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*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: Sun, 14 Dec 2008 10:54:54 -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/14/t1229277455qagf7z0mqx0okn3.htm/, Retrieved Sun, 14 Dec 2008 18:57:38 +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/14/t1229277455qagf7z0mqx0okn3.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:

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Dataseries X:

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11554.5 13182.1 14800.1 12150.7 14478.2 13253.9 12036.8 12653.2 14035.4 14571.4 15400.9 14283.2 14485.3 14196.3 15559.1 13767.4 14634 14381.1 12509.9 12122.3 13122.3 13908.7 13456.5 12441.6 12953 13057.2 14350.1 13830.2 13755.5 13574.4 12802.6 11737.3 13850.2 15081.8 13653.3 14019.1 13962 13768.7 14747.1 13858.1 13188 13693.1 12970 11392.8 13985.2 14994.7 13584.7 14257.8 13553.4 14007.3 16535.8 14721.4 13664.6 16805.9 13829.4 13735.6 15870.5 15962.4 15744.1 16083.7 14863.9 15533.1 17473.1 15925.5 15573.7 17495 14155.8 14913.9 17250.4 15879.8 17647.8 17749.9 17111.8 16934.8 20280 16238.2 17896.1 18089.3 15660 16162.4 17850.1 18520.4 18524.7 16843.7

