*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: Mon, 15 Dec 2008 02:50:05 -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/15/t1229334797tefc3f4r0s2ds1v.htm/, Retrieved Mon, 15 Dec 2008 10:53:19 +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/15/t1229334797tefc3f4r0s2ds1v.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)

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Dataseries X:

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31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835

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 'George Udny Yule' @ 72.249.76.132 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[16]) 4 26105 - - - - - - - 5 22397 - - - - - - - 6 23843 - - - - - - - 7 21705 - - - - - - - 8 18089 - - - - - - - 9 20764 - - - - - - - 10 25316 - - - - - - - 11 17704 - - - - - - - 12 15548 - - - - - - - 13 28029 - - - - - - - 14 29383 - - - - - - - 15 36438 - - - - - - - 16 32034 - - - - - - - 17 22679 22397 12533.1072 32260.8928 0.4777 0.0278 0.5 0.0278 18 24319 23843 13979.1072 33706.8928 0.4623 0.5915 0.5 0.0518 19 18004 21705 11841.1072 31568.8928 0.231 0.3017 0.5 0.0201 20 17537 18089 8225.1072 27952.8928 0.4563 0.5067 0.5 0.0028 21 20366 20764 10900.1072 30627.8928 0.4685 0.7393 0.5 0.0126 22 22782 25316 15452.1072 35179.8928 0.3073 0.8373 0.5 0.091 23 19169 17704 7840.1072 27567.8928 0.3855 0.1565 0.5 0.0022 24 13807 15548 5684.1072 25411.8928 0.3647 0.2359 0.5 5e-04 25 29743 28029 18165.1072 37892.8928 0.3667 0.9976 0.5 0.2131 26 25591 29383 19519.1072 39246.8928 0.2256 0.4715 0.5 0.2992 27 29096 36438 26574.1072 46301.8928 0.0723 0.9844 0.5 0.8092 28 26482 32034 22170.1072 41897.8928 0.135 0.7203 0.5 0.5 29 22405 22397 8447.349 36346.651 0.4996 0.283 0.4842 0.0879 30 27044 23843 9893.349 37792.651 0.3264 0.5801 0.4733 0.1249 31 17970 21705 7755.349 35654.651 0.2999 0.2266 0.6985 0.0734 32 18730 18089 4139.349 32038.651 0.4641 0.5067 0.5309 0.025 33 19684 20764 6814.349 34713.651 0.4397 0.6125 0.5223 0.0567 34 19785 25316 11366.349 39265.651 0.2185 0.7856 0.6391 0.1726 35 18479 17704 3754.349 31653.651 0.4566 0.385 0.4185 0.022 36 10698 15548 1598.349 29497.651 0.2478 0.3402 0.5966 0.0103 37 31956 28029 14079.349 41978.651 0.2906 0.9926 0.4048 0.2868 38 29506 29383 15433.349 43332.651 0.4931 0.3589 0.7029 0.3548 39 34506 36438 22488.349 50387.651 0.393 0.835 0.8489 0.732 40 27165 32034 18084.349 45983.651 0.2469 0.3642 0.7823 0.5 41 26736 22397 5312.2365 39481.7635 0.3093 0.2922 0.4996 0.1345 42 23691 23843 6758.2365 40927.7635 0.493 0.37 0.3567 0.1737 43 18157 21705 4620.2365 38789.7635 0.342 0.4099 0.6659 0.118 44 17328 18089 1004.2365 35173.7635 0.4652 0.4969 0.4707 0.0548 45 18205 20764 3679.2365 37848.7635 0.3845 0.6533 0.5493 0.098 46 20995 25316 8231.2365 42400.7635 0.31 0.7927 0.7371 0.2204 47 17382 17704 619.2365 34788.7635 0.4853 0.3529 0.4646 0.0501 48 9367 15548 -1536.7635 32632.7635 0.2391 0.4167 0.711 0.0293 49 31124 28029 10944.2365 45113.7635 0.3613 0.9839 0.3262 0.323 50 26551 29383 12298.2365 46467.7635 0.3726 0.4208 0.4944 0.3805 51 30651 36438 19353.2365 53522.7635 0.2534 0.8717 0.5877 0.6933 52 25859 32034 14949.2365 49118.7635 0.2393 0.563 0.7118 0.5 53 25100 22397 2669.2143 42124.7857 0.3941 0.3654 0.3332 0.1692 54 25778 23843 4115.2143 43570.7857 0.4238 0.4503 0.506 0.2079 55 20418 21705 1977.2143 41432.7857 0.4491 0.3429 0.6378 0.1524 56 18688 18089 -1638.7857 37816.7857 0.4763 0.4085 0.5301 0.083 57 20424 20764 1036.2143 40491.7857 0.4865 0.5817 0.6003 0.1314 58 24776 25316 5588.2143 45043.7857 0.4786 0.6865 0.6661 0.2522 59 19814 17704 -2023.7857 37431.7857 0.417 0.2411 0.5128 0.0773 60 12738 15548 -4179.7857 