Voorspelling Dollar 3 mei

*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: Mon, 20 Dec 2010 23:17:44 +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/21/t1292886937dteex8a6ovs88ys.htm/, Retrieved Tue, 21 Dec 2010 00:15:37 +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/2010/Dec/21/t1292886937dteex8a6ovs88ys.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)

User-defined keywords:

Dataseries X:

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1.3866 1.3582 1.3332 1.3595 1.3617 1.3684 1.3394 1.3262 1.3173 1.3085 1.327 1.3182 1.293 1.291 1.2984 1.2795 1.299 1.3174 1.326 1.3111 1.2816 1.276 1.2849 1.2818 1.2829 1.2796 1.3008 1.2967 1.2938 1.2833 1.2823 1.2765 1.2634 1.2596 1.2705 1.2591 1.2798 1.2763 1.2795 1.2782 1.2644 1.2596 1.2615 1.2555 1.2555 1.2658 1.2565 1.2783 1.2786 1.2782 1.2905 1.3042 1.2942 1.313 1.3671 1.3549 1.3558 1.3507 1.3494 1.3607 1.3295 1.3193 1.3308 1.3246 1.3392 1.3425 1.3496 1.3255 1.3231 1.3273 1.3276 1.3173 1.3196 1.3058 1.2966 1.2932 1.2947 1.305 1.3232 1.3125 1.2992 1.3266 1.3275 1.3223 1.3403 1.3322 1.3363 1.3425 1.3574 1.3683 1.3623 1.3563 1.3518 1.3494 1.3612 1.369 1.3771 1.3972 1.401 1.3908 1.3901 1.3856 1.4098 1.422 1.4238 1.4207 1.4095 1.4177 1.3866 1.3959 1.4102 1.3969 1.4004 1.385 1.389 1.384 1.392 1.3932 1.3858 1.3978 1.4029 1.394 1.4096 1.4058 1.4134 1.4096 1.4049 1.4009 1.3897 1.4019 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 '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[336]) 331 1.3486 - - - - - - - 332 1.3373 - - - - - - - 333 1.3339 - - - - - - - 334 1.3311 - - - - - - - 335 1.3321 - - - - - - - 336 1.329 - - - - - - - 337 1.3245 1.3281 1.307 1.3489 0.3677 0.4659 0.1931 0.4659 338 1.3256 1.3278 1.2978 1.3572 0.4412 0.5876 0.3425 0.4686 339 1.3315 1.3276 1.2908 1.3635 0.4156 0.5434 0.4241 0.4694 340 1.3238 1.3277 1.2851 1.3691 0.4272 0.4281 0.417 0.475 341 1.3089 1.3274 1.2797 1.3736 0.2159 0.5611 0.4734 0.4734 342 1.2924 1.3274 1.2743 1.3786 0.0905 0.76 0.5435 0.4749 343 1.2727 1.3273 1.2694 1.3831 0.0274 0.8902 0.5243 0.4766 344 1.2746 1.3273 1.2648 1.3873 0.0424 0.9629 0.4456 0.478 345 1.2969 1.3273 1.2606 1.3912 0.1752 0.9472 0.543 0.4795 346 1.2698 1.3273 1.2565 1.3948 0.0475 0.8113 0.7034 0.4803 347 1.2686 1.3273 1.2527 1.3983 0.0526 0.9437 0.8322 0.4812 348 1.2587 1.3273 1.249 1.4016 0.0353 0.9391 0.925 0.4821 349 1.2492 1.3273 1.2455 1.4048 0.0242 0.9586 0.9086 0.4828 350 1.2349 1.3273 1.2421 1.4078 0.0123 0.9713 0.7702 0.4834 351 1.2428 1.3273 1.2388 1.4108 0.0236 0.985 0.9115 0.484 352 1.227 1.3273 1.2356 1.4136 0.0114 0.9725 0.9088 0.4845 353 1.2334 1.3273 1.2326 1.4163 0.0193 0.9864 0.9345 0.485 354 1.2497 1.3273 1.2296 1.4189 0.0485 0.9777 0.9526 0.4854 355 1.236 1.3273 1.2267 1.4215 0.0287 0.9468 0.9727 0.4858 356 1.2223 