*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, 15 Dec 2010 17:12:20 +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/15/t1292433123ub3pg7u46vucmbb.htm/, Retrieved Wed, 15 Dec 2010 18:12:03 +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/15/t1292433123ub3pg7u46vucmbb.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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186448 190530 194207 190855 200779 204428 207617 212071 214239 215883 223484 221529 225247 226699 231406 232324 237192 236727 240698 240688 245283 243556 247826 245798 250479 249216 251896 247616 249994 246552 248771 247551 249745 245742 249019 245841 248771 244723 246878 246014 248496 244351 248016 246509 249426 247840 251035 250161 254278 250801 253985 249174 251287 247947 249992 243805 255812 250417 253033 248705 253950 251484 251093 245996 252721 248019 250464 245571 252690 250183 253639 254436 265280 268705 270643 271480

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 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[52]) 48 250161 - - - - - - - 49 254278 - - - - - - - 50 250801 - - - - - - - 51 253985 - - - - - - - 52 249174 - - - - - - - 53 251287 252634.8357 249360.1389 255867.6251 0.2069 0.9821 0.1596 0.9821 54 247947 249421.8019 244963.5679 253801.7355 0.2546 0.202 0.2686 0.5441 55 249992 250966.4372 245528.8164 256288.7151 0.3599 0.8669 0.1331 0.7454 56 243805 248116.5141 240874.3706 255153.183 0.1149 0.3007 0.3842 0.3842 57 255812 251436.847 242096.9546 260442.0102 0.1705 0.9517 0.513 0.6888 58 250417 247545.4226 236228.5404 258367.0822 0.3015 0.0672 0.471 0.384 59 253033 250077.8659 236934.0854 262564.5011 0.3214 0.4788 0.5054 0.5564 60 248705 247011.1694 231691.1473 261434.9783 0.409 0.2066 0.6685 0.3844 61 253950 250110.9924 232405.9489 266643.0047 0.3245 0.5662 0.2496 0.5442 62 251484 246666.2243 226276.563 265494.5752 0.308 0.2242 0.3481 0.397 63 251093 249054.3317 226574.8947 269666.3444 0.4231 0.4086 0.3526 0.4955 64 245996 245902.8201 220627.3818 268812.1133 0.4968 0.3285 0.4053 0.3898 65 252721 249228.4076 221303.8945 274324.9617 0.3925 0.5997 0.3562 0.5017 66 248019 245674.229 214469.6893 273339.3604 0.434 0.3088 0.3403 0.4021 67 250464 248058.892 214419.5659 277652.0801 0.4367 0.5011 0.4204 0.4706 68 245571 244990.0885 207892.421 277166.0661 0.4859 0.3694 0.4756 0.3994 69 252690 248273.4375 208304.1896 282646.0049 0.4006 0.5612 0.3999 0.4795 70 250183 244709.4753 200708.6829 281924.5984 0.3866 0.3371 0.4308 0.4071 71 253639 247143.821 200378.8419 286371.1862 0.3728 0.4397 0.4341 0.4596 72 254436 244034.0366 193029.4859 286085.3712 0.3139 0.3272 0.4714 0.4053 73 265280 247336.7992 193201.9891 291588.7103 0.2134 0.3766 0.4063 0.4676 74 268705 243775.7975 184692.6769 291104.61 0.1509 0.1866 0.3954 0.4116 75 270643 246204.576 183997.6851 295598.1028 0.1661 0.186 0.384 0.4531 76 271480 243088.231 175642.3355 295522.4967 0.1443 0.1515 0.3357 0.41 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 53 0.0065 -0.0053 0 1816661.1699 0 0 54 0.009 -0.0059 0.0056 2175040.6431 1995850.9065 1412.7459 55 0.0108 -0.0039 0.005 949527.7982 1647076.5371 1283.3848 56 0.0145 -0.0174 0.0081 18589154.2553 5882595.9666 2425.4064 57 0.0183 0.0174 0.01 19141963.5411 8534469.4815 2921.3814 58 0.0223 0.0116 0.0103 8245956.8902 8486384.0496 2913.1399 59 0.0255 0.0118 0.0105 8732817.4449 8521588.8204 2919.1761 60 0.0298 0.0069 0.01 2869062.0243 7815022.9709 2795.5363 61 0.0337 0.0153 0.0106 14737979.0553 8584240.3136 2929.8874 62 0.0389 0.0195 0.0115 23210962.4732 10046912.5296 3169.6865 63 0.0422 0.0082 0.0112 4156168.6175 9511390.3557 3084.0542 64 0.0475 4e-04 0.0103 8682.4948 8719498.034 2952.8796 65 0.0514 0.014 0.0106 12198201.5475 8987090.612 2997.8477 66 0.0575 0.0095 0.0105 5497951.0602 8737866.3583 2955.9882 67 0.0609 0.0097 0.0105 5784544.3355 8540978.2234 2922.4952 68 0.067 0.0024 0.01 337458.1907 8028258.2214 2833.4181 69 0.0706 0.0178 0.0104 19506024.5311 8703420.9455 2950.1561 70 0.0776 0.0224 0.0111 29959472.8137 9884312.7159 3143.9327 71 0.081 0.0263 0.0119 42187349.8645 11584472.5658 3403.597 72 0.0879 0.0426 0.0134 108200841.9479 16415291.0349 4051.5788 73 0.0913 0.0725 0.0162 321958453.3534 30964965.4311 5564.6173 74 0.0991 0.1023 0.0201 621465137.397 57805882.3386 7603.018 75 0.1024 0.0993 0.0236 597236566.3143 81259390.3376 9014.3991 76 0.1101 0.1168 0.0275 806092547.4216 111460771.8827 10557.4984

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433123ub3pg7u46vucmbb/1kurn1292433136.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433123ub3pg7u46vucmbb/1kurn1292433136.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433123ub3pg7u46vucmbb/2rvog1292433136.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292433123ub3pg7u46vucmbb/2rvog1292433136.ps (open in new window)

Parameters (Session):

par1 = 24 ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 2.0 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; par6 = 3 ; par7 = 0 ; 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')

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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