35275.7857 0.3901 0.3358 0.7304 0.0507 61 31566 28029 8301.2143 47756.7857 0.3626 0.9356 0.3792 0.3453 62 30111 29383 9655.2143 49110.7857 0.4712 0.4141 0.6108 0.3961 63 30019 36438 16710.2143 56165.7857 0.2618 0.7352 0.7173 0.6691 64 31934 32034 12306.2143 51761.7857 0.496 0.5793 0.7302 0.5 65 25826 22397 340.6651 44453.3349 0.3803 0.1984 0.4051 0.1959 66 26835 23843 1786.6651 45899.3349 0.3952 0.4301 0.4317 0.2333 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 17 0.2247 0.0126 3e-04 79524 1590.48 39.8808 18 0.2111 0.02 4e-04 226576 4531.52 67.3166 19 0.2319 -0.1705 0.0034 13697401 273948.02 523.4004 20 0.2782 -0.0305 6e-04 304704 6094.08 78.0646 21 0.2424 -0.0192 4e-04 158404 3168.08 56.2857 22 0.1988 -0.1001 0.002 6421156 128423.12 358.3617 23 0.2843 0.0827 0.0017 2146225 42924.5 207.1823 24 0.3237 -0.112 0.0022 3031081 60621.62 246.2146 25 0.1795 0.0612 0.0012 2937796 58755.92 242.3962 26 0.1713 -0.1291 0.0026 14379264 287585.28 536.2698 27 0.1381 -0.2015 0.004 53904964 1078099.28 1038.3156 28 0.1571 -0.1733 0.0035 30824704 616494.08 785.1714 29 0.3178 4e-04 0 64 1.28 1.1314 30 0.2985 0.1343 0.0027 10246401 204928.02 452.6898 31 0.3279 -0.1721 0.0034 13950225 279004.5 528.2088 32 0.3935 0.0354 7e-04 410881 8217.62 90.6511 33 0.3428 -0.052 0.001 1166400 23328 152.7351 34 0.2811 -0.2185 0.0044 30591961 611839.22 782.2015 35 0.402 0.0438 9e-04 600625 12012.5 109.6016 36 0.4578 -0.3119 0.0062 23522500 470450 685.8936 37 0.2539 0.1401 0.0028 15421329 308426.58 555.3617 38 0.2422 0.0042 1e-04 15129 302.58 17.3948 39 0.1953 -0.053 0.0011 3732624 74652.48 273.2261 40 0.2222 -0.152 0.003 23707161 474143.22 688.5806 41 0.3892 0.1937 0.0039 18826921 376538.42 613.6273 42 0.3656 -0.0064 1e-04 23104 462.08 21.496 43 0.4016 -0.1635 0.0033 12588304 251766.08 501.763 44 0.4819 -0.0421 8e-04 579121 11582.42 107.6217 45 0.4198 -0.1232 0.0025 6548481 130969.62 361.8973 46 0.3443 -0.1707 0.0034 18671041 373420.82 611.0817 47 0.4924 -0.0182 4e-04 103684 2073.68 45.5377 48 0.5606 -0.3975 0.008 38204761 764095.22 874.1254 49 0.311 0.1104 0.0022 9579025 191580.5 437.6991 50 0.2967 -0.0964 0.0019 8020224 160404.48 400.5053 51 0.2392 -0.1588 0.0032 33489369 669787.38 818.4054 52 0.2721 -0.1928 0.0039 38130625 762612.5 873.2769 53 0.4494 0.1207 0.0024 7306209 146124.18 382.2619 54 0.4221 0.0812 0.0016 3744225 74884.5 273.6503 55 0.4637 -0.0593 0.0012 1656369 33127.38 182.0093 56 0.5564 0.0331 7e-04 358801 7176.02 84.7114 57 0.4847 -0.0164 3e-04 115600 2312 48.0833 58 0.3976 -0.0213 4e-04 291600 5832 76.3675 59 0.5685 0.1192 0.0024 4452100 89042 298.3991 60 0.6474 -0.1807 0.0036 7896100 157922 397.394 61 0.3591 0.1262 0.0025 12510369 250207.38 500.2073 62 0.3426 0.0248 5e-04 529984 10599.68 102.9547 63 0.2762 -0.1762 0.0035 41203561 824071.22 907.7837 64 0.3142 -0.0031 1e-04 10000 200 14.1421 65 0.5024 0.1531 0.0031 11758041 235160.82 484.9338 66 0.472 0.1255 0.0025 8952064 179041.28 423.1327

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229334797tefc3f4r0s2ds1v/1do481229334603.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229334797tefc3f4r0s2ds1v/1do481229334603.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229334797tefc3f4r0s2ds1v/2gxm21229334603.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/15/t1229334797tefc3f4r0s2ds1v/2gxm21229334603.ps (open in new window)

Parameters (Session):

par1 = 50 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 50 ; par2 = 1 ; par3 = 0 ; 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 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')

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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