ws10

*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 11:16:04 -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/10/t1260469005miaq9yyl61benyz.htm/, Retrieved Thu, 10 Dec 2009 19:16:48 +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/10/t1260469005miaq9yyl61benyz.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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325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 310631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224

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[34]) 22 298423 - - - - - - - 23 310631 - - - - - - - 24 329765 - - - - - - - 25 335083 - - - - - - - 26 327616 - - - - - - - 27 309119 - - - - - - - 28 295916 - - - - - - - 29 291413 - - - - - - - 30 291542 - - - - - - - 31 284678 - - - - - - - 32 276475 - - - - - - - 33 272566 - - - - - - - 34 264981 - - - - - - - 35 263290 275098.5995 265768.4789 284428.7201 0.0066 0.9832 0 0.9832 36 296806 288258.7659 273313.6256 303203.9062 0.1312 0.9995 0 0.9989 37 303598 292535.448 271822.9165 313247.9795 0.1476 0.3431 0 0.9954 38 286994 288108.9499 264016.7366 312201.1632 0.4639 0.1038 7e-04 0.9701 39 276427 273788.8638 247730.1655 299847.5621 0.4214 0.1603 0.0039 0.7462 40 266424 262476.2446 234278.6433 290673.8458 0.3919 0.1661 0.0101 0.4309 41 267153 258583.4031 227745.1668 289421.6394 0.293 0.3091 0.0185 0.3421 42 268381 259216.4237 226032.1625 292400.6849 0.2942 0.3196 0.0281 0.3667 43 262522 254132.5784 219147.1114 289118.0454 0.3192 0.2124 0.0435 0.2717 44 255542 247377.7243 210700.9029 284054.5457 0.3313 0.2092 0.06 0.1734 45 253158 244025.3359 205506.1715 282544.5004 0.3211 0.2789 0.0732 0.1431 46 243803 238184.0859 197850.1887 278517.983 0.3924 0.2334 0.0964 0.0964 47 250741 246365.1744 201841.482 290888.8668 0.4236 0.5449 0.2281 0.2063 48 280445 256687.7449 207677.0833 305698.4065 0.171 0.594 0.0543 0.3701 49 285257 259914.2148 205836.9979 313991.4317 0.1792 0.2284 0.0567 0.4271 50 270976 256431.421 198258.6102 314604.2319 0.3121 0.1657 0.1516 0.3867 51 261076 245239.135 183906.8318 306571.4383 0.3064 0.2054 0.1595 0.2641 52 255603 236334.7824 171842.2146 300827.3502 0.2791 0.2261 0.1802 0.192 53 260376 233204.5805 165268.7594 301140.4015 0.2165 0.2591 0.1637 0.1796 54 263903 233682.7541 162490.5254 304874.9827 0.2027 0.2312 0.1697 0.1944 55 264291 229711.3412 155670.5489 303752.1335 0.18 0.1827 0.1925 0.1752 56 263276 224406.8503 147658.6747 301155.0258 0.1604 0.1542 0.2133 0.1501 57 262572 221743.9074 142226.3741 301261.4408 0.1571 0.153 0.2194 0.1433 58 256167 217121.4829 134876.3206 299366.6452 0.1761 0.1394 0.2624 0.127 59 264221 223580.9641 137186.7509 309975.1773 0.1783 0.2299 0.2689 0.1738 60 293860 231732.1756 141004.4965 322459.8548 0.0898 0.2414 0.1463 0.2363 61 300713 234271.7761 138850.6118 329692.9404 0.0862 0.1105 0.1475 0.2641 62 287224 231516.5117 131940.8102 331092.2131 0.1364 0.0866 0.2187 0.255 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 35 0.0173 -0.0429 0 139443022.3636 0 0 36 0.0265 0.0297 0.0363 73055210.5206 106249116.4421 10307.7212 37 0.0361 0.0378 0.0368 122380057.0904 111626096.6582 10565.3252 38 0.0427 -0.0039 0.0286 1243113.3165 84030350.8228 9166.807 39 0.0486 0.0096 0.0248 6959762.5902 68616233.1763 8283.4916 40 0.0548 0.015 0.0232 15584773.0635 59777656.4908 7731.6012 41 0.0608 0.0331 0.0246 73437990.9707 61729132.8451 7856.789 42 0.0653 0.0354 0.0259 83989458.5509 64511673.5583 8031.9159 43 0.0702 0.033 0.0267 70382394.8922 65163975.9287 8072.4207 44 0.0756 0.033 0.0273 66655397.8984 65313118.1257 8081.6532 45 0.0805 0.0374 0.0283 83405552.6708 66957884.9025 8182.7798 46 0.0864 0.0236 0.0279 31572196.1506 64009077.5065 8000.5673 47 0.0922 0.0178 0.0271 19147849.3055 60558213.7988 7781.9158 48 0.0974 0.0926 0.0318 564407170.4907 96547424.991 9825.8549 49 0.1062 0.0975 0.0362 642256763.2638 132928047.5426 11529.4426 50 0.1157 0.0567 0.0374 211544777.0027 137841593.1338 11740.5959 51 0.1276 0.0646 0.039 250806291.7939 144486575.4079 12020.2569 52 0.1392 0.0815 0.0414 371264208.5661 157085332.8056 12533.3688 53 0.1486 0.1165 0.0453 738286039.7788 187674843.6989 13699.4468 54 0.1554 0.1293 0.0495 913263265.0296 223954264.7655 14965.1016 55 0.1644 0.1505 0.0544 1195752801.8127 270230385.5772 16438.6856 56 0.1745 0.1732 0.0598 1510810801.9781 326620404.5046 18072.6424 57 0.183 0.1841 0.0652 1666933141.4308 384894871.3274 19618.7378 58 0.1933 0.1798 0.0699 1524552406.2208 432380601.948 20793.7635 59 0.1971 0.1818 0.0744 1651612515.7663 481149878.5007 21935.1289 60 0.1998 0.2681 0.0819 3859866560.2027 611100520.1046 24720.4474 61 0.2078 0.2836 0.0893 4414436233.8814 751964805.8001 27421.9767 62 0.2194 0.2406 0.0947 3103324254.3528 835941928.9627 28912.6604

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/10/t1260469005miaq9yyl61benyz/104a51260468962.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260469005miaq9yyl61benyz/104a51260468962.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260469005miaq9yyl61benyz/21f4x1260468962.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/10/t1260469005miaq9yyl61benyz/21f4x1260468962.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ; par5 = 1 ; par6 = 1 ; par7 = 1 ; par8 = 3 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 1 ; 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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