Het aantal werklozen in België

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Jan 2011 20:21:55 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv.htm/, Retrieved Sun, 16 Jan 2011 21:20:31 +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/2011/Jan/16/t1295209231yfbasvszczuxfrv.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

591000 589000 584000 573000 567000 569000 621000 629000 628000 612000 595000 597000 593000 590000 580000 574000 573000 573000 620000 626000 620000 588000 566000 557000 561000 549000 532000 526000 511000 499000 555000 565000 542000 527000 510000 514000 517000 508000 493000 490000 469000 478000 528000 534000 518000 506000 502000 516000 528000 533000 536000 537000 524000 536000 587000 597000 581000 564000 558000 575000

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.605601200667205 beta 0.574371375563579 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 593000 592132.745726496 867.254273504019 14 590000 589747.35477792 252.645222079707 15 580000 580369.302629229 -369.30262922938 16 574000 575361.13989045 -1361.13989045052 17 573000 575153.86042317 -2153.86042317026 18 573000 575383.976318032 -2383.97631803178 19 620000 613437.158107581 6562.84189241868 20 626000 625399.695969745 600.304030255415 21 620000 625210.123494242 -5210.12349424232 22 588000 604689.459805047 -16689.4598050467 23 566000 569994.967986863 -3994.96798686287 24 557000 560473.666012373 -3473.66601237305 25 561000 544693.495883168 16306.5041168323 26 549000 547271.496389238 1728.50361076160 27 532000 534911.057225064 -2911.05722506379 28 526000 523457.428379339 2542.57162066118 29 511000 522144.463208206 -11144.4632082059 30 499000 510554.68054853 -11554.6805485296 31 555000 537108.32821396 17891.6717860395 32 565000 548046.262426642 16953.7375733579 33 542000 555623.362675674 -13623.3626756745 34 527000 522708.373081629 4291.6269183713 35 510000 510252.984302774 -252.984302773606 36 514000 509031.283994896 4968.71600510419 37 517000 514929.554999308 2070.44500069227 38 508000 506949.21348631 1050.78651369008 39 493000 495925.352070624 -2925.35207062418 40 490000 490185.839858291 -185.839858290623 41 469000 484445.213622628 -15445.2136226278 42 478000 471215.947426457 6784.05257354304 43 528000 527994.950030993 5.04996900691185 44 534000 529014.912166739 4985.08783326135 45 518000 514405.144774376 3594.85522562399 46 506000 502093.296460545 3906.70353945548 47 502000 490588.634126016 11411.3658739841 48 516000 505523.863839219 10476.1361607809 49 528000 522563.614712935 5436.38528706529 50 533000 526339.601461736 6660.39853826433 51 536000 529216.053822505 6783.94617749495 52 537000 545885.557147777 -8885.5571477774 53 524000 541280.575902911 -17280.5759029109 54 536000 547491.078516169 -11491.0785161685 55 587000 595956.258313888 -8956.25831388799 56 597000 595823.509934264 1176.49006573646 57 581000 579344.310048633 1655.68995136651 58 564000 566291.939237156 -2291.93923715572 59 558000 552147.911058549 5852.08894145116 60 575000 559568.553501807 15431.4464981928 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 61 575566.200684589 559032.197710462 592100.203658715 62 572586.289216197 549741.525218819 595431.053213574 63 565214.804157095 533833.35864091 596596.249673281 64 562973.061323415 521400.700173436 604545.422473395 65 554906.104078392 501817.180334731 607995.027822054 66 574343.895694665 508606.043005512 640081.748383818 67 635243.653842779 555849.020001359 714638.2876842 68 652122.352250302 558150.473692804 746094.2308078 69 642301.616333532 532897.613563598 751705.619103467 70 633295.654209262 507656.385723422 758934.922695102 71 631154.886973796 488519.561174709 773790.212772884 72 644177.258714143 483820.720718289 804533.796709998

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/1trdk1295209311.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/1trdk1295209311.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/27vug1295209311.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/27vug1295209311.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/3b20a1295209311.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/16/t1295209231yfbasvszczuxfrv/3b20a1295209311.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ;

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

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) 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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.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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