*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 07:09:16 -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/t1260540945jfv5hsypf5ajt3z.htm/, Retrieved Fri, 11 Dec 2009 15:15:47 +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/t1260540945jfv5hsypf5ajt3z.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)

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Dataseries X:

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9051 8823 8776 8255 7969 8758 8693 8271 7790 7769 8170 8209 9395 9260 9018 8501 8500 9649 9319 8830 8436 8169 8269 7945 9144 8770 8834 7837 7792 8616 8518 7940 7545 7531 7665 7599 8444 8549 7986 7335 7287 7870 7839 7327 7259 6964 7271 6956 7608 7692 7255 6804 6655 7341 7602 7086 6625 6272 6576 6491 7649 7400 6913 6532 6486 7295 7556 7088 6952 6773 6917 7371 8221 7953 8027 7287 8076 8933 9433 9479 9199 9469 10015 10999 13009 13699 13895 13248 13973 15095 15201 14823 14538 14547 14407

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 4 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[67]) 55 7602 - - - - - - - 56 7086 - - - - - - - 57 6625 - - - - - - - 58 6272 - - - - - - - 59 6576 - - - - - - - 60 6491 - - - - - - - 61 7649 - - - - - - - 62 7400 - - - - - - - 63 6913 - - - - - - - 64 6532 - - - - - - - 65 6486 - - - - - - - 66 7295 - - - - - - - 67 7556 - - - - - - - 68 7088 6982.3207 6581.4021 7383.2393 0.3027 0.0025 0.3061 0.0025 69 6952 6789.6608 6299.5556 7279.766 0.2581 0.1164 0.7449 0.0011 70 6773 6455.4471 5852.1368 7058.7573 0.1511 0.0534 0.7244 2e-04 71 6917 6705.803 6036.3433 7375.2627 0.2682 0.422 0.648 0.0064 72 7371 6495.7652 5760.1646 7231.3659 0.0098 0.1309 0.5051 0.0024 73 8221 7493.0864 6690.7065 8295.4662 0.0377 0.6172 0.3517 0.4389 74 7953 7419.5235 6550.8938 8288.1532 0.1143 0.0353 0.5176 0.3791 75 8027 6906.6448 5984.8501 7828.4395 0.0086 0.013 0.4946 0.0837 76 7287 6454.1855 5485.574 7422.797 0.046 7e-04 0.4374 0.0129 77 8076 6401.922 5383.0939 7420.7501 6e-04 0.0443 0.4358 0.0132 78 8933 7204.9615 6133.5222 8276.4008 8e-04 0.0555 0.4346 0.2604 79 9433 7438.5747 6321.4031 8555.7462 2e-04 0.0044 0.4184 0.4184 80 9479 6838.5341 5603.8085 8073.2598 0 0 0.3461 0.1274 81 9199 6545.9881 5225.0459 7866.9303 0 0 0.2734 0.067 82 9469 6256.5458 4833.7336 7679.358 0 0 0.2384 0.0367 83 10015 6525.0959 5021.2336 8028.9582 0 1e-04 0.3048 0.0895 84 10999 6316.9501 4739.8877 7894.0124 0 0 0.0951 0.0618 85 13009 7378.1217 5727.8042 9028.4391 0 0 0.1584 0.4163 86 13699 7278.0325 5549.7177 9006.3474 0 0 0.222 0.3763 87 13895 6791.7731 4992.1914 8591.3548 0 0 0.0893 0.2026 88 13248 6325.5617 4464.1161 8187.0073 0 0 0.1557 0.0976 89 13973 6252.0863 4329.5457 8174.6268 0 0 0.0315 0.0919 90 15095 7096.107 5107.7904 9084.4235 0 0 0.0351 0.3252 91 15201 7372.451 5320.4032 9424.4989 0 0 0.0245 0.4304 92 14823 6752.8756 4555.9408 8949.8104 0 0 0.0075 0.2368 93 14538 6467.4262 4164.8255 8770.0269 0 0 0.01 0.1771 94 14547 6181.2783 3754.7262 8607.8305 0 0 0.004 0.1334 95 14407 6481.4694 3947.7478 9015.191 0 0 0.0031 0.2029 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 68 0.0293 0.0151 0 11168.1126 0 0 69 0.0368 0.0239 0.0195 26354.0072 18761.0599 136.971 70 0.0477 0.0492 0.0294 100839.8692 46120.663 214.7572 71 0.0509 0.0315 0.0299 44604.1791 45741.542 213.8727 72 0.0578 0.1347 0.0509 766035.8914 189800.4119 435.6609 73 0.0546 0.0971 0.0586 529858.2804 246476.7233 496.4642 74 0.0597 0.0719 0.0605 284597.2088 251922.507 501.9188 75 0.0681 0.1622 0.0732 1255195.7726 377331.6652 614.2733 76 0.0766 0.129 0.0794 693579.9963 412470.3686 642.2386 77 0.0812 0.2615 0.0976 2802537.2302 651477.0548 807.1413 78 0.0759 0.2398 0.1106 2986117.0292 863717.0525 929.3638 79 0.0766 0.2681 0.1237 3977732.4727 1123218.3375 1059.82 80 0.0921 0.3861 0.1439 6972059.9162 1573129.2281 1254.2445 81 0.103 0.4053 0.1625 7038472.1148 1963510.8629 1401.2533 82 0.116 0.5135 0.1859 10319861.9768 2520600.9372 1587.6401 83 0.1176 0.5348 0.2077 12179430.7611 3124277.8012 1767.5627 84 0.1274 0.7412 0.2391 21921591.3271 4230002.1262 2056.6969 85 0.1141 0.7632 0.2682 31706790.9044 5756490.3917 2399.2687 86 0.1212 0.8822 0.3006 41228823.0065 7623455.2661 2761.0605 87 0.1352 1.0459 0.3378 50455832.1589 9765074.1108 3124.9119 88 0.1501 1.0944 0.3738 47920151.8175 11581982.573 3403.2312 89 0.1569 1.2349 0.413 59612508.902 13765188.3152 3710.1467 90 0.143 1.1272 0.444 63982289.9772 15948540.5614 3993.5624 91 0.142 1.0619 0.4698 61286178.7072 17837608.8175 4223.4593 92 0.166 1.1951 0.4988 65126907.6337 19729180.7701 4441.7542 93 0.1816 1.2479 0.5276 65134161.877 21475526.1973 4634.1694 94 0.2003 1.3534 0.5582 69985298.8692 23272184.4444 4824.1253 95 0.1994 1.2228 0.5819 62814034.902 24684393.3893 4968.3391

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540945jfv5hsypf5ajt3z/1smx81260540551.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540945jfv5hsypf5ajt3z/1smx81260540551.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540945jfv5hsypf5ajt3z/278j31260540551.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260540945jfv5hsypf5ajt3z/278j31260540551.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

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