*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: Tue, 28 Dec 2010 00:28:29 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293495975tsj84vt6j97m5a1.htm/, Retrieved Tue, 28 Dec 2010 01:26:15 +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/2010/Dec/28/t1293495975tsj84vt6j97m5a1.htm/}, year = {2010}, } @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 = {2010}, 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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364 351 380 319 322 386 221 187 343 342 365 313 356 337 389 326 343 357 220 218 391 425 332 298 360 336 325 393 301 426 265 210 429 440 357 431 442 422 544 420 396 482 261 211 448 468 464 425 415 433 531 457 380 481 302 216 509 417 370

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 'RServer@AstonUniversity' @ vre.aston.ac.uk 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[35]) 29 301 - - - - - - - 30 426 - - - - - - - 31 265 - - - - - - - 32 210 - - - - - - - 33 429 - - - - - - - 34 440 - - - - - - - 35 357 - - - - - - - 36 431 303.2283 250.3254 378.4141 4e-04 0.0805 7e-04 0.0805 37 442 353.3562 285.8912 453.1971 0.0409 0.0637 0.9586 0.4715 38 422 329.4179 269.0278 417.1165 0.0193 0.0059 0.9962 0.2688 39 544 328.4242 268.19 415.9135 0 0.018 0.0121 0.261 40 420 394.9325 314.2884 518.3849 0.3453 0.009 0.2371 0.7265 41 396 302.857 249.9109 378.1688 0.0077 0.0011 0.0794 0.0794 42 482 417.9367 329.7582 555.3406 0.1804 0.6228 0.4261 0.8076 43 261 268.5283 224.8318 328.9209 0.4035 0 0 0.002 44 211 214.101 183.7441 254.0932 0.4396 0.0108 0 0 45 448 422.7957 333.0009 563.236 0.3625 0.9984 0.0454 0.8208 46 468 437.5451 342.7854 587.4122 0.3452 0.4456 0.5907 0.8539 47 464 353.9269 286.0911 454.5031 0.016 0.0131 0.2061 0.4761 48 425 307.6544 236.9137 423.6834 0.0237 0.0041 0.0016 0.2023 49 415 348.0577 262.3568 495.2738 0.1864 0.1528 0.8768 0.4526 50 433 321.2832 245.5825 447.4364 0.0413 0.0727 0.9567 0.2895 51 531 332.2762 252.4314 467.1118 0.0019 0.0716 0.0463 0.3597 52 457 396.8997 291.8139 587.6724 0.2685 0.0841 0.2325 0.6591 53 380 305.1137 235.1958 419.5453 0.0998 0.0046 0.0033 0.1871 54 481 410.8751 299.9448 615.5276 0.2509 0.6163 0.4462 0.6971 55 302 271.757 213.3657 363.686 0.2595 0 0.0011 0.0346 56 216 217.9542 176.7239 278.703 0.4749 0.0033 0 0 57 509 417.2906 303.6917 628.3397 0.1972 0.9692 0.1455 0.7122 58 417 435.3396 314.1313 664.9784 0.4378 0.2648 0.4267 0.7481 59 370 351.1683 264.0871 501.5188 0.403 0.1954 0.3535 0.4697 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 36 0.1265 0.4214 0 16325.6153 0 0 37 0.1442 0.2509 0.3361 7857.7265 12091.6709 109.9621 38 0.1358 0.281 0.3178 8571.4419 10918.2612 104.4905 39 0.1359 0.6564 0.4024 46472.9185 19806.9255 140.7371 40 0.1595 0.0635 0.3346 628.3774 15971.2159 126.3773 41 0.1269 0.3075 0.3301 8675.6268 14755.2844 121.4713 42 0.1677 0.1533 0.3049 4104.1117 13233.6883 115.0378 43 0.1147 -0.028 0.2703 56.6755 11586.5617 107.6409 44 0.0953 -0.0145 0.2418 9.6161 10300.2344 101.4901 45 0.1695 0.0596 0.2236 635.2583 9333.7368 96.6113 46 0.1748 0.0696 0.2096 927.5028 8569.5337 92.5718 47 0.145 0.311 0.2181 12116.0965 8865.0806 94.1546 48 0.1924 0.3814 0.2306 13770.0007 9242.3822 96.1373 49 0.2158 0.1923 0.2279 4481.2771 8902.3032 94.352 50 0.2003 0.3477 0.2359 12480.6537 9140.8599 95.6078 51 0.207 0.5981 0.2585 39491.1661 11037.7541 105.0607 52 0.2452 0.1514 0.2522 3612.0438 10600.9476 102.9609 53 0.1913 0.2454 0.2518 5607.9524 10323.559 101.6049 54 0.2541 0.1707 0.2476 4917.5027 10039.0297 100.195 55 0.1726 0.1113 0.2408 914.6418 9582.8103 97.8918 56 0.1422 -0.009 0.2297 3.8187 9126.6678 95.5336 57 0.258 0.2198 0.2293 8410.6116 9094.1198 95.3631 58 0.2691 -0.0421 0.2211 336.3403 8713.3468 93.3453 59 0.2184 0.0536 0.2141 354.6331 8365.0671 91.4607

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293495975tsj84vt6j97m5a1/1rc331293496105.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293495975tsj84vt6j97m5a1/1rc331293496105.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293495975tsj84vt6j97m5a1/25mju1293496105.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293495975tsj84vt6j97m5a1/25mju1293496105.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = -0.7 ; par3 = 0 ; par4 = 1 ; par5 = 6 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; par10 = TRUE ;

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,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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