1.3273 1.2238 1.424 0.0166 0.9679 0.9566 0.4862 357 1.2309 1.3273 1.221 1.4264 0.0283 0.9811 0.9764 0.4865 358 1.2255 1.3273 1.2183 1.4287 0.0246 0.9687 0.9652 0.4868 359 1.2384 1.3273 1.2157 1.431 0.0465 0.9728 0.9287 0.4871 360 1.2307 1.3273 1.2131 1.4333 0.037 0.9499 0.9544 0.4874 361 1.2155 1.3273 1.2106 1.4354 0.0214 0.96 0.9715 0.4876 362 1.2218 1.3273 1.2081 1.4376 0.0304 0.9765 0.9567 0.4879 363 1.2268 1.3273 1.2056 1.4397 0.0398 0.9671 0.9621 0.4881 364 1.206 1.3273 1.2032 1.4417 0.0189 0.9574 0.9361 0.4883 365 1.1959 1.3273 1.2008 1.4437 0.0135 0.9794 0.948 0.4885 366 1.1942 1.3273 1.1985 1.4457 0.0138 0.9852 0.9679 0.4887 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 337 0.008 -0.0027 0 0 0 0 338 0.0113 -0.0017 0.0022 0 0 0.003 339 0.0138 0.0029 0.0024 0 0 0.0033 340 0.0159 -0.0029 0.0026 0 0 0.0035 341 0.0178 -0.014 0.0048 3e-04 1e-04 0.0088 342 0.0197 -0.0263 0.0084 0.0012 3e-04 0.0164 343 0.0214 -0.0412 0.0131 0.003 7e-04 0.0256 344 0.023 -0.0397 0.0164 0.0028 9e-04 0.0304 345 0.0245 -0.0229 0.0171 9e-04 9e-04 0.0304 346 0.026 -0.0433 0.0198 0.0033 0.0012 0.0341 347 0.0273 -0.0442 0.022 0.0034 0.0014 0.037 348 0.0286 -0.0517 0.0245 0.0047 0.0016 0.0406 349 0.0298 -0.0588 0.0271 0.0061 0.002 0.0446 350 0.031 -0.0696 0.0301 0.0085 0.0025 0.0496 351 0.0321 -0.0637 0.0324 0.0071 0.0028 0.0526 352 0.0332 -0.0756 0.0351 0.0101 0.0032 0.0568 353 0.0342 -0.0707 0.0372 0.0088 0.0036 0.0596 354 0.0352 -0.0585 0.0384 0.006 0.0037 0.0607 355 0.0362 -0.0688 0.04 0.0083 0.0039 0.0627 356 0.0372 -0.0791 0.0419 0.011 0.0043 0.0655 357 0.0381 -0.0726 0.0434 0.0093 0.0045 0.0673 358 0.039 -0.0767 0.0449 0.0104 0.0048 0.0692 359 0.0399 -0.067 0.0459 0.0079 0.0049 0.0702 360 0.0407 -0.0728 0.047 0.0093 0.0051 0.0715 361 0.0416 -0.0842 0.0485 0.0125 0.0054 0.0735 362 0.0424 -0.0795 0.0497 0.0111 0.0056 0.075 363 0.0432 -0.0757 0.0506 0.0101 0.0058 0.0761 364 0.044 -0.0914 0.0521 0.0147 0.0061 0.0782 365 0.0448 -0.099 0.0537 0.0173 0.0065 0.0806 366 0.0455 -0.1003 0.0552 0.0177 0.0069 0.0829

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292886937dteex8a6ovs88ys/13x9f1292887059.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292886937dteex8a6ovs88ys/13x9f1292887059.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292886937dteex8a6ovs88ys/2szsj1292887060.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t1292886937dteex8a6ovs88ys/2szsj1292887060.ps (open in new window)

Parameters (Session):

par1 = 15 ; par2 = 1.9 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 15 ; par2 = 1.9 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par1 <- 30 #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 <- 5 #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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