 116.3 146.9 97.4 89.4 132.1 139.8 129 112.5 121.9 121.7 123.1

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 '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]) 20 117.9 - - - - - - - 21 106.3 - - - - - - - 22 122.3 - - - - - - - 23 125.5 - - - - - - - 24 148.4 - - - - - - - 25 126.3 - - - - - - - 26 99.6 - - - - - - - 27 140.4 - - - - - - - 28 80.3 - - - - - - - 29 92.6 - - - - - - - 30 138.5 - - - - - - - 31 110.9 - - - - - - - 32 119.6 - - - - - - - 33 105 106.9199 84.653 131.7838 0.4399 0.1588 0.5195 0.1588 34 109 122.4648 97.7729 149.9338 0.1683 0.8936 0.5047 0.581 35 129.4 117.0478 90.6593 146.8026 0.2079 0.702 0.2888 0.4332 36 148.6 151.1618 120.683 185.0686 0.4411 0.8958 0.5634 0.966 37 101.4 126.4501 97.0756 159.7016 0.0699 0.0958 0.5035 0.6568 38 134.8 103.7793 77.2959 134.1568 0.0227 0.561 0.6063 0.1537 39 143.7 141.3307 109.9218 176.6815 0.4477 0.6414 0.5206 0.8859 40 81.6 80.9184 57.2664 108.6489 0.4808 0 0.5174 0.0031 41 90.3 87.4714 62.7533 116.2846 0.4237 0.6552 0.3636 0.0144 42 141.5 135.2346 103.6988 170.9509 0.3655 0.9932 0.4289 0.8045 43 140.7 118.8113 89.2396 152.6077 0.1021 0.0941 0.6768 0.4818 44 140.2 121.1038 91.1051 155.3646 0.1373 0.1311 0.5343 0.5343 45 100.2 110.1666 78.1435 147.6754 0.3013 0.0583 0.6064 0.311 46 125.7 120.8572 86.7247 160.6404 0.4057 0.8456 0.7204 0.5247 47 119.6 119.4137 84.5069 160.3403 0.4964 0.3817 0.3162 0.4964 48 134.7 151.6663 111.9571 197.3911 0.2335 0.9154 0.5523 0.9154 49 109 126.9169 90.1369 169.9746 0.2074 0.3616 0.8773 0.6305 50 116.3 105.0556 71.735 144.7131 0.2892 0.4227 0.0708 0.2361 51 146.9 141.6168 102.2083 187.437 0.4106 0.8606 0.4645 0.8268 52 97.4 81.6957 52.2856 117.6411 0.1959 2e-04 0.5021 0.0194 53 89.4 88.0551 57.2977 125.3954 0.4719 0.3119 0.4531 0.0489 54 132.1 135.8179 96.5853 181.7213 0.4369 0.9763 0.4042 0.7557 55 139.8 119.5731 82.8117 163.0678 0.181 0.2862 0.1705 0.4995 56 129 121.633 84.3906 165.6634 0.3715 0.2093 0.2043 0.5361 57 112.5 110.7576 72.5474 157.0212 0.4706 0.2198 0.6727 0.354 58 121.9 121.4375 80.7946 170.3328 0.4926 0.6399 0.4322 0.5294 59 121.7 119.9274 78.699 169.8077 0.4722 0.4691 0.5051 0.5051 60 123.1 152.2827 105.2778 207.9386 0.152 0.8593 0.7321 0.8751 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.1186 -0.018 0 3.6861 0 0 34 0.1144 -0.1099 0.064 181.302 92.4941 9.6174 35 0.1297 0.1055 0.0778 152.5763 112.5215 10.6076 36 0.1144 -0.0169 0.0626 6.5627 86.0318 9.2753 37 0.1342 -0.1981 0.0897 627.5081 194.327 13.9401 38 0.1493 0.2989 0.1246 962.2867 322.3203 17.9533 39 0.1276 0.0168 0.1092 5.6135 277.0765 16.6456 40 0.1748 0.0084 0.0966 0.4645 242.5 15.5724 41 0.1681 0.0323 0.0894 8.0008 216.4445 14.7121 42 0.1347 0.0463 0.0851 39.2557 198.7257 14.097 43 0.1451 0.1842 0.0941 479.1153 224.2156 14.9738 44 0.1443 0.1577 0.0994 364.6662 235.9198 15.3597 45 0.1737 -0.0905 0.0987 99.3329 225.4132 15.0138 46 0.1679 0.0401 0.0946 23.453 210.9874 14.5254 47 0.1749 0.0016 0.0884 0.0347 196.9239 14.033 48 0.1538 -0.1119 0.0898 287.8544 202.6071 14.234 49 0.1731 -0.1412 0.0928 321.0137 209.5722 14.4766 50 0.1926 0.107 0.0936 126.4363 204.9535 14.3162 51 0.1651 0.0373 0.0907 27.9121 195.6355 13.987 52 0.2245 0.1922 0.0957 246.6264 198.1851 14.0778 53 0.2164 0.0153 0.0919 1.8088 188.8338 13.7417 54 0.1724 -0.0274 0.089 13.8227 180.8788 13.4491 55 0.1856 0.1692 0.0925 409.127 190.8026 13.8131 56 0.1847 0.0606 0.0911 54.2731 185.1139 13.6057 57 0.2131 0.0157 0.0881 3.0361 177.8308 13.3353 58 0.2054 0.0038 0.0849 0.2139 170.9994 13.0767 59 0.2122 0.0148 0.0823 3.1421 164.7824 12.8368 60 0.1865 -0.1916 0.0862 851.629 189.3127 13.7591

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260390958ty0onizw526ohqy/1fbuy1260390868.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260390958ty0onizw526ohqy/1fbuy1260390868.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260390958ty0onizw526ohqy/2qfmt1260390868.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260390958ty0onizw526ohqy/2qfmt1260390868.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; 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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