*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 09:52:49 -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/t1260550492s675h80pl85qjpo.htm/, Retrieved Fri, 11 Dec 2009 17:54:54 +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/t1260550492s675h80pl85qjpo.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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902.2 891.9 874 930.9 944.2 935.9 937.1 885.1 892.4 987.3 946.3 799.6 875.4 846.2 880.6 885.7 868.9 882.5 789.6 773.3 804.3 817.8 836.7 721.8 760.8 841.4 1045.6 949.2 850.1 957.4 851.8 913.9 888 973.8 927.6 833 879.5 797.3 834.5 735.1 835 892.8 697.2 821.1 732.7 797.6 866.3 826.3 778.6 779.2 951 692.3 841.4 857.3 760.7 841.2 810.3 1007.4 931.3 931.2

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]) 20 773.3 - - - - - - - 21 804.3 - - - - - - - 22 817.8 - - - - - - - 23 836.7 - - - - - - - 24 721.8 - - - - - - - 25 760.8 - - - - - - - 26 841.4 - - - - - - - 27 1045.6 - - - - - - - 28 949.2 - - - - - - - 29 850.1 - - - - - - - 30 957.4 - - - - - - - 31 851.8 - - - - - - - 32 913.9 - - - - - - - 33 888 997.4115 897.0936 1097.7294 0.0163 0.9486 0.9999 0.9486 34 973.8 926.9334 754.7226 1099.1442 0.2969 0.6712 0.8929 0.559 35 927.6 979.0292 793.3119 1164.7465 0.2936 0.522 0.9335 0.7541 36 833 875.0492 662.1683 1087.9302 0.3493 0.3143 0.9209 0.3603 37 879.5 867.4423 627.8751 1107.0096 0.4607 0.6109 0.8085 0.3519 38 797.3 974.5049 724.1988 1224.8111 0.0826 0.7715 0.8514 0.6825 39 834.5 1172.5299 903.6431 1441.4167 0.0069 0.9969 0.8226 0.9703 40 735.1 1052.8738 768.9991 1336.7484 0.0141 0.9342 0.7629 0.8314 41 835 970.3963 677.1551 1263.6375 0.1827 0.9421 0.7893 0.6471 42 892.8 1066.8805 760.3773 1373.3837 0.1328 0.9309 0.7581 0.836 43 697.2 950.8896 634.3471 1267.432 0.0581 0.6405 0.7302 0.5906 44 821.1 1021.4386 696.7915 1346.0857 0.1132 0.9749 0.7419 0.7419 45 732.7 1094.8118 722.8798 1466.7439 0.0282 0.9254 0.8621 0.8298 46 797.6 1020.1765 591.9647 1448.3884 0.1542 0.9059 0.5841 0.6867 47 866.3 1075.3035 625.0759 1525.531 0.1814 0.8867 0.7399 0.7589 48 826.3 963.4851 479.731 1447.2392 0.2892 0.6531 0.7015 0.5796 49 778.6 954.2784 439.4689 1469.0878 0.2518 0.687 0.6121 0.5611 50 779.2 1061.3309 528.3749 1594.2869 0.1497 0.8508 0.8342 0.7062 51 951 1253.8154 696.1602 1811.4706 0.1436 0.9524 0.9297 0.8839 52 692.3 1133.3384 555.2818 1711.395 0.0674 0.7318 0.9115 0.7716 53 841.4 1049.4347 455.9707 1642.8987 0.246 0.8809 0.7606 0.6728 54 857.3 1142.1422 530.2153 1754.069 0.1808 0.8323 0.7878 0.7676 55 760.7 1025.3956 398.5771 1652.2141 0.2039 0.7004 0.8476 0.6363 56 841.2 1094.0531 454.2166 1733.8897 0.2193 0.8464 0.7985 0.7095 57 810.3 1164.8382 482.0129 1847.6634 0.1544 0.8236 0.8926 0.7643 58 1007.4 1089.3191 356.1069 1822.5312 0.4133 0.7721 0.7822 0.6804 59 931.3 1142.5675 384.5297 1900.6054 0.2924 0.6366 0.7625 0.7228 60 931.2 1028.9033 236.8738 1820.9328 0.4045 0.5954 0.6919 0.612 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0513 -0.1097 0 11970.8776 0 0 34 0.0948 0.0506 0.0801 2196.4765 7083.677 84.1646 35 0.0968 -0.0525 0.0709 2644.9596 5604.1045 74.8606 36 0.1241 -0.0481 0.0652 1768.1387 4645.1131 68.1551 37 0.1409 0.0139 0.0549 145.3872 3745.1679 61.1978 38 0.131 -0.1818 0.0761 31401.5932 8354.5721 91.4033 39 0.117 -0.2883 0.1064 114264.2368 23484.5242 153.2466 40 0.1376 -0.3018 0.1308 100980.1694 33171.4799 182.1304 41 0.1542 -0.1395 0.1318 18332.1592 31522.6665 177.5462 42 0.1466 -0.1632 0.1349 30304.0252 31400.8023 177.2027 43 0.1698 -0.2668 0.1469 64358.3913 34396.9468 185.4641 44 0.1622 -0.1961 0.151 40135.5594 34875.1645 186.7489 45 0.1733 -0.3308 0.1649 131124.9771 42278.9962 205.6186 46 0.2142 -0.2182 0.1687 49540.3088 42797.6614 206.876 47 0.2136 -0.1944 0.1704 43682.4532 42856.6475 207.0185 48 0.2562 -0.1424 0.1686 18819.7402 41354.3408 203.3577 49 0.2752 -0.1841 0.1695 30862.8849 40737.1964 201.8346 50 0.2562 -0.2658 0.1749 79597.8323 42896.1206 207.1138 51 0.2269 -0.2415 0.1784 91697.1626 45464.5965 213.2243 52 0.2602 -0.3891 0.1889 194514.8724 52917.1103 230.0372 53 0.2885 -0.1982 0.1894 43278.4323 52458.1256 229.0374 54 0.2734 -0.2494 0.1921 81135.0724 53761.6232 231.8655 55 0.3119 -0.2581 0.195 70063.7611 54470.4118 233.389 56 0.2984 -0.2311 0.1965 63934.71 54864.7576 234.2323 57 0.2991 -0.3044 0.2008 125697.308 57698.0596 240.2042 58 0.3434 -0.0752 0.196 6710.7346 55737.0086 236.0869 59 0.3385 -0.1849 0.1956 44633.9698 55325.785 235.2143 60 0.3927 -0.095 0.192 9545.9313 53690.7902 231.7127

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550492s675h80pl85qjpo/1it8h1260550367.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550492s675h80pl85qjpo/1it8h1260550367.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550492s675h80pl85qjpo/27czi1260550367.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260550492s675h80pl85qjpo/27czi1260550367.ps (open in new window)

Parameters (Session):

par1 = 10 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 10 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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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