Jan-Pieter Onzea-Exponential Smoothing-werkloosheid

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 04:52:40 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/24/t121162640571mapbfh0raoqi6.htm/, Retrieved Sat, 24 May 2008 12:53:28 +0200

User-defined keywords:

Dataseries X:

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476 475 470 461 455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514

Text written by user:

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 470 475 -5 4 461 470 -9 5 455 461 -6 6 456 455 1 7 517 456 61 8 525 517 8 9 523 525 -2 10 519 523 -4 11 509 519 -10 12 512 509 3 13 519 512 7 14 517 519 -2 15 510 517 -7 16 509 510 -1 17 501 509 -8 18 507 501 6 19 569 507 62 20 580 569 11 21 578 580 -2 22 565 578 -13 23 547 565 -18 24 555 547 8 25 562 555 7 26 561 562 -1 27 555 561 -6 28 544 555 -11 29 537 544 -7 30 543 537 6 31 594 543 51 32 611 594 17 33 613 611 2 34 611 613 -2 35 594 611 -17 36 595 594 1 37 591 595 -4 38 589 591 -2 39 584 589 -5 40 573 584 -11 41 567 573 -6 42 569 567 2 43 621 569 52 44 629 621 8 45 628 629 -1 46 612 628 -16 47 595 612 -17 48 597 595 2 49 593 597 -4 50 590 593 -3 51 580 590 -10 52 574 580 -6 53 573 574 -1 54 573 573 0 55 620 573 47 56 626 620 6 57 620 626 -6 58 588 620 -32 59 566 588 -22 60 557 566 -9 61 561 557 4 62 549 561 -12 63 532 549 -17 64 526 532 -6 65 511 526 -15 66 499 511 -12 67 555 499 56 68 565 555 10 69 542 565 -23 70 527 542 -15 71 510 527 -17 72 514 510 4 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 514 476.730593266743 551.269406733257 74 514 461.293099536229 566.706900463771 75 514 449.447493970049 578.552506029951 76 514 439.461186533486 588.538813466514 77 514 430.663073063349 597.336926936651 78 514 422.708970487272 605.291029512728 79 514 415.394418272886 612.605581727114 80 514 408.586199072457 619.413800927543 81 514 402.191779800229 625.808220199771 82 514 396.143787679692 631.856212320308 83 514 390.391361706641 637.608638293359 84 514 384.894987940098 643.105012059902

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/12ypg1211626354.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/12ypg1211626354.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/20vn51211626354.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/20vn51211626354.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/3406f1211626354.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t121162640571mapbfh0raoqi6/3406f1211626354.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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