ws10

*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 07:45:40 -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/t126054281012js10y2bgqvnt5.htm/, Retrieved Fri, 11 Dec 2009 15:46:53 +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/t126054281012js10y2bgqvnt5.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:

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5594 5585 5710 5511 5403 5826 5884 5965 5960 6064 6046 5954 5952 5960 5983 5996 6021 6094 6202 6276 6306 6342 6345 6328 6191 6261 6253 6198 6247 6293 6381 6448 6470 6516 6532 6526 6533 6498 6507 6464 6453 6468 6497 6808 6793 6907 6792 6757 6734 6654 6589 6469 6521 6448 6410 6528 6445 6458 6215 6167

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[32]) 20 6276 - - - - - - - 21 6306 - - - - - - - 22 6342 - - - - - - - 23 6345 - - - - - - - 24 6328 - - - - - - - 25 6191 - - - - - - - 26 6261 - - - - - - - 27 6253 - - - - - - - 28 6198 - - - - - - - 29 6247 - - - - - - - 30 6293 - - - - - - - 31 6381 - - - - - - - 32 6448 - - - - - - - 33 6470 6452.4266 6273.0359 6631.8173 0.4239 0.5193 0.9452 0.5193 34 6516 6502.0465 6251.4346 6752.6585 0.4566 0.599 0.8947 0.6637 35 6532 6553.6893 6245.3799 6861.9988 0.4452 0.5947 0.9077 0.7492 36 6526 6540.9414 6130.379 6951.5038 0.4716 0.517 0.8453 0.6714 37 6533 6509.9021 5998.1573 7021.6468 0.4648 0.4754 0.889 0.5937 38 6498 6517.9786 5946.0293 7089.9278 0.4727 0.4795 0.8107 0.5948 39 6507 6540.8132 5924.1055 7157.521 0.4572 0.5541 0.8198 0.616 40 6464 6537.4399 5866.4665 7208.4132 0.4151 0.5354 0.8393 0.6031 41 6453 6521.4299 5792.5287 7250.3311 0.427 0.5614 0.7697 0.5783 42 6468 6522.3955 5747.3591 7297.432 0.4453 0.5697 0.7191 0.5746 43 6497 6533.561 5719.978 7347.144 0.4649 0.5627 0.6434 0.5817 44 6808 6533.8678 5679.4854 7388.2503 0.2647 0.5337 0.5781 0.5781 45 6793 6526.1734 5629.2146 7423.1321 0.2799 0.269 0.5488 0.5678 46 6907 6525.2919 5590.0451 7460.5387 0.2119 0.2874 0.5078 0.5643 47 6792 6530.5369 5560.9628 7500.1109 0.2986 0.2233 0.4988 0.5663 48 6757 6531.603 5527.6204 7535.5855 0.33 0.3056 0.5044 0.5648 49 6734 6528.0683 5489.1006 7567.036 0.3488 0.3329 0.4963 0.56 50 6654 6527.0233 5454.902 7599.1447 0.4082 0.3526 0.5212 0.5574 51 6589 6529.377 5426.2638 7632.4903 0.4578 0.4124 0.5159 0.5575 52 6469 6530.3046 5396.702 7663.9071 0.4578 0.4596 0.5456 0.5566 53 6521 6528.7575 5364.6672 7692.8478 0.4948 0.5401 0.5507 0.5541 54 6448 6527.9813 5334.3433 7721.6193 0.4478 0.5046 0.5392 0.5522 55 6410 6528.9838 5307.0503 7750.9172 0.4243 0.5517 0.5205 0.5517 56 6528 6529.6078 5279.9593 7779.2563 0.499 0.5744 0.3312 0.5509 57 6445 6528.9688 5251.8454 7806.0922 0.4487 0.5006 0.3427 0.5494 58 6458 6528.4816 5224.4713 7832.4919 0.4578 0.5499 0.2847 0.5481 59 6215 6528.8812 5198.7681 7858.9942 0.3219 0.5416 0.3491 0.5474 60 6167 6529.2529 5173.554 7884.9518 0.3002 0.6752 0.371 0.5468 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 33 0.0142 0.0027 0 308.8251 0 0 34 0.0197 0.0021 0.0024 194.6991 251.7621 15.867 35 0.024 -0.0033 0.0027 470.427 324.6504 18.0181 36 0.032 -0.0023 0.0026 223.2456 299.2992 17.3003 37 0.0401 0.0035 0.0028 533.515 346.1424 18.6049 38 0.0448 -0.0031 0.0028 399.1425 354.9757 18.8408 39 0.0481 -0.0052 0.0032 1143.3327 467.5982 21.624 40 0.0524 -0.0112 0.0042 5393.4116 1083.3248 32.9139 41 0.057 -0.0105 0.0049 4682.6512 1483.25 38.513 42 0.0606 -0.0083 0.0052 2958.8742 1630.8124 40.3833 43 0.0635 -0.0056 0.0053 1336.707 1604.0756 40.0509 44 0.0667 0.042 0.0083 75148.4532 7732.7737 87.9362 45 0.0701 0.0409 0.0108 71196.4572 12614.5955 112.3147 46 0.0731 0.0585 0.0142 145701.0863 22120.7734 148.7305 47 0.0757 0.04 0.016 68362.9704 25203.5866 158.7564 48 0.0784 0.0345 0.0171 50803.8106 26803.6006 163.7181 49 0.0812 0.0315 0.018 42407.8665 27721.4985 166.4977 50 0.0838 0.0195 0.018 16123.0711 27077.1415 164.5513 51 0.0862 0.0091 0.0176 3554.8968 25839.1286 160.7455 52 0.0886 -0.0094 0.0172 3758.2515 24735.0847 157.2739 53 0.091 -0.0012 0.0164 60.1781 23560.0892 153.493 54 0.0933 -0.0123 0.0162 6397.0114 22779.9493 150.9303 55 0.0955 -0.0182 0.0163 14157.1413 22405.0446 149.6831 56 0.0976 -2e-04 0.0156 2.5851 21471.6088 146.5319 57 0.0998 -0.0129 0.0155 7050.7592 20894.7748 144.5503 58 0.1019 -0.0108 0.0153 4967.6567 20282.1933 142.4156 59 0.1039 -0.0481 0.0166 98521.3793 23179.941 152.2496 60 0.1059 -0.0555 0.0179 131227.145 27038.7697 164.4347

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/11/t126054281012js10y2bgqvnt5/1lpjw1260542738.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126054281012js10y2bgqvnt5/1lpjw1260542738.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126054281012js10y2bgqvnt5/2tmem1260542738.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/11/t126054281012js10y2bgqvnt5/2tmem1260542738.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

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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