Voorspelling Dollar 3 mei

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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 23:09:08 +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/t12928865041dye540y8rrwefb.htm/, Retrieved Tue, 21 Dec 2010 00:08:24 +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/t12928865041dye540y8rrwefb.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:

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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[340]) 335 1.3321 - - - - - - - 336 1.329 - - - - - - - 337 1.3245 - - - - - - - 338 1.3256 - - - - - - - 339 1.3315 - - - - - - - 340 1.3238 - - - - - - - 341 1.3089 1.3236 1.3025 1.3444 0.0837 0.4906 0.3038 0.4906 342 1.2924 1.3232 1.2933 1.3525 0.0198 0.8301 0.4651 0.4837 343 1.2727 1.3233 1.2865 1.3591 0.0028 0.9543 0.4495 0.4886 344 1.2746 1.3238 1.2813 1.3651 0.0098 0.9923 0.3566 0.4991 345 1.2969 1.3231 1.2755 1.3693 0.1325 0.9804 0.4887 0.4887 346 1.2698 1.3231 1.2701 1.3743 0.0205 0.8425 0.707 0.4895 347 1.2686 1.3231 1.2652 1.3788 0.0276 0.9696 0.8599 0.49 348 1.2587 1.3231 1.2607 1.383 0.0175 0.9628 0.9505 0.4908 349 1.2492 1.3231 1.2565 1.3869 0.0115 0.9762 0.9321 0.4918 350 1.2349 1.3231 1.2524 1.3905 0.0052 0.9841 0.7767 0.4917 351 1.2428 1.3231 1.2486 1.394 0.0132 0.9926 0.9296 0.4921 352 1.227 1.3231 1.2449 1.3973 0.0056 0.983 0.9248 0.4924 353 1.2334 1.3231 1.2414 1.4005 0.0116 0.9925 0.9485 0.4927 354 1.2497 1.3231 1.238 1.4035 0.0369 0.9856 0.9641 0.493 355 1.236 1.3231 1.2347 1.4064 0.0203 0.9578 0.9809 0.4932 356 1.2223 1.3231 1.2315 1.4092 0.0109 0.9762 0.9661 0.4934 357 1.2309 1.3231 1.2285 1.412 0.021 0.9869 0.9829 0.4936 358 1.2255 1.3231 1.2255 1.4146 0.0183 0.9758 0.9726 0.4938 359 1.2384 1.3231 1.2226 1.4171 0.0388 0.979 0.9369 0.494 360 1.2307 1.3231 1.2197 1.4196 0.0304 0.9572 0.9615 0.4941 361 1.2155 1.3231 1.217 1.422 0.0165 0.9664 0.977 0.4943 362 1.2218 1.3231 1.2143 1.4244 0.025 0.9813 0.9628 0.4944 363 1.2268 1.3231 1.2116 1.4267 0.0342 0.9723 0.9676 0.4945 364 1.206 1.3231 1.209 1.4289 0.0151 0.9627 0.9416 0.4947 365 1.1959 1.3231 1.2065 1.4311 0.0105 0.9832 0.9532 0.4948 366 1.1942 1.3231 1.204 1.4332 0.0109 0.9882 0.9722 0.4949 Univariate ARIMA Extrapolation Forecast Performance time % S.E. PE MAPE Sq.E MSE RMSE 341 0.008 -0.0111 0 2e-04 0 0 342 0.0113 -0.0233 0.0172 9e-04 6e-04 0.0241 343 0.0138 -0.0382 0.0242 0.0026 0.0012 0.0352 344 0.0159 -0.0371 0.0274 0.0024 0.0015 0.0392 345 0.0178 -0.0198 0.0259 7e-04 0.0014 0.0369 346 0.0197 -0.0403 0.0283 0.0028 0.0016 0.0401 347 0.0215 -0.0412 0.0301 0.003 0.0018 0.0425 348 0.0231 -0.0487 0.0325 0.0041 0.0021 0.0458 349 0.0246 -0.0559 0.0351 0.0055 0.0025 0.0497 350 0.026 -0.0666 0.0382 0.0078 0.003 0.0548 351 0.0273 -0.0607 0.0403 0.0064 0.0033 0.0576 352 0.0286 -0.0726 0.043 0.0092 0.0038 0.0617 353 0.0298 -0.0678 0.0449 0.008 0.0041 0.0643 354 0.031 -0.0555 0.0456 0.0054 0.0042 0.065 355 0.0321 -0.0658 0.047 0.0076 0.0044 0.0667 356 0.0332 -0.0762 0.0488 0.0102 0.0048 0.0693 357 0.0343 -0.0697 0.05 0.0085 0.005 0.0709 358 0.0353 -0.0737 0.0513 0.0095 0.0053 0.0726 359 0.0363 -0.064 0.052 0.0072 0.0054 0.0733 360 0.0372 -0.0698 0.0529 0.0085 0.0055 0.0744 361 0.0382 -0.0813 0.0542 0.0116 0.0058 0.0763 362 0.0391 -0.0765 0.0553 0.0103 0.006 0.0776 363 0.0399 -0.0728 0.056 0.0093 0.0062 0.0785 364 0.0408 -0.0885 0.0574 0.0137 0.0065 0.0805 365 0.0416 -0.0961 0.0589 0.0162 0.0069 0.0828 366 0.0425 -0.0974 0.0604 0.0166 0.0072 0.0851

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t12928865041dye540y8rrwefb/1sggr1292886544.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928865041dye540y8rrwefb/1sggr1292886544.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928865041dye540y8rrwefb/2hhdl1292886544.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/21/t12928865041dye540y8rrwefb/2hhdl1292886544.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 <- 26 #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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