*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: Fri, 11 Dec 2009 08:47:09 -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/11/t1260546462kas8s9pf80y57vj.htm/, Retrieved Fri, 11 Dec 2009 16:47:44 +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/11/t1260546462kas8s9pf80y57vj.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:

» Textbox « » Textfile « » CSV «

255 280.2 299.9 339.2 374.2 393.5 389.2 381.7 375.2 369 357.4 352.1 346.5 342.9 340.3 328.3 322.9 314.3 308.9 294 285.6 281.2 280.3 278.8 274.5 270.4 263.4 259.9 258 262.7 284.7 311.3 322.1 327 331.3 333.3 321.4 327 320 314.7 316.7 314.4 321.3 318.2 307.2 301.3 287.5 277.7 274.4 258.8 253.3 251 248.4 249.5 246.1 244.5 243.6 244 240.8 249.8 248 259.4 260.5 260.8 261.3 259.5 256.6 257.9 256.5 254.2 253.3 253.8 255.5 257.1 257.3 253.2 252.8 252 250.7 252.2 250 251 253.4 251.2 255.6 261.1 258.9 259.9 261.2 264.7 267.1 266.4 267.7 268.6 267.5 268.5 268.5 270.5 270.9 270.1 269.3 269.8 270.1 264.9 263.7 264.8 263.7 255.9 276.2 360.1 380.5 373.7 369.8 366.6 359.3 345.8 326.2 324.5 328.1 327.5 324.4 316.5 310.9 301.5 291.7 290.4 287.4 277.7 281.6 288 276 272.9 283 283.3 276.8 284.5 282.7 281.2 287.4 283.1 284 285.5 289.2 292.5 296.4 305.2 303.9 311.5 316.3 316.7 322.5 3 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 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[332]) 320 292.1 - - - - - - - 321 291.9 - - - - - - - 322 282.5 - - - - - - - 323 277.9 - - - - - - - 324 287.5 - - - - - - - 325 289.2 - - - - - - - 326 285.6 - - - - - - - 327 293.2 - - - - - - - 328 290.8 - - - - - - - 329 283.1 - - - - - - - 330 275 - - - - - - - 331 287.8 - - - - - - - 332 287.8 - - - - - - - 333 287.4 284.5819 264.3269 304.8369 0.3925 0.3777 0.2394 0.3777 334 284 286.1327 249.0674 323.198 0.4551 0.4733 0.5762 0.4649 335 277.8 287.0441 237.15 336.9382 0.3583 0.5476 0.6403 0.4882 336 277.6 287.4762 225.7542 349.1982 0.3769 0.6207 0.4997 0.4959 337 304.9 287.3275 215.0808 359.5742 0.3168 0.6041 0.4797 0.4949 338 294 286.824 205.6187 368.0292 0.4312 0.3313 0.5118 0.4906 339 300.9 286.2795 197.627 374.932 0.3733 0.4322 0.4392 0.4866 340 324 285.9419 191.0093 380.8746 0.216 0.3787 0.4601 0.4847 341 332.9 285.9022 185.4072 386.3973 0.1797 0.2287 0.5218 0.4852 342 341.6 286.0974 180.3627 391.832 0.1518 0.1928 0.5815 0.4874 343 333.4 286.3793 175.4757 397.2829 0.203 0.1646 0.49 0.49 344 348.2 286.602 170.5149 402.6891 0.1492 0.2147 0.4919 0.4919 345 344.7 286.6847 165.4487 407.9207 0.1741 0.16 0.4954 0.4928 346 344.7 286.6291 160.3888 412.8695 0.1836 0.1836 0.5163 0.4927 347 329.3 286.4967 155.4893 417.5041 0.261 0.1919 0.5518 0.4922 348 323.5 286.3657 150.8604 421.871 0.2956 0.2673 0.5504 0.4917 349 323.2 286.2927 146.5294 426.0559 0.3024 0.3009 0.3971 0.4916 350 317.4 286.2938 142.4488 430.1387 0.3358 0.3075 0.4582 0.4918 351 330.1 286.3485 138.5327 434.1643 0.2809 0.3403 0.4235 0.4923 352 329.2 286.4187 134.6988 438.1386 0.2902 0.2863 0.3137 0.4929 353 334.9 286.4696 130.8976 442.0415 0.2709 0.2952 0.2793 0.4933 354 315.8 286.4843 127.1211 445.8475 0.3592 0.2758 0.2489 0.4935 355 315.4 286.4662 123.3912 449.5412 0.364 0.3622 0.2863 0.4936 356 319.6 286.432 119.7393 453.1246 0.3483 0.3667 0.2338 0.4936 357 317.3 286.4008 116.188 456.6137 0.361 0.3511 0.251 0.4936 358 313.8 286.3855 112.7421 460.0289 0.3785 0.3636 0.2552 0.4936 359 315.8 286.3884 109.3894 463.3874 0.3723 0.3807 0.3173 0.4938 360 311.3 286.4033 106.1094 466.6972 0.3933 0.3746 0.3434 0.4939 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 333 0.0363 0.0099 0 7.9418 0 0 334 0.0661 -0.0075 0.0087 4.5484 6.2451 2.499 335 0.0887 -0.0322 0.0165 85.4539 32.648 5.7138 336 0.1095 -0.0344 0.021 97.5392 48.8708 6.9908 337 0.1283 0.0612 0.029 308.7924 100.8551 10.0427 338 0.1444 0.025 0.0283 51.4956 92.6286 9.6244 339 0.158 0.0511 0.0316 213.7586 109.9329 10.4849 340 0.1694 0.1331 0.0443 1448.4165 277.2433 16.6506 341 0.1793 0.1644 0.0576 2208.792 491.8598 22.1779 342 0.1886 0.194 0.0713 3080.5431 750.7282 27.3994 343 0.1976 0.1642 0.0797 2210.9503 883.4756 29.7233 344 0.2067 0.2149 0.091 3794.3151 1126.0456 33.5566 345 0.2158 0.2024 0.0995 3365.778 1298.3327 36.0324 346 0.2247 0.2026 0.1069 3372.2285 1446.4681 38.0325 347 0.2333 0.1494 0.1097 1832.1228 1472.1784 38.369 348 0.2414 0.1297 0.111 1378.9558 1466.352 38.293 349 0.2491 0.1289 0.112 1362.1492 1460.2224 38.2129 350 0.2563 0.1087 0.1119 967.597 1432.8543 37.8531 351 0.2634 0.1528 0.114 1914.192 1458.1879 38.1862 352 0.2703 0.1494 0.1158 1830.2426 1476.7906 38.429 353 0.2771 0.1691 0.1183 2345.5064 1518.1581 38.9635 354 0.2838 0.1023 0.1176 859.4106 1488.215 38.5774 355 0.2904 0.101 0.1169 837.1658 1459.9085 38.2087 356 0.2969 0.1158 0.1168 1100.1191 1444.9173 38.0121 357 0.3032 0.1079 0.1165 954.7582 1425.3109 37.7533 358 0.3094 0.0957 0.1157 751.5539 1399.3972 37.4085 359 0.3153 0.1027 0.1152 865.0426 1379.6063 37.1431 360 0.3212 0.0869 0.1142 619.8448 1352.4719 36.776

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546462kas8s9pf80y57vj/1mjh91260546424.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546462kas8s9pf80y57vj/1mjh91260546424.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546462kas8s9pf80y57vj/2nc7e1260546424.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t1260546462kas8s9pf80y57vj/2nc7e1260546424.ps (open in new window)

Parameters (Session):

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

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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