Paper_ARIMAF

*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 15:45:18 +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/t1293550993ql6wjzd50xa4ng3.htm/, Retrieved Tue, 28 Dec 2010 16:43:15 +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/t1293550993ql6wjzd50xa4ng3.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)

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Dataseries X:

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112.52 112.39 112.24 112.10 109.85 111.89 111.88 111.48 110.98 110.42 107.90 109.46 109.11 109.26 109.99 110.17 110.28 109.13 110.15 109.39 108.45 108.23 107.44 104.86 106.23 105.85 104.95 104.46 104.66 103.05 104.16 104.08 104.20 103.68 103.69 101.29 103.03 102.90 102.68 102.98 103.47 101.72 102.82 102.74 102.38 101.81 101.88 99.60 100.93 100.85 100.93 101.10 101.10 99.31 100.33 99.99 99.82 99.65 99.06 96.92 98.20 98.54 98.71 98.20 98.29 96.67 97.69 97.78 97.44 96.92 96.84 95.05 96.33 96.33 96.16 96.50 96.33 94.71 95.82 95.47 95.82 95.99 95.73 93.77 94.71 94.62 94.79 94.88 94.79 93.43 94.37 94.62 94.45 94.37 94.20 92.66 93.51 93.60 93.60 93.77 93.60 92.41 93.60 93.34 92.92 92.07 91.89 90.27 91.72 91.98 91.81 91.98 91.30 89.93 90.87 90.53 90.27 90.10 89.68 87.89

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 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[96]) 84 93.77 - - - - - - - 85 94.71 - - - - - - - 86 94.62 - - - - - - - 87 94.79 - - - - - - - 88 94.88 - - - - - - - 89 94.79 - - - - - - - 90 93.43 - - - - - - - 91 94.37 - - - - - - - 92 94.62 - - - - - - - 93 94.45 - - - - - - - 94 94.37 - - - - - - - 95 94.2 - - - - - - - 96 92.66 - - - - - - - 97 93.51 93.5425 92.5626 94.5477 0.4748 0.9573 0.0114 0.9573 98 93.6 93.5246 92.4234 94.6579 0.4481 0.5101 0.0291 0.9326 99 93.6 93.5783 92.3664 94.8292 0.4865 0.4865 0.0288 0.9249 100 93.77 93.6562 92.3419 95.0164 0.4349 0.5323 0.0389 0.9244 101 93.6 93.5893 92.1848 95.0463 0.4943 0.404 0.0531 0.8944 102 92.41 92.2143 90.7749 93.7098 0.3988 0.0347 0.0556 0.2796 103 93.6 93.1443 91.5897 94.7638 0.2906 0.8129 0.069 0.7211 104 93.34 93.1672 91.5354 94.8707 0.4212 0.3093 0.0473 0.7203 105 92.92 93.1055 91.4035 94.8855 0.4191 0.3981 0.0694 0.6881 106 92.07 93.0152 91.2479 94.8669 0.1585 0.5401 0.0758 0.6465 107 91.89 92.8197 90.9951 94.7348 0.1707 0.7786 0.0789 0.5649 108 90.27 91.2056 89.3941 93.1079 0.1675 0.2404 0.067 0.067 109 91.72 92.1265 90.0471 94.325 0.3585 0.951 0.1087 0.3172 110 91.98 92.1092 89.9118 94.4402 0.4567 0.6283 0.105 0.3216 111 91.81 92.161 89.8481 94.6222 0.3899 0.5573 0.1259 0.3455 112 91.98 92.2361 89.8118 94.8237 0.4231 0.6266 0.1227 0.3741 113 91.3 92.1716 89.6493 94.8712 0.2634 0.5553 0.1499 0.3614 114 89.93 90.8456 88.3136 93.5592 0.2542 0.3714 0.1292 0.095 115 90.87 91.7425 89.0586 94.6292 0.2768 0.8908 0.1036 0.2667 116 90.53 91.7647 88.9898 94.7566 0.2093 0.7211 0.151 0.2788 117 90.27 91.7051 88.8484 94.7926 0.1811 0.7722 0.2203 0.2722 118 90.1 91.6181 88.6846 94.7957 0.1745 0.7972 0.3902 0.2602 119 89.68 91.4296 88.43 94.6855 0.1461 0.7883 0.3908 0.2294 120 87.89 89.8722 86.9163 93.0814 0.113 0.5467 0.404 0.0443 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 97 0.0055 -3e-04 0 0.0011 0 0 98 0.0062 8e-04 6e-04 0.0057 0.0034 0.058 99 0.0068 2e-04 5e-04 5e-04 0.0024 0.049 100 0.0074 0.0012 6e-04 0.0129 0.005 0.071 101 0.0079 1e-04 5e-04 1e-04 0.0041 0.0637 102 0.0083 0.0021 8e-04 0.0383 0.0098 0.0988 103 0.0089 0.0049 0.0014 0.2077 0.038 0.195 104 0.0093 0.0019 0.0014 0.0298 0.037 0.1924 105 0.0098 -0.002 0.0015 0.0344 0.0367 0.1916 106 0.0102 -0.0102 0.0024 0.8934 0.1224 0.3498 107 0.0105 -0.01 0.0031 0.8644 0.1898 0.4357 108 0.0106 -0.0103 0.0037 0.8754 0.247 0.497 109 0.0122 -0.0044 0.0037 0.1652 0.2407 0.4906 110 0.0129 -0.0014 0.0036 0.0167 0.2247 0.474 111 0.0136 -0.0038 0.0036 0.1232 0.2179 0.4668 112 0.0143 -0.0028 0.0035 0.0656 0.2084 0.4565 113 0.0149 -0.0095 0.0039 0.7597 0.2408 0.4907 114 0.0152 -0.0101 0.0042 0.8383 0.274 0.5235 115 0.0161 -0.0095 0.0045 0.7613 0.2997 0.5474 116 0.0166 -0.0135 0.0049 1.5244 0.3609 0.6008 117 0.0172 -0.0156 0.0055 2.0595 0.4418 0.6647 118 0.0177 -0.0166 0.006 2.3045 0.5265 0.7256 119 0.0182 -0.0191 0.0065 3.061 0.6367 0.7979 120 0.0182 -0.0221 0.0072 3.929 0.7738 0.8797

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550993ql6wjzd50xa4ng3/11z791293551113.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550993ql6wjzd50xa4ng3/11z791293551113.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550993ql6wjzd50xa4ng3/2q1431293551113.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/28/t1293550993ql6wjzd50xa4ng3/2q1431293551113.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = -1.4 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = -1.4 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 1 ; 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')

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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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