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 '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[48]) 36 14019.1 - - - - - - - 37 13962 - - - - - - - 38 13768.7 - - - - - - - 39 14747.1 - - - - - - - 40 13858.1 - - - - - - - 41 13188 - - - - - - - 42 13693.1 - - - - - - - 43 12970 - - - - - - - 44 11392.8 - - - - - - - 45 13985.2 - - - - - - - 46 14994.7 - - - - - - - 47 13584.7 - - - - - - - 48 14257.8 - - - - - - - 49 13553.4 13955.5687 12754.9595 15156.1778 0.2557 0.3109 0.4958 0.3109 50 14007.3 13888.3399 12500.6042 15276.0756 0.4333 0.6819 0.5671 0.3009 51 16535.8 14964.6874 13277.2201 16652.1546 0.034 0.8669 0.5998 0.7942 52 14721.4 13911.1045 11680.7593 16141.4498 0.2382 0.0105 0.5186 0.3803 53 13664.6 13380.705 10938.4576 15822.9524 0.4099 0.141 0.5615 0.2407 54 16805.9 13871.45 11080.7995 16662.1006 0.0197 0.5578 0.5498 0.3931 55 13829.4 13073.9085 9932.3215 16215.4955 0.3187 0.0099 0.5258 0.2301 56 13735.6 11600.8213 8246.4365 14955.2061 0.1061 0.0964 0.5484 0.0603 57 15870.5 14138.6885 10472.8178 17804.5592 0.1772 0.5853 0.5327 0.4746 58 15962.4 15136.4835 11216.4654 19056.5015 0.3398 0.3568 0.5283 0.6698 59 15744.1 13783.7766 9654.0965 17913.4567 0.1761 0.1506 0.5376 0.411 60 16083.7 14403.6181 10012.6507 18794.5855 0.2266 0.2748 0.5259 0.5259 61 14863.9 14120.1007 9037.2298 19202.9716 0.3871 0.2245 0.5865 0.4788 62 15533.1 14072.8198 8583.6091 19562.0306 0.301 0.3888 0.5093 0.4737 63 17473.1 15113.5936 9112.4598 21114.7274 0.2205 0.4455 0.3211 0.6101 64 15925.5 14085.6659 7456.0297 20715.3021 0.2932 0.1583 0.4255 0.4797 65 15573.7 13553.4292 6498.7979 20608.0605 0.2873 0.2549 0.4877 0.4224 66 17495 14027.3555 6443.0368 21611.6742 0.1851 0.3447 0.2364 0.4763 67 14155.8 13250.2914 5159.916 21340.6668 0.4132 0.1519 0.4442 0.4036 68 14913.9 11766.9026 3267.235 20266.5702 0.234 0.2909 0.3249 0.2829 69 17250.4 14301.1447 5323.0057 23279.2836 0.2598 0.4468 0.3659 0.5038 70 15879.8 15310.7828 5912.3288 24709.2368 0.4528 0.3429 0.446 0.5869 71 17647.8 13947.5251 4161.1081 23733.9421 0.2293 0.3494 0.3595 0.4752 72 17749.9 14570.4086 4364.7383 24776.0789 0.2707 0.2773 0.3857 0.5239 73 17111.8 14291.3818 3342.8576 25239.9061 0.3068 0.2679 0.4592 0.5024 74 16934.8 14236.7982 2743.9007 25729.6957 0.3227 0.312 0.4125 0.4986 75 20280 15282.4354 3169.307 27395.5637 0.2094 0.3946 0.3615 0.5658 76 16238.2 14254.508 1424.413 27084.603 0.3809 0.1787 0.3993 0.4998 77 17896.1 13718.6425 329.7983 27107.4868 0.2704 0.3561 0.393 0.4685 78 18089.3 14196.6509 168.1644 28225.1375 0.2933 0.3026 0.3225 0.4966 79 15660 13417.7141 -1234.795 28070.2231 0.3821 0.266 0.4607 0.4553 80 16162.4 11933.3815 -3259.825 27126.5879 0.2927 0.3153 0.3503 0.3821 81 17850.1 14470.0852 -1319.3781 30259.5486 0.3374 0.4168 0.365 0.5105 82 18520.4 15477.6632 -859.1241 31814.4505 0.3575 0.388 0.4808 0.5582 83 18524.7 14114.8818 -2737.6522 30967.4158 0.304 0.3042 0.3406 0.4934 84 16843.7 14738.77 -2654.6827 32132.2228 0.4063 0.3348 0.3672 0.5216 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 49 0.0439 -0.0288 8e-04 161739.6294 4492.7675 67.0281 50 0.051 0.0086 2e-04 14151.5158 393.0977 19.8267 51 0.0575 0.105 0.0029 2468394.8867 68566.5246 261.8521 52 0.0818 0.0582 0.0016 656578.7252 18238.2979 135.0492 53 0.0931 0.0212 6e-04 80596.3649 2238.7879 47.3158 54 0.1026 0.2115 0.0059 8610996.5742 239194.3493 489.075 55 0.1226 0.0578 0.0016 570767.4201 15854.6506 125.9153 56 0.1475 0.184 0.0051 4557280.1959 126591.1166 355.7965 57 0.1323 0.1225 0.0034 2999171.1451 83310.3096 288.6353 58 0.1321 0.0546 0.0015 682138.142 18948.2817 137.6528 59 0.1529 0.1422 0.004 3842867.8584 106746.3294 326.7206 60 0.1555 0.1166 0.0032 2822675.1412 78407.6428 280.0136 61 0.1837 0.0527 0.0015 553237.4039 15367.7057 123.9666 62 0.199 0.1038 0.0029 2132418.2524 59233.8403 243.38 63 0.2026 0.1561 0.0043 5567270.3562 154646.3988 393.2511 64 0.2401 0.1306 0.0036 3384989.4695 94027.4853 306.639 65 0.2656 0.1491 0.0041 4081494.1441 113374.8373 336.7118 66 0.2759 0.2472 0.0069 12024558.4618 334015.5128 577.9408 67 0.3115 0.0683 0.0019 819945.7825 22776.2717 150.9181 68 0.3685 0.2674 0.0074 9903592.6674 275099.7963 524.4996 69 0.3203 0.2062 0.0057 8698106.8422 241614.079 491.5426 70 0.3132 0.0372 0.001 323780.5361 8993.9038 94.8362 71 0.358 0.2653 0.0074 13692034.5552 380334.2932 616.7125 72 0.3574 0.2182 0.0061 10109165.6805 280810.1578 529.9152 73 0.3909 0.1974 0.0055 7954758.611 220965.517 470.0697 74 0.4119 0.1895 0.0053 7279213.614 202200.3782 449.667 75 0.4044 0.327 0.0091 24975652.4185 693768.1227 832.9274 76 0.4592 0.1392 0.0039 3935033.8362 109306.4954 330.6153 77 0.4979 0.3045 0.0085 17451150.9197 484754.1922 696.2429 78 0.5042 0.2742 0.0076 15152716.9094 420908.803 648.7748 79 0.5572 0.1671 0.0046 5027846.2409 139662.3956 373.7143 80 0.6496 0.3544 0.0098 17884597.7296 496794.3814 704.8364 81 0.5567 0.2336 0.0065 11424499.9124 317347.2198 563.3358 82 0.5385 0.1966 0.0055 9258247.2595 257173.535 507.1228 83 0.6092 0.3124 0.0087 19446496.2385 540180.4511 734.9697 84 0.6021 0.1428 0.004 4430730.1737 123075.8382 350.8217

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277455qagf7z0mqx0okn3/1vznb1229277293.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277455qagf7z0mqx0okn3/1vznb1229277293.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277455qagf7z0mqx0okn3/2lnci1229277293.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/14/t1229277455qagf7z0mqx0okn3/2lnci1229277293.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = 1.3 ; par3 = 1 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; 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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