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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:32:39 +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/May/18/t1305728919z606mmlb8vw5l6x.htm/, Retrieved Wed, 18 May 2011 16:28:42 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W101

Dataseries X:

» Textbox « » Textfile « » CSV «

112 118 132 129 121 135 41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.434024876116231 beta 0.0235454462485613 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 24693 16499.6822141416 8193.31778585835 14 22205 18809.2068164445 3395.79318355548 15 21725 20908.6825934264 816.31740657361 16 27192 27978.7524046476 -786.752404647617 17 21790 23125.1738906074 -1335.17389060741 18 13253 14163.7331851727 -910.733185172672 19 37702 58248.0957497042 -20546.0957497042 20 30364 44327.9749576895 -13963.9749576895 21 32609 39154.9333721622 -6545.93337216225 22 30212 29932.0376240915 279.962375908468 23 29965 26948.5536399519 3016.44636004808 24 28352 22167.8558174645 6184.14418253547 25 25814 26061.6972848267 -247.697284826732 26 22414 21519.4052631722 894.594736827818 27 20506 20963.5963054745 -457.596305474475 28 28806 26174.1427955893 2631.85720441071 29 22228 22345.4951637003 -117.4951637003 30 13971 13885.6212337636 85.3787662364448 31 36845 46565.3194198647 -9720.31941986469 32 35338 39333.2064281112 -3995.20642811118 33 35022 43361.8976467778 -8339.89764677778 34 34777 36513.3933886801 -1736.39338868012 35 26887 33675.6054000075 -6788.6054000075 36 23970 25795.2146240836 -1825.21462408355 37 22780 22719.4816362814 60.5183637185874 38 17351 19285.5767356151 -1934.57673561512 39 21382 16929.6017006082 4452.39829939185 40 24561 25264.8105540579 -703.810554057916 41 17409 19205.1730698177 -1796.17306981768 42 11514 11487.7744451401 26.225554859886 43 31514 33172.0540280012 -1658.05402800116 44 27071 32406.8249611713 -5335.82496117131 45 29462 32369.5114830342 -2907.51148303417 46 26105 31387.9854488681 -5282.98544886815 47 22397 24512.1655776422 -2115.16557764221 48 23843 21588.2272133871 2254.77278661292 49 21705 21334.4070080031 370.592991996942 50 18089 17051.0524505998 1037.94754940016 51 20764 19301.2517057897 1462.74829421032 52 25316 23096.9400387391 2219.05996126091 53 17704 17725.2942103492 -21.294210349155 54 15548 11678.4955108657 3869.5044891343 55 28029 37352.037113629 -9323.03711362901 56 29383 30758.2593364618 -1375.25933646177 57 36438 34121.1516086704 2316.84839132958 58 32034 33574.2292605012 -1540.22926050121 59 22679 29351.3992151774 -6672.39921517738 60 24319 26934.8187184 -2615.81871839999 61 18004 23272.0011869629 -5268.0011869629 62 17537 16978.8523824325 558.147617567523 63 20366 19068.9517143222 1297.04828567777 64 22782 22896.8372777057 -114.837277705727 65 19169 15920.6486148097 3248.35138519032 66 13807 13272.4498740578 534.550125942218 67 29743 27194.4232295975 2548.5767704025 68 25591 30200.9438543089 -4609.9438543089 69 29096 33882.2225492444 -4786.22254924438 70 26482 28413.560639652 -1931.56063965198 71 22405 21567.4313915379 837.568608462072 72 27044 24494.7354868066 2549.26451319343 73 17970 21001.2951992048 -3031.29519920484 74 18730 18902.4883985025 -172.48839850253 75 19684 21227.6183614609 -1543.61836146091 76 19785 23009.3864451343 -3224.38644513427 77 18479 16656.5873856487 1822.41261435128 78 10698 12310.3773432403 -1612.37734324029 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 79 23919.9879523217 15109.0978710251 32730.8780336182 80 21923.779135937 12413.8757479612 31433.6825239129 81 26444.0147580714 15525.5252398737 37362.504276269 82 24724.7974779631 13375.9860271019 36073.6089288244 83 20520.8986590938 9349.65867011725 31692.1386480704 84 23634.0572920484 10870.8076563588 36397.3069277381 85 16694.8314281832 5316.64527588659 28073.0175804797 86 17429.5278148737 5062.67170407915 29796.3839256683 87 18872.045352868 5189.47411435172 32554.6165913843 88 20164.9121887727 5166.5414051048 35163.2829724406 89 17973.9778765122 3440.11018954645 32507.8455634779 90 11018.7779004907 3414.46816987244 18623.0876311089

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/1aixg1305729156.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/1aixg1305729156.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/215xz1305729156.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/215xz1305729156.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/3wium1305729156.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t1305728919z606mmlb8vw5l6x/3wium1305729156.ps (open in new window)

Parameters (Session):

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

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=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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