WS10 verbetering

*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 05:17:45 -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/t1260620347wx1iyl761f4gccw.htm/, Retrieved Sat, 12 Dec 2009 13:19:09 +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/t1260620347wx1iyl761f4gccw.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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128.6 128.9 129.06 129.23 129.27 129.33 129.35 129.31 129.4 129.49 129.47 129.46 129.45 129.28 129.2 129.25 129.14 129.11 129.02 129.08 128.99 129.11 129.08 129.19 129.23 129.25 129.31 129.33 129.39 129.55 129.43 129.45 129.57 129.76 129.92 130.08 130.41 130.84 131.24 131.49 131.74 132.34 133.5 134.43 136.5 137.41 138.02 138.15 138.24 138.2 138.31 138.65 139.3 139.8 140.52 141.57 141.77 141.66 141.36 141.17

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[32]) 20 129.08 - - - - - - - 21 128.99 - - - - - - - 22 129.11 - - - - - - - 23 129.08 - - - - - - - 24 129.19 - - - - - - - 25 129.23 - - - - - - - 26 129.25 - - - - - - - 27 129.31 - - - - - - - 28 129.33 - - - - - - - 29 129.39 - - - - - - - 30 129.55 - - - - - - - 31 129.43 - - - - - - - 32 129.45 - - - - - - - 33 129.57 129.3699 129.2378 129.5019 0.0015 0.117 1 0.117 34 129.76 129.276 129.0803 129.4716 0 0.0016 0.9518 0.0406 35 129.92 129.2351 128.941 129.5292 0 2e-04 0.8493 0.076 36 130.08 129.2435 128.8534 129.6335 0 3e-04 0.6059 0.1497 37 130.41 129.186 128.7146 129.6573 0 1e-04 0.4273 0.1361 38 130.84 129.2995 128.775 129.8239 0 0 0.5733 0.2869 39 131.24 129.2306 128.6631 129.798 0 0 0.3919 0.2242 40 131.49 129.2477 128.6447 129.8508 0 0 0.3946 0.2555 41 131.74 129.1903 128.5476 129.833 0 0 0.2712 0.2142 42 132.34 129.1602 128.4796 129.8407 0 0 0.1308 0.2019 43 133.5 129.2141 128.4939 129.9343 0 0 0.2784 0.2604 44 134.43 129.2385 128.4843 129.9927 0 0 0.2913 0.2913 45 136.5 129.2644 128.496 130.0328 0 0 0.2178 0.3179 46 137.41 129.3332 128.5542 130.1123 0 0 0.1415 0.3845 47 138.02 129.312 128.5275 130.0964 0 0 0.0644 0.3651 48 138.15 129.3227 128.5358 130.1096 0 0 0.0296 0.3756 49 138.24 129.2878 128.498 130.0775 0 0 0.0027 0.3436 50 138.2 129.2674 128.4736 130.0611 0 0 1e-04 0.326 51 138.31 129.2318 128.4323 130.0313 0 0 0 0.2964 52 138.65 129.27 128.4649 130.075 0 0 0 0.3306 53 139.3 129.227 128.4167 130.0372 0 0 0 0.2948 54 139.8 129.2432 128.4288 130.0577 0 0 0 0.3094 55 140.52 129.1977 128.3789 130.0164 0 0 0 0.2729 56 141.57 129.2317 128.4088 130.0546 0 0 0 0.3015 57 141.77 129.1888 128.361 130.0167 0 0 0 0.2682 58 141.66 129.2369 128.4044 130.0695 0 0 0 0.308 59 141.36 129.2087 128.3711 130.0463 0 0 0 0.2862 60 141.17 129.2552 128.413 130.0975 0 0 0 0.3252 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 5e-04 0.0015 0 0.0401 0 0 34 8e-04 0.0037 0.0026 0.2343 0.1372 0.3704 35 0.0012 0.0053 0.0035 0.4691 0.2478 0.4978 36 0.0015 0.0065 0.0043 0.6998 0.3608 0.6007 37 0.0019 0.0095 0.0053 1.4983 0.5883 0.767 38 0.0021 0.0119 0.0064 2.3732 0.8858 0.9412 39 0.0022 0.0155 0.0077 4.0379 1.3361 1.1559 40 0.0024 0.0173 0.0089 5.0277 1.7975 1.3407 41 0.0025 0.0197 0.0101 6.501 2.3202 1.5232 42 0.0027 0.0246 0.0116 10.1113 3.0993 1.7605 43 0.0028 0.0332 0.0135 18.3688 4.4874 2.1183 44 0.003 0.0402 0.0158 26.9517 6.3594 2.5218 45 0.003 0.056 0.0188 52.354 9.8975 3.146 46 0.0031 0.0624 0.022 65.234 13.8501 3.7216 47 0.0031 0.0673 0.025 75.8298 17.9821 4.2405 48 0.0031 0.0683 0.0277 77.9213 21.7283 4.6614 49 0.0031 0.0692 0.0301 80.1428 25.1644 5.0164 50 0.0031 0.0691 0.0323 79.7921 28.1993 5.3103 51 0.0032 0.0702 0.0343 82.4136 31.0527 5.5725 52 0.0032 0.0726 0.0362 87.9845 33.8993 5.8223 53 0.0032 0.0779 0.0382 101.4656 37.1167 6.0923 54 0.0032 0.0817 0.0402 111.4455 40.4953 6.3636 55 0.0032 0.0876 0.0422 128.1953 44.3083 6.6565 56 0.0032 0.0955 0.0445 152.2343 48.8052 6.9861 57 0.0033 0.0974 0.0466 158.2855 53.1845 7.2928 58 0.0033 0.0961 0.0485 154.3323 57.0748 7.5548 59 0.0033 0.094 0.0502 147.6536 60.4295 7.7736 60 0.0033 0.0922 0.0517 141.9619 63.3414 7.9587

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/12/t1260620347wx1iyl761f4gccw/1mdn71260620261.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260620347wx1iyl761f4gccw/1mdn71260620261.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260620347wx1iyl761f4gccw/2uwyj1260620261.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/12/t1260620347wx1iyl761f4gccw/2uwyj1260620261.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; 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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