*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 27 Jan 2010 03:13:03 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g.htm/, Retrieved Wed, 27 Jan 2010 11:13:32 +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/Jan/27/t1264587208uynzc2t7lg2ad2g.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

1.61 1.58 1.69 1.78 1.76 1.83 1.8 1.57 1.45 1.4 1.55 1.58 1.58 1.59 1.8 1.99 2.06 2.06 2.08 2 1.85 1.77 1.7 1.66 1.67 1.73 1.91 2.02 2.07 2.15 2.1 1.68 1.68 1.65 1.72 1.73 1.76 1.84 1.99 2.05 2.12 2.13 2.08 1.88 1.81 1.81 1.88 1.87 1.87 1.9 2.01 2.05 2.16 2.18 2.15 2.12 2.04 2.04 2.06 1.93 1.86 1.94 2.35 2.46 2.59 2.66 2.41 2.18 2.13 2.11 2.12 2.16 2.07 2.2 2.29 2.32 2.37 2.38 2.38 2.28 2.22 2.25 2.3 2.3 2.23 2.27 2.3 2.32 2.41 2.43 2.45 2.47 2.46 2.5 2.46 2.43 2.37 2.45 2.53 2.56 2.62 2.67 2.62 2.6 2.53 2.49 2.48 2.44

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.836733274783946 beta 0.00571230996515615 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.58 1.48268696581197 0.0973130341880326 14 1.59 1.56672749438373 0.0232725056162744 15 1.8 1.78392708414244 0.0160729158575561 16 1.99 1.97767936097688 0.0123206390231181 17 2.06 2.05876753830416 0.00123246169583524 18 2.06 2.07266709281064 -0.0126670928106405 19 2.08 2.03404254957561 0.0459574504243911 20 2 1.86594077428288 0.134059225717118 21 1.85 1.87636411278813 -0.0263641127881282 22 1.77 1.81409656056281 -0.0440965605628096 23 1.7 1.92886424513356 -0.228864245133563 24 1.66 1.76710342877101 -0.107103428771011 25 1.67 1.69343333267237 -0.0234333326723666 26 1.73 1.66335111787722 0.0666488821227764 27 1.91 1.91487515117494 -0.0048751511749392 28 2.02 2.08959217569594 -0.0695921756959352 29 2.07 2.09904464225383 -0.0290446422538309 30 2.15 2.08391008415052 0.0660899158494783 31 2.1 2.11970110363563 -0.0197011036356267 32 1.68 1.90967640861885 -0.229676408618849 33 1.68 1.58645139454636 0.0935486054536363 34 1.65 1.61908997848727 0.0309100215127311 35 1.72 1.76427655219160 -0.0442765521915973 36 1.73 1.77555296131678 -0.0455529613167778 37 1.76 1.76604599447201 -0.00604599447200727 38 1.84 1.76430414069630 0.075695859303704 39 1.99 2.01084819617850 -0.0208481961784972 40 2.05 2.16068516977695 -0.110685169776952 41 2.12 2.14122867646356 -0.0212286764635632 42 2.13 2.14705851521806 -0.0170585152180607 43 2.08 2.09776444445036 -0.0177644444503615 44 1.88 1.85358228037756 0.0264177196224447 45 1.81 1.79713972655720 0.0128602734427978 46 1.81 1.75137932947343 0.0586206705265735 47 1.88 1.90695173536237 -0.0269517353623734 48 1.87 1.93207368290545 -0.0620736829054451 49 1.87 1.91467217075956 -0.0446721707595563 50 1.9 1.89325033310556 0.00674966689444045 51 2.01 2.06530694104696 -0.0553069410469638 52 2.05 2.17044360355169 -0.120443603551688 53 2.16 2.15618038634051 0.00381961365948635 54 2.18 2.18252274793323 -0.00252274793322771 55 2.15 2.14421839533253 0.00578160466747102 56 2.12 1.92600642662259 0.193993573377411 57 2.04 2.00742260011159 0.0325773998884089 58 2.04 1.98558148479818 0.0544185152018208 59 2.06 2.12359675187947 -0.0635967518794693 60 1.93 2.11207726879975 -0.182077268799748 61 1.86 1.99628719183693 -0.136287191836930 62 1.94 1.90534694284039 0.0346530571596109 63 2.35 2.08949628623537 0.260503713764634 64 2.46 