ws 11 f

*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: Wed, 09 Dec 2009 14:45:45 -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/09/t1260395194l3h1c6pdvijw04n.htm/, Retrieved Wed, 09 Dec 2009 22:46:37 +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/09/t1260395194l3h1c6pdvijw04n.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?

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Dataseries X:

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87,28 87,28 87,09 86,92 87,59 90,72 90,69 90,3 89,55 88,94 88,41 87,82 87,07 86,82 86,4 86,02 85,66 85,32 85 84,67 83,94 82,83 81,95 81,19 80,48 78,86 69,47 68,77 70,06 73,95 75,8 77,79 81,57 83,07 84,34 85,1 85,25 84,26 83,63 86,44 85,3 84,1 83,36 82,48 81,58 80,47 79,34 82,13 81,69 80,7 79,88 79,16 78,38 77,42 76,47 75,46 74,48 78,27 80,7 79,91 78,75 77,78 81,14 81,08 80,03 78,91 78,01 76,9 75,97 81,93 80,27 78,67 77,42 76,16 74,7 76,39 76,04 74,65 73,29 71,79 74,39 74,91 74,54 73,08 72,75 71,32 70,38 70,35 70,01 69,36 67,77 69,26 69,8 68,38 67,62 68,39 66,95 65,21 66,64 63,45 60,66 62,34 60,32 58,64 60,46 58,59 61,87 61,85 67,44 77,06 91,74 93,15 94,15 93,11 91,51 89,96 88,16 86,98 88,03 86,24 84,65 83,23 81,7 80,25 78,8 77,51 76,2 75,04 74 75,49 77,14 76,15 76,27 78,19 76,49 77,31 76,65 74,99 73,51 72,07 70,59 71,96 76,29 74,86 74,93 71,9 71,01 77,47 75,78 76 etc...

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[330]) 318 46.53 - - - - - - - 319 50.51 - - - - - - - 320 47.58 - - - - - - - 321 48.05 - - - - - - - 322 46.84 - - - - - - - 323 47.67 - - - - - - - 324 49.16 - - - - - - - 325 55.54 - - - - - - - 326 55.82 - - - - - - - 327 58.22 - - - - - - - 328 56.19 - - - - - - - 329 57.77 - - - - - - - 330 63.19 - - - - - - - 331 54.76 63.8276 54.1244 73.5308 0.0335 0.5512 0.9964 0.5512 332 55.74 65.273 50.5816 79.9644 0.1017 0.9196 0.9909 0.6095 333 62.54 65.195 46.3708 84.0192 0.3911 0.8376 0.9629 0.5827 334 61.39 64.2163 41.4832 86.9494 0.4037 0.5575 0.933 0.5353 335 69.6 63.427 37.9517 88.9023 0.3174 0.5623 0.8873 0.5073 336 79.23 63.9526 36.2957 91.6095 0.1395 0.3445 0.8528 0.5215 337 80 64.839 35.1773 94.5008 0.1582 0.1708 0.7305 0.5434 338 93.68 65.0392 33.1108 96.9676 0.0394 0.1792 0.7143 0.5452 339 107.63 64.3268 30.152 98.5015 0.0065 0.0461 0.6369 0.526 340 100.18 63.7552 27.621 99.8893 0.0241 0.0087 0.6592 0.5122 341 97.3 63.9732 26.2205 101.7259 0.0418 0.0301 0.6263 0.5162 342 90.45 64.6347 25.3223 103.9471 0.099 0.0517 0.5287 0.5287 343 80.64 64.8428 23.8635 105.822 0.225 0.1103 0.6852 0.5315 344 80.58 64.4163 21.7145 107.118 0.2291 0.2282 0.6548 0.5224 345 75.82 63.9551 19.6797 108.2305 0.2997 0.2309 0.525 0.5135 346 85.59 64.0418 18.3791 109.7044 0.1775 0.3066 0.5453 0.5146 347 89.35 64.4901 17.505 111.4752 0.1499 0.1894 0.4156 0.5216 348 89.42 64.7028 16.3337 113.0719 0.1583 0.159 0.278 0.5244 349 104.73 64.4452 14.6522 114.2382 0.0564 0.1628 0.2702 0.5197 350 95.32 64.1006 12.9552 115.2459 0.1158 0.0597 0.1285 0.5139 351 89.27 64.1043 11.7262 116.4823 0.1732 0.1214 0.0517 0.5136 352 90.44 64.4067 10.849 117.9644 0.1704 0.1814 0.0952 0.5178 353 86.97 64.5935 9.8286 119.3585 0.2116 0.1775 0.1209 0.52 354 79.98 64.4502 8.4488 120.4516 0.2934 0.2153 0.1814 0.5176 355 81.22 64.1971 6.9974 121.3969 0.2798 0.2943 0.2866 0.5138 356 87.35 64.1619 5.8408 122.483 0.2179 0.2832 0.2906 0.513 357 83.64 64.3587 4.9603 123.7571 0.2623 0.224 0.3526 0.5154 358 82.22 64.5138 4.0283 124.9993 0.2831 0.2677 0.2473 0.5171 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 331 0.0776 -0.1421 0 82.221 0 0 332 0.1148 -0.146 0.1441 90.8779 86.5494 9.3032 333 0.1473 -0.0407 0.1096 7.049 60.0493 7.7491 334 0.1806 -0.044 0.0932 7.9878 47.0339 6.8581 335 0.2049 0.0973 0.094 38.1056 45.2483 6.7267 336 0.2206 0.2389 0.1182 233.3994 76.6068 8.7525 337 0.2334 0.2338 0.1347 229.8544 98.4993 9.9247 338 0.2505 0.4404 0.1729 820.2947 188.7237 13.7377 339 0.2711 0.6732 0.2285 1875.1691 376.1065 19.3935 340 0.2892 0.5713 0.2628 1326.7683 471.1727 21.7065 341 0.3011 0.5209 0.2862 1110.6756 529.3093 23.0067 342 0.3103 0.3994 0.2957 666.43 540.7361 23.2537 343 0.3224 0.2436 0.2917 249.5519 518.3373 22.767 344 0.3382 0.2509 0.2888 261.2662 499.9751 22.3601 345 0.3532 0.1855 0.2819 140.7763 476.0285 21.8181 346 0.3638 0.3365 0.2853 464.3265 475.2971 21.8013 347 0.3717 0.3855 0.2912 618.0141 483.6922 21.993 348 0.3814 0.382 0.2962 610.9404 490.7616 22.1531 349 0.3942 0.6251 0.3135 1622.8659 550.346 23.4595 350 0.4071 0.487 0.3222 974.6533 571.5614 23.9073 351 0.4169 0.3926 0.3256 633.3132 574.5019 23.9688 352 0.4243 0.4042 0.3291 677.7327 579.1942 24.0665 353 0.4326 0.3464 0.3299 500.7056 575.7817 23.9955 354 0.4433 0.241 0.3262 241.1746 561.8397 23.7032 355 0.4546 0.2652 0.3237 289.7777 550.9572 23.4725 356 0.4638 0.3614 0.3252 537.6879 550.4469 23.4616 357 0.4709 0.2996 0.3242 371.7687 543.8292 23.3201 358 0.4783 0.2745 0.3225 313.5099 535.6035 23.1431

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260395194l3h1c6pdvijw04n/1lmfk1260395143.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260395194l3h1c6pdvijw04n/1lmfk1260395143.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260395194l3h1c6pdvijw04n/29zel1260395143.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/09/t1260395194l3h1c6pdvijw04n/29zel1260395143.ps (open in new window)

Parameters (Session):

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

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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