WS 10

*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: Sat, 12 Dec 2009 04:57:08 -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/12/t12606190831u66vr8rt2drnt2.htm/, Retrieved Sat, 12 Dec 2009 12:58:06 +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/12/t12606190831u66vr8rt2drnt2.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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153,4 145 137,7 148,3 152,2 169,4 168,6 161,1 174,1 179 190,6 190 181,6 174,8 180,5 196,8 193,8 197 216,3 221,4 217,9 229,7 227,4 204,2 196,6 198,8 207,5 190,7 201,6 210,5 223,5 223,8 231,2 244 234,7 250,2 265,7 287,6 283,3 295,4 312,3 333,8 347,7 383,2 407,1 413,6 362,7 321,9 239,4 191 159,7 163,4 157,6 166,2 176,7 198,3 226,2 216,2 235,9 226,9

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 '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[36]) 24 204.2 - - - - - - - 25 196.6 - - - - - - - 26 198.8 - - - - - - - 27 207.5 - - - - - - - 28 190.7 - - - - - - - 29 201.6 - - - - - - - 30 210.5 - - - - - - - 31 223.5 - - - - - - - 32 223.8 - - - - - - - 33 231.2 - - - - - - - 34 244 - - - - - - - 35 234.7 - - - - - - - 36 250.2 - - - - - - - 37 265.7 265.7 237.771 293.629 0.5 0.8616 1 0.8616 38 287.6 281.2 218.7488 343.6512 0.4204 0.6867 0.9951 0.8347 39 283.3 296.7 192.1991 401.2009 0.4008 0.5678 0.9528 0.8084 40 295.4 312.2 159.2264 465.1736 0.4148 0.6444 0.9402 0.7865 41 312.3 327.7 120.5727 534.8273 0.4421 0.6201 0.8836 0.7683 42 333.8 343.2 76.7739 609.6261 0.4724 0.5899 0.8355 0.7531 43 347.7 358.7 28.2392 689.1608 0.474 0.5587 0.7887 0.7401 44 383.2 374.2 -24.7065 773.1065 0.4824 0.5518 0.77 0.7288 45 407.1 389.7 -81.7964 861.1964 0.4712 0.5108 0.745 0.719 46 413.6 405.2 -142.8073 953.2073 0.488 0.4973 0.7179 0.7103 47 362.7 420.7 -207.5482 1048.9482 0.4282 0.5088 0.7191 0.7026 48 321.9 436.2 -275.8536 1148.2536 0.3765 0.5802 0.6957 0.6957 49 239.4 451.7 -347.5782 1250.9782 0.3013 0.6249 0.6758 0.6894 50 191 467.2 -422.5931 1356.9931 0.2715 0.6921 0.6538 0.6837 51 159.7 482.7 -500.783 1466.183 0.2599 0.7195 0.6545 0.6784 52 163.4 498.2 -582.0438 1578.4438 0.2718 0.7305 0.6435 0.6736 53 157.6 513.7 -666.2812 1693.6812 0.2771 0.7197 0.631 0.6692 54 166.2 529.2 -753.409 1811.809 0.2895 0.7149 0.6174 0.6651 55 176.7 544.7 -843.348 1932.748 0.3017 0.7035 0.6096 0.6612 56 198.3 560.2 -936.0251 2056.4251 0.3177 0.6923 0.5917 0.6577 57 226.2 575.7 -1031.3729 2182.7729 0.335 0.6773 0.5815 0.6543 58 216.2 591.2 -1129.3286 2311.7286 0.3346 0.6612 0.5802 0.6512 59 235.9 606.7 -1229.8334 2443.2334 0.3462 0.6616 0.6027 0.6482 60 226.9 622.2 -1332.8327 2577.2327 0.3459 0.6507 0.6183 0.6454 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 37 0.0536 0 0 0 0 0 38 0.1133 0.0228 0.0114 40.96 20.48 4.5255 39 0.1797 -0.0452 0.0226 179.56 73.5067 8.5736 40 0.25 -0.0538 0.0304 282.24 125.69 11.2112 41 0.3225 -0.047 0.0337 237.16 147.984 12.1649 42 0.3961 -0.0274 0.0327 88.36 138.0467 11.7493 43 0.47 -0.0307 0.0324 121 135.6114 11.6452 44 0.5439 0.0241 0.0314 81 128.785 11.3483 45 0.6173 0.0446 0.0328 302.76 148.1156 12.1703 46 0.69 0.0207 0.0316 70.56 140.36 11.8474 47 0.7619 -0.1379 0.0413 3364 433.4182 20.8187 48 0.8329 -0.262 0.0597 13064.49 1486.0075 38.5488 49 0.9028 -0.47 0.0912 45071.29 4838.7215 69.5609 50 0.9717 -0.5912 0.127 76286.44 9942.13 99.7102 51 1.0395 -0.6692 0.1631 104329 16234.588 127.415 52 1.1063 -0.672 0.1949 112091.04 22225.6162 149.0826 53 1.172 -0.6932 0.2242 126807.21 28377.4747 168.4562 54 1.2366 -0.6859 0.2499 131769 34121.4483 184.7199 55 1.3001 -0.6756 0.2723 135424 39453.1616 198.6282 56 1.3627 -0.646 0.291 130971.61 44029.084 209.8311 57 1.4242 -0.6071 0.306 122150.25 47749.1395 218.5158 58 1.4848 -0.6343 0.3209 140625 51970.7695 227.971 59 1.5444 -0.6112 0.3336 137492.64 55689.1117 235.9854 60 1.6031 -0.6353 0.3461 156262.09 59879.6525 244.7032

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t12606190831u66vr8rt2drnt2/1qccg1260619026.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606190831u66vr8rt2drnt2/1qccg1260619026.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606190831u66vr8rt2drnt2/258xg1260619026.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t12606190831u66vr8rt2drnt2/258xg1260619026.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 2 ; 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 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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