Japan Forecast

*Unverified author*

R Software Module: rwasp_arimaforecasting.wasp (opens new window with default values)

Title produced by software: ARIMA Forecasting

Date of computation: Thu, 18 Dec 2008 04:39:04 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/18/t1229600424rfm08hj3j62bc8e.htm/, Retrieved Thu, 18 Dec 2008 12:40:24 +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/2008/Dec/18/t1229600424rfm08hj3j62bc8e.htm/}, year = {2008}, } @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 = {2008}, 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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122.36 123.33 123.04 124.53 125.13 125.85 126.50 126.53 127.07 124.55 124.90 124.32 122.84 123.31 123.31 124.87 124.64 124.73 124.90 124.04 123.28 123.86 122.29 124.09 124.54 125.65 125.70 125.53 125.61 125.55 125.41 127.60 124.68 124.41 126.43 126.38 125.78 124.70 125.07 125.25 126.58 127.13 125.82 123.70 124.39 123.70 124.42 121.05 121.02 123.23 121.32 120.91 120.72 123.31 119.58 119.53 120.59 118.63 118.47 111.81 114.71 117.34 115.77 118.38 117.84 118.83 120.02 116.21 117.08 120.20 119.83 118.92 118.03 117.71 119.55 116.13 115.97 115.99 114.96 116.46 116.55 113.05 117.44 118.84 117.06 117.54 119.31 118.72 121.55 122.61 121.53 123.31 124.07 123.59 122.97 123.22 123.04 122.96 122.81 122.81 122.62 120.82 119.41 121.56 121.59 118.50 118.77 118.86 117.60 119.90 121.83 121.84 122.12 122.12 121.36 119.66 119.32 120.36 117.06 117.48 115.60 113.86 116.92 117.75 117.75 115.31 116.28 115.22 115.65 115.11 118.67 118.04 116.50 119.78 119.95 120.37 119.79 119.43 121.06 121.74 121.09 122.97 120.50 117.18 115.03 113.36 112.59 111.65 111.98 114.87 114.67 114.09 114.77 117.05 117.22 113.18 110.95 112.14 112.72 110.01 110.29 110.74 110.32 105.89 108.97 109.34 106.57 99.49 101.81 104.29 109.73 105.06 107.97 108.13 109.86 108.95 111.20 110.69 106.10 105.68 104.12 104.71 104.30 103.52 107.76 107.80 107.30 108.64 105.03 108.30 107.21 109.27 109.50 111.68 111.80 111.75 106.68 106.37 105.76 109.01 109.01 109.01 109.01 107.69 105.19 105.48 102.22 100.54 105.00 105.44 107.89 108.64 106.70 109.10 105.23 108.41 108.80 110.39 110.22 110.86 108.58 107.70 106.62 109.84 107.16 107.26 108.70 109.85 109.41 112.36 111.03 110.67 109.21 113.58 113.88 114.08 112.33 113.92 114.41 114.57 115.35 113.13 113.29 112.56 113.06 113.46 115.39 116.62 117.04 117.42 115.62 115.16 115.69 112.85 114.05 112.00 113.74 116.26 118.63 116.49 118.23 116.83 118.82 114.36 112.02 113.24 109.75 110.33 112.86 113.04 113.80 110.90 109.96 108.69 108.84 108.47 108.07 107.94 108.11 108.11 106.81 105.58 105.61 106.52 103.86 104.60 104.73 105.12 104.76 103.85 103.83 103.22 101.64 102.13 104.33 104.92 107.78 104.49 102.80 102.86 104.51 104.73 102.58 99.93 101.41 101.05 99.86 101.11 100.89 101.09 98.31 98.08 99.55 99.62 97.37 98.16 97.98 98.15 97.10 97.24 96.70 96.64 100.65 96.75 97.74 97.92 98.34 93.84 97.80 96.20 95.99 95.18 95.95 92.23 91.78 92.97 89.76 92.88 96.23 95.79 93.97 93.90 93.60 93.96 88.69 88.57 85.62 86.25 85.33 83.33 77.78 78.70 72.05 80.75 81.41 82.65 75.85 75.70 78.25 77.41 76.84 74.25 74.95 68.78 73.21 73.26 78.67 75.63 74.99 83.87 79.62 80.13 79.76 78.20 78.05 79.05 73.32 75.17 73.26 73.72 73.57 70.60 71.25 74.22 73.32 73.01 74.21 75.32 71.73 71.94 72.94 72.47 71.94 74.30 74.30

