*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 07:29:05 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/11/t1260541841crcngbgmzgxl15q.htm/, Retrieved Fri, 11 Dec 2009 15:30:43 +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/t1260541841crcngbgmzgxl15q.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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267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710

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[39]) 27 276836 - - - - - - - 28 275216 - - - - - - - 29 274352 - - - - - - - 30 271311 - - - - - - - 31 289802 - - - - - - - 32 290726 - - - - - - - 33 292300 - - - - - - - 34 278506 - - - - - - - 35 269826 - - - - - - - 36 265861 - - - - - - - 37 269034 - - - - - - - 38 264176 - - - - - - - 39 255198 - - - - - - - 40 253353 254214.4743 242942.0474 265486.9012 0.4405 0.4321 1e-04 0.4321 41 246057 257801.9113 240668.591 274935.2316 0.0895 0.6946 0.0292 0.6171 42 235372 266942.7431 244405.8285 289479.6577 0.003 0.9653 0.352 0.8465 43 258556 271147.9501 247363.0349 294932.8652 0.1497 0.9984 0.0621 0.9056 44 260993 270810.0139 246903.7698 294716.2579 0.2104 0.8425 0.0513 0.8997 45 254663 271189.5454 247128.1135 295250.9773 0.0891 0.7969 0.0428 0.9037 46 250643 272745.5474 248457.6711 297033.4237 0.0372 0.9278 0.321 0.9216 47 243422 273518.9606 249145.779 297892.1422 0.0078 0.9671 0.6168 0.9297 48 247105 273436.5645 249051.8106 297821.3185 0.0172 0.9921 0.7287 0.9287 49 248541 273458.628 249059.5374 297857.7186 0.0227 0.9829 0.6389 0.9288 50 245039 273722.1169 249299.9514 298144.2824 0.0107 0.9784 0.7782 0.9314 51 237080 273865.2303 249431.8386 298298.6219 0.0016 0.9896 0.9329 0.9329 52 237085 273847.824 249412.9466 298282.7014 0.0016 0.9984 0.9499 0.9327 53 225554 273843.781 249407.1081 298280.4539 1e-04 0.9984 0.9871 0.9326 54 226839 273888.0958 249447.9685 298328.223 1e-04 0.9999 0.999 0.933 55 247934 273914.6909 249472.6893 298356.6925 0.0186 0.9999 0.891 0.9333 56 248333 273911.3251 249469.1256 298353.5246 0.0201 0.9814 0.8499 0.9333 57 246969 273909.214 249466.7943 298351.6338 0.0154 0.9799 0.9386 0.9332 58 245098 273916.602 249473.6165 298359.5876 0.0104 0.9846 0.969 0.9333 59 246263 273921.557 249478.2402 298364.8738 0.0133 0.9896 0.9928 0.9334 60 255765 273920.95 249477.6069 298364.2931 0.0727 0.9867 0.9842 0.9334 61 264319 273920.3324 249476.9666 298363.6982 0.2207 0.9273 0.9791 0.9334 62 268347 273921.5504 249478.0909 298365.01 0.3274 0.7793 0.9897 0.9334 63 273046 273922.4746 249478.9556 298365.9936 0.472 0.6726 0.9984 0.9334 64 273963 273922.3722 249478.8497 298365.8948 0.4987 0.528 0.9984 0.9334 65 267430 273922.2206 249478.6968 298365.7444 0.3013 0.4987 0.9999 0.9334 66 271993 273922.4185 249478.8792 298365.9578 0.4385 0.6987 0.9999 0.9334 67 292710 273922.5908 249479.0408 298366.1408 0.066 0.5615 0.9814 0.9334 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 40 0.0226 -0.0034 0 742137.9807 0 0 41 0.0339 -0.0456 0.0245 137942941.4061 69342539.6934 8327.2168 42 0.0431 -0.1183 0.0557 996711820.8327 378465633.4065 19454.1932 43 0.0448 -0.0464 0.0534 158557206.2969 323488526.6291 17985.7868 44 0.045 -0.0363 0.05 96373761.2553 278065573.5543 16675.2983 45 0.0453 -0.0609 0.0518 273126702.2189 277242428.3318 16650.5984 46 0.0454 -0.081 0.056 488522602.1213 307425310.3017 17533.5481 47 0.0455 -0.11 0.0627 905827035.9639 382225526.0095 19550.5889 48 0.0455 -0.0963 0.0665 693351291.6333 416795055.5232 20415.5592 49 0.0455 -0.0911 0.0689 620888185.6116 437204368.5321 20909.4325 50 0.0455 -0.1048 0.0722 822721194.3841 472251352.7004 21731.3449 51 0.0455 -0.1343 0.0774 1353153165.2046 545659837.0758 23359.3629 52 0.0455 -0.1342 0.0817 1351505226.6208 607647943.9639 24650.5161 53 0.0455 -0.1763 0.0885 2331902952.061 730809015.9708 27033.4795 54 0.0455 -0.1718 0.0941 2213617411.6785 829662909.018 28803.8697 55 0.0455 -0.0948 0.0941 674996298.6091 819996245.8674 28635.5766 56 0.0455 -0.0934 0.0941 654250715.4852 810246508.7861 28464.8293 57 0.0455 -0.0984 0.0943 725775132.0428 805553654.5226 28382.2771 58 0.0455 -0.1052 0.0949 830511822.6548 806867242.319 28405.4087 59 0.0455 -0.101 0.0952 764995775.9481 804773669.0005 28368.5331 60 0.0455 -0.0663 0.0938 329638520.236 782148185.726 27966.9123 61 0.0455 -0.0351 0.0911 92185584.6725 750786249.3145 27400.479 62 0.0455 -0.0204 0.0881 31075612.3582 719494482.4903 26823.3943 63 0.0455 -0.0032 0.0845 768207.6714 689547554.3728 26259.2375 64 0.0455 1e-04 0.0811 1650.6142 661965718.2225 25728.6945 65 0.0455 -0.0237 0.0789 42148927.8098 638126610.8989 25261.168 66 0.0455 -0.007 0.0763 3722655.6727 614630168.1128 24791.7359 67 0.0455 0.0686 0.076 352966744.5359 605285045.8422 24602.5415

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260541841crcngbgmzgxl15q/1nswg1260541743.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260541841crcngbgmzgxl15q/1nswg1260541743.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260541841crcngbgmzgxl15q/2pbzs1260541743.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260541841crcngbgmzgxl15q/2pbzs1260541743.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; 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 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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