*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: Fri, 04 Dec 2009 08:04:59 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628.htm/, Retrieved Fri, 04 Dec 2009 16:06:16 +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/2009/Dec/04/t1259939172qbupw8d5owqd628.htm/}, year = {2009}, } @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 = {2009}, 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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455 456 517 525 523 519 509 512 519 517 510 509 501 507 569 580 578 565 547 555 562 561 555 544 537 543 594 611 613 611 594 595 591 589 584 573 567 569 621 629 628 612 595 597 593 590 580 574 573 573 620 626 620 588 566 557 561 549 532 526 511 499 555 565 542 527 510 514 517 508 493 490 469 478 528 534 518 506 502 516 528 533 536 537 524 536 587 597 581 564

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.906716756463771 beta 0.161303402714018 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 501 477.36411568469 23.6358843153104 14 507 508.737656888438 -1.73765688843827 15 569 573.0868308734 -4.08683087339978 16 580 583.691408167292 -3.69140816729248 17 578 580.990102846686 -2.99010284668611 18 565 567.804956761505 -2.80495676150542 19 547 557.477105238679 -10.4771052386786 20 555 550.729654670869 4.27034532913115 21 562 562.032785957684 -0.0327859576843821 22 561 559.505441466726 1.49455853327368 23 555 553.015676152597 1.98432384740272 24 544 554.144649566413 -10.1446495664131 25 537 538.489914752371 -1.48991475237074 26 543 540.662601297118 2.33739870288230 27 594 608.694561837865 -14.6945618378645 28 611 604.542250616395 6.45774938360466 29 613 606.819217352304 6.18078264769554 30 611 598.422816283702 12.5771837162981 31 594 599.896870725808 -5.8968707258075 32 595 599.056049737648 -4.05604973764764 33 591 601.727567908138 -10.7275679081380 34 589 586.883590097115 2.11640990288470 35 584 578.133451097452 5.8665489025484 36 573 579.627309598472 -6.62730959847158 37 567 566.345753136637 0.654246863362914 38 569 570.039498371553 -1.03949837155278 39 621 634.832382917607 -13.832382917607 40 629 632.514245841616 -3.51424584161623 41 628 622.735620023555 5.2643799764445 42 612 610.833592377694 1.16640762230645 43 595 595.808827467011 -0.80882746701127 44 597 596.092466954692 0.9075330453079 45 593 599.688692757083 -6.688692757083 46 590 587.345963810518 2.65403618948153 47 580 577.20712009121 2.79287990878981 48 574 572.183238952645 1.81676104735516 49 573 565.861429140981 7.13857085901907 50 573 574.867786819753 -1.86778681975318 51 620 637.551480369679 -17.5514803696786 52 626 631.669886919662 -5.6698869196623 53 620 619.307955669593 0.692044330407157 54 588 601.028391871878 -13.0283918718781 55 566 569.543672124262 -3.54367212426234 56 557 563.037735417609 -6.03773541760893 57 561 554.06351226212 6.93648773787982 58 549 551.781480708785 -2.7814807087849 59 532 533.448497776438 -1.44849777643765 60 526 520.456972300121 5.54302769987873 61 511 514.60077667424 -3.60077667423991 62 499 507.372225536103 -8.37222553610292 63 555 547.509589983155 7.49041001684463 64 565 560.422328321901 4.57767167809902 65 542 556.202888754084 -14.2028887540840 66 527 521.150029304187 5.84997069581323 67 510 507.805532031215 2.19446796878498 68 514 505.593148761295 8.40685123870549 69 517 512.205034467199 4.79496553280057 70 508 508.68416094887 -0.68416094886993 71 493 494.675223013624 -1.67522301362391 72 490 484.003042415311 5.9969575846888 73 469 479.708725773371 -10.7087257733709 74 478 466.004736122053 11.9952638779475 75 528 527.376617670917 0.62338232908337 76 534 536.049662457725 -2.04966245772505 77 518 526.160612169776 -8.16061216977585 78 506 501.662353506621 4.33764649337888 79 502 489.483806058041 12.5161939419589 80 516 501.001956163277 14.9980438367234 81 528 518.05137376458 9.94862623542042 82 533 524.069009907978 8.93099009202217 83 536 524.916465077561 11.0835349224392 84 537 534.559315974289 2.44068402571122 85 524 532.404508643861 -8.40450864386094 86 536 531.27154515529 4.72845484471009 87 587 599.076817238046 -12.0768172380461 88 597 603.244136809009 -6.24413680900909 89 581 593.67169170928 -12.6716917092793 90 564 569.365601685006 -5.36560168500637 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 91 550.831518797796 535.704880127584 565.958157468008 92 552.658046829374 530.667581587187 574.648512071562 93 554.882651899764 526.31249226132 583.452811538207 94 549.190992721756 514.421724165481 583.96026127803 95 538.274955498514 497.633118837529 578.9167921595 96 531.967718547043 485.125805550542 578.809631543544 97 521.376289153361 468.668977268996 574.083601037726 98 524.968025583507 464.896770212826 585.039280954188 99 580.451063453985 506.402523682629 654.49960322534 100 592.380356152948 508.815697400668 675.945014905228 101 585.255286759573 494.570513253785 675.940060265361 102 572.23232009109 473.816801599748 670.647838582431

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/1fu9t1259939097.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/1fu9t1259939097.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/2bg4a1259939097.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/2bg4a1259939097.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/311m91259939097.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/04/t1259939172qbupw8d5owqd628/311m91259939097.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

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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