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 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 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[375]) 374 78.2 - - - - - - - 375 78.05 - - - - - - - 376 79.05 78.1806 74.1989 82.1624 0.3344 0.5256 0.5256 0.5256 377 73.32 78.2568 73.3019 83.2118 0.0254 0.3769 0.3769 0.5326 378 75.17 78.3056 72.5861 84.0251 0.1413 0.9562 0.9562 0.5349 379 73.26 78.3281 72.025 84.6313 0.0575 0.837 0.837 0.5345 380 73.72 78.3386 71.5315 85.1457 0.0918 0.9282 0.9282 0.5331 381 73.57 78.3431 71.0813 85.6049 0.0988 0.8939 0.8939 0.5315 382 70.6 78.345 70.661 86.029 0.0241 0.8884 0.8884 0.53 383 71.25 78.3458 70.264 86.4275 0.0426 0.9698 0.9698 0.5286 384 74.22 78.3461 69.8861 86.8061 0.1696 0.9499 0.9499 0.5273 385 73.32 78.3462 69.5245 87.1679 0.1321 0.8204 0.8204 0.5262 386 73.01 78.3463 69.1773 87.5152 0.127 0.8587 0.8587 0.5252 387 74.21 78.3463 68.8428 87.8498 0.1968 0.8645 0.8645 0.5244 388 75.32 78.3463 68.5197 88.1729 0.273 0.7953 0.7953 0.5236 389 71.73 78.3463 68.2068 88.4858 0.1005 0.7207 0.7207 0.5228 390 71.94 78.3463 67.9034 88.7892 0.1146 0.8928 0.8928 0.5222 391 72.94 78.3463 67.6085 89.0841 0.1619 0.8789 0.8789 0.5216 392 72.47 78.3463 67.3215 89.3711 0.1481 0.8318 0.8318 0.521 393 71.94 78.3463 67.0417 89.6509 0.1333 0.8459 0.8459 0.5205 394 74.3 78.3463 66.7688 89.9238 0.2467 0.8609 0.8609 0.52 395 74.3 78.3463 66.5021 90.1905 0.2516 0.7484 0.7484 0.5196 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 376 0.026 0.0111 6e-04 0.7558 0.0378 0.1944 377 0.0323 -0.0631 0.0032 24.3723 1.2186 1.1039 378 0.0373 -0.04 0.002 9.8319 0.4916 0.7011 379 0.0411 -0.0647 0.0032 25.6861 1.2843 1.1333 380 0.0443 -0.059 0.0029 21.3316 1.0666 1.0328 381 0.0473 -0.0609 0.003 22.7825 1.1391 1.0673 382 0.05 -0.0989 0.0049 59.985 2.9992 1.7318 383 0.0526 -0.0906 0.0045 50.35 2.5175 1.5867 384 0.0551 -0.0527 0.0026 17.0246 0.8512 0.9226 385 0.0574 -0.0642 0.0032 25.2628 1.2631 1.1239 386 0.0597 -0.0681 0.0034 28.4757 1.4238 1.1932 387 0.0619 -0.0528 0.0026 17.1088 0.8554 0.9249 388 0.064 -0.0386 0.0019 9.1584 0.4579 0.6767 389 0.066 -0.0844 0.0042 43.7754 2.1888 1.4794 390 0.068 -0.0818 0.0041 41.0406 2.052 1.4325 391 0.0699 -0.069 0.0035 29.228 1.4614 1.2089 392 0.0718 -0.075 0.0038 34.5309 1.7265 1.314 393 0.0736 -0.0818 0.0041 41.0406 2.052 1.4325 394 0.0754 -0.0516 0.0026 16.3725 0.8186 0.9048 395 0.0771 -0.0516 0.0026 16.3725 0.8186 0.9048

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229600424rfm08hj3j62bc8e/1j9i41229600331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229600424rfm08hj3j62bc8e/1j9i41229600331.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229600424rfm08hj3j62bc8e/2zeik1229600331.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Dec/18/t1229600424rfm08hj3j62bc8e/2zeik1229600331.ps (open in new window)

Parameters (Session):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 2 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 20 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 2 ; par7 = 0 ; par8 = 2 ; 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,fx)) (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.se <- array(0, dim=fx) perf.mse <- 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$pred[i] perf.mape[i] = perf.mape[i] + abs(perf.pe[i]) perf.se[i] = (x[nx+i] - forecast$pred[i])^2 perf.mse[i] = perf.mse[i] + perf.se[i] 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 = perf.mape / fx perf.mse = perf.mse / fx perf.rmse = sqrt(perf.mse) 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[1:12] <- 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.mape[i],4)) a<-table.element(a,round(perf.se[i],4)) a<-table.element(a,round(perf.mse[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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