ws 8 - exponential smoothing single

*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 28 Nov 2010 09:11:22 +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/Nov/28/t1290935422ag48sowosq2v1g9.htm/, Retrieved Sun, 28 Nov 2010 10:10:26 +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/Nov/28/t1290935422ag48sowosq2v1g9.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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444 454 469 471 443 437 444 451 457 460 454 439 441 446 459 456 433 424 430 428 424 419 409 397 397 413 413 390 385 397 398 406 412 409 404 412 418 434 431 406 416 424 427 401

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 69 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.99991938208817 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 454 444 10 3 469 453.999193820882 15.0008061791183 4 471 468.99879066633 2.00120933366998 5 443 470.999838666682 -27.9998386666824 6 437 443.002257288525 -6.0022572885249 7 444 437.000483889449 6.99951611055116 8 451 443.999435713627 7.00056428637265 9 457 450.999435629126 6.00056437087443 10 460 456.999516247031 3.00048375296933 11 454 459.999758107265 -5.99975810726534 12 439 454.00048368797 -15.0004836879701 13 441 439.001209307671 1.99879069232867 14 446 440.999838861668 5.00016113833180 15 459 445.99959689745 13.0004031025498 16 456 458.998951934649 -2.99895193464891 17 433 456.000241769243 -23.0002417692427 18 424 433.001854231463 -9.00185423146303 19 430 424.000725710691 5.99927428930926 20 428 429.999516351034 -1.99951635103429 21 424 428.000161196833 -4.00016119683289 22 419 424.000322484643 -5.00032248464271 23 409 419.000403115557 -10.0004031155572 24 397 409.000806211617 -12.0008062116166 25 397 397.000967479937 -0.000967479937060034 26 413 397.000000077996 15.9999999220038 27 413 412.998710113417 0.00128988658303797 28 390 412.999999896012 -22.999999896012 29 385 390.001854211964 -5.00185421196369 30 397 385.000403239042 11.9995967609582 31 398 396.999032617566 1.00096738243366 32 406 397.9999193041 8.00008069590018 33 412 405.9993550502 6.00064494980018 34 409 411.999516240535 -2.99951624053455 35 404 409.000241814736 -5.00024181473583 36 412 404.000403109054 7.99959689094624 37 418 411.999355089203 6.00064491079684 38 434 417.999516240538 16.0004837594623 39 431 433.998710074411 -2.99871007441101 40 406 431.000241749744 -25.0002417497444 41 416 406.002015467285 9.9979845327149 42 424 415.999193983364 8.00080601663552 43 427 423.999354991726 3.00064500827398 44 401 426.999758094265 -25.9997580942652 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 45 401.002096046206 378.410552230622 423.593639861790 46 401.002096046206 369.054116202926 432.950075889486 47 401.002096046206 361.874497344499 440.129694747912 48 401.002096046206 355.821740312137 446.182451780274 49 401.002096046206 350.48912634186 451.515065750552 50 401.002096046206 345.668058849853 456.336133242558 51 401.002096046206 341.23461963518 460.769572457232 52 401.002096046206 337.108068151279 464.896123941133 53 401.002096046206 333.2323213326 468.771870759811 54 401.002096046206 329.566545171112 472.437646921299 55 401.002096046206 326.079913130041 475.92427896237 56 401.002096046206 322.748475957302 479.255716135109

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/1j30e1290935412.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/1j30e1290935412.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/2j30e1290935412.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/2j30e1290935412.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/3cv0h1290935412.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/28/t1290935422ag48sowosq2v1g9/3cv0h1290935412.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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