2.44863387588456 0.0113661241154368 65 2.59 2.56596459389842 0.0240354061015844 66 2.66 2.60929961171829 0.0507003882817103 67 2.41 2.61825196880358 -0.208251968803575 68 2.18 2.25202404324695 -0.0720240432469472 69 2.13 2.08357336036995 0.0464266396300488 70 2.11 2.07602531226766 0.0339746877323392 71 2.12 2.1767078876263 -0.0567078876263016 72 2.16 2.15068285222554 0.00931714777445602 73 2.07 2.20250388389495 -0.132503883894955 74 2.2 2.14264522796776 0.0573547720322414 75 2.29 2.38277937437592 -0.0927793743759198 76 2.32 2.40406441601359 -0.0840644160135908 77 2.37 2.44158461606873 -0.0715846160687259 78 2.38 2.40677856904803 -0.0267785690480333 79 2.38 2.30576696162897 0.0742330383710317 80 2.28 2.19663887689812 0.0833611231018758 81 2.22 2.17677962795706 0.0432203720429358 82 2.25 2.1637369144865 0.0862630855135018 83 2.3 2.29283652165931 0.00716347834068687 84 2.3 2.33081079607892 -0.0308107960789186 85 2.23 2.32548530904424 -0.0954853090442436 86 2.27 2.32736038699631 -0.0573603869963124 87 2.3 2.44620979007434 -0.146209790074337 88 2.32 2.42316846522228 -0.103168465222284 89 2.41 2.44560767394966 -0.0356076739496585 90 2.43 2.44725849261619 -0.0172584926161896 91 2.45 2.36978841171978 0.0802115882802243 92 2.47 2.26626559413031 0.203734405869694 93 2.46 2.34026087604981 0.119739123950191 94 2.5 2.39832497519922 0.101675024800781 95 2.46 2.52753317899041 -0.0675331789904101 96 2.43 2.49657656118980 -0.0665765611898044 97 2.37 2.45036474545687 -0.080364745456869 98 2.45 2.47078777772548 -0.0207877777254817 99 2.53 2.60557889866838 -0.0755788986683825 100 2.56 2.64884794990773 -0.0888479499077328 101 2.62 2.69455242979988 -0.0745524297998825 102 2.67 2.66667893299608 0.00332106700392165 103 2.62 2.62250668591578 -0.00250668591578318 104 2.6 2.46970714551195 0.130292854488054 105 2.53 2.46795601964556 0.0620439803544404 106 2.49 2.47393785834857 0.0160621416514268 107 2.48 2.5026180948813 -0.0226180948812997 108 2.44 2.50834753620686 -0.0683475362068608 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 2.45734220021959 2.29063229477104 2.62405210566815 110 2.55405960846692 2.33617645524042 2.77194276169343 111 2.69672192969166 2.43714891742680 2.95629494195653 112 2.80084815055025 2.50502945079008 3.09666685031042 113 2.92343749880781 2.59500789965651 3.2518670979591 114 2.97122383781036 2.61282278598009 3.32962488964063 115 2.9238705779611 2.53752111175853 3.31022004416367 116 2.79541150493603 2.38272389949007 3.208099110382 117 2.67343577773733 2.23572807531673 3.11114348015793 118 2.6196380346561 2.15801253808131 3.08126353123089 119 2.62812856066394 2.14352302156882 3.11273409975906 120 2.64499053911791 2.13821387143904 3.15176720679678

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/1a8w31264587181.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/1a8w31264587181.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/2rtnq1264587181.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/2rtnq1264587181.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/31j6o1264587181.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/27/t1264587208uynzc2t7lg2ad2g/31j6o1264587181.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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