Toon Raeman - Opg.10 - Exponential Smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 18 Aug 2008 05:00:08 -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/Aug/18/t1219057293rgd83u2b6esmq6o.htm/, Retrieved Mon, 18 Aug 2008 11:01:33 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

12.11 11.42 11.71 12.04 12.21 12 12.36 12.32 12.96 12.79 13.19 12.34 13.25 12.54 12.77 12.96 13 13.61 13.8 14.16 14.27 14.69 15.01 15.09 15.14 14.2 13.83 14.31 14.04 14.9 14.92 15.36 15.5 15.65 16.18 15.44 15.58 15.24 15.33 16.07 15.82 15.87 15.72 17.07 16.83 17.52 17.76 17.36 17.95 16.71 17.14 16.72 17.26 17.24 17.69 18.13 18.08 18.18 18.18 17.64 17.89 16.82 16.61 16.66 17.02 16.91 17.18 18.06 17.58 17.48 17.54 17.44 17.79 16.79 16.19 16.62 16.39 16.54 17.26 18 17.29 18.16 17.82 17.48 18.31 17.04 17.03 16.97 17.11 17.12 17.69 18.5 18.27 18.45 18.35 18.03

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.553590492930469 beta 0.0620502955838186 gamma 0.64547702995407 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 13.25 12.5417222222222 0.708277777777772 14 12.54 12.234214758365 0.305785241635011 15 12.77 12.6598117814810 0.110188218519037 16 12.96 12.9384131674550 0.0215868325449780 17 13 12.9974571859856 0.00254281401435286 18 13.61 13.5806292970590 0.0293707029410264 19 13.8 13.7567453026929 0.0432546973071055 20 14.16 14.1574498407564 0.00255015924358837 21 14.27 14.3202916659892 -0.0502916659892492 22 14.69 14.7750698842658 -0.0850698842657582 23 15.01 15.1085063557543 -0.0985063557543349 24 15.09 15.1936207863540 -0.103620786353964 25 15.14 15.1522660045593 -0.0122660045592724 26 14.2 14.3355811263814 -0.135581126381437 27 13.83 14.4510059011042 -0.621005901104201 28 14.31 14.2647027817538 0.0452972182462172 29 14.04 14.2976074671984 -0.257607467198365 30 14.9 14.7017792547852 0.198220745214778 31 14.92 14.9384557675841 -0.0184557675841415 32 15.36 15.2542353991606 0.105764600839418 33 15.5 15.4235013171936 0.0764986828063652 34 15.65 15.9073153080154 -0.257315308015365 35 16.18 16.1044770449433 0.0755229550566767 36 15.44 16.2533870995686 -0.813387099568642 37 15.58 15.7899836138805 -0.20998361388048 38 15.24 14.7660671301286 0.47393286987136 39 15.33 15.0377322839105 0.292267716089532 40 16.07 15.5390663778461 0.530933622153883 41 15.82 15.7602798101487 0.0597201898513191 42 15.87 16.4891132425697 -0.619113242569734 43 15.72 16.2004574328931 -0.480457432893106 44 17.07 16.2699718125737 0.800028187426346 45 16.83 16.8126915729787 0.0173084270212485 46 17.52 17.1630666712953 0.356933328704734 47 17.76 17.8127925057252 -0.0527925057251615 48 17.36 17.6467393251675 -0.286739325167499 49 17.95 17.6790504077276 0.270949592272448 50 16.71 17.1652612012099 -0.455261201209886 51 17.14 16.8850875160411 0.254912483958851 52 16.72 17.4481302730138 -0.728130273013786 53 17.26 16.8069269908387 0.453073009161255 54 17.24 17.5417926427331 -0.301792642733119 55 17.69 17.4635355855551 0.226464414444894 56 18.13 18.3124262795372 -0.182426279537186 57 18.08 18.0710453193624 0.0089546806375509 58 18.18 18.4996859804297 -0.319685980429693 59 18.18 18.6185665064751 -0.438566506475077 60 17.64 18.1200759135896 -0.480075913589573 61 17.89 18.1479474344342 -0.257947434434232 62 16.82 17.0558357886584 -0.235835788658363 63 16.61 17.0330312119843 -0.423031211984252 64 16.66 16.8454850184927 -0.185485018492692 65 17.02 16.7716605178769 0.248339482123114 66 16.91 17.0952578583092 -0.185257858309193 67 17.18 17.1573146607440 0.0226853392560216 68 18.06 17.6921602125943 0.367839787405742 69 17.58 17.7460347472905 -0.16603474729051 70 17.48 17.9125826769409 -0.432582676940886 71 17.54 17.8603081356006 -0.320308135600616 72 17.44 17.3449842139328 0.0950157860672505 73 17.79 17.7046421423112 0.0853578576887912 74 16.79 16.7701605779739 0.0198394220261022 75 16.19 16.8049462408868 -0.614946240886802 76 16.62 16.5430042751156 0.0769957248843589 77 16.39 16.7119065360177 -0.32190653601765 78 16.54 16.5477077371023 -0.00770773710234351 79 17.26 16.7268981953042 0.533101804695839 80 18 17.6202191052574 0.379780894742595 81 17.29 17.5037383242314 -0.213738324231358 82 18.16 17.5423029498674 0.617697050132616 83 17.82 18.1151123980704 -0.295112398070394 84 17.48 17.7455839947709 -0.265583994770950 85 18.31 17.9026206639317 0.407379336068335 86 17.04 17.1383760214255 -0.0983760214254765 87 17.03 16.9315941866410 0.0984058133590189 88 16.97 17.2952292466832 -0.325229246683243 89 17.11 17.1439955058378 -0.0339955058378081 90 17.12 17.2570812991928 -0.137081299192847 91 17.69 17.5434047504660 0.146595249533977 92 18.5 18.1882239328409 0.311776067159077 93 18.27 17.8703830973402 0.399616902659787 94 18.45 18.5164476564008 -0.0664476564008467 95 18.35 18.4523736719747 -0.102373671974746 96 18.03 18.2095487333393 -0.179548733339342 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 18.62257809115 17.9861831339668 19.2589730483332 98 17.4875384905696 16.7492998889955 18.2257770921436 99 17.3957563588290 16.5580030921750 18.233509625483 100 17.5833029663163 16.6471100324796 18.5194959001530 101 17.7076602463500 16.6733334060261 18.7419870866739 102 17.8226585680239 16.6900020867522 18.9553150492955 103 18.2841151081918 17.0525920494332 19.5156381669505 104 18.9078469264473 17.5766809748438 20.2390128780507 105 18.4444812569794 17.0127243980959 19.876238115863 106 18.7230598851572 17.1896390231492 20.2564807471652 107 18.6757345524730 17.0394845529365 20.3119845520096 108 18.4611773561199 16.7208650206992 20.2014896915405

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/1weou1219057201.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/1weou1219057201.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/2ta0t1219057201.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/2ta0t1219057201.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/3xhmp1219057201.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/18/t1219057293rgd83u2b6esmq6o/3xhmp1219057201.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=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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