Bierprijzen - Quinten Bollaerts - triple

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 May 2008 11:52:53 -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/May/25/t1211738212qeuc2k34huhw7nk.htm/, Retrieved Sun, 25 May 2008 19:56:56 +0200

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Dataseries X:

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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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.910118454309823 beta 0.000748304930753182 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.41 0.407890277777778 0.00210972222222183 14 0.41 0.410350036361519 -0.000350036361519312 15 0.41 0.410570884874142 -0.000570884874142252 16 0.41 0.410173679614221 -0.000173679614221101 17 0.41 0.409721193241008 0.000278806758992112 18 0.41 0.409680712946643 0.000319287053356931 19 0.41 0.409677291964427 0.000322708035573382 20 0.41 0.409677204260315 0.000322795739684967 21 0.41 0.409677416216122 0.000322583783877783 22 0.42 0.419677654961474 0.000322345038525573 23 0.42 0.419677895952116 0.000322104047884297 24 0.42 0.419678136980441 0.000321863019558666 25 0.42 0.417784669608979 0.00221533039102056 26 0.42 0.420121945245926 -0.000121945245926514 27 0.42 0.420533176840395 -0.000533176840395111 28 0.42 0.42020866081545 -0.000208660815449846 29 0.42 0.41976765279113 0.000232347208870221 30 0.42 0.419691140804208 0.000308859195791766 31 0.42 0.419681143187661 0.00031885681233923 32 0.42 0.419680162142441 0.000319837857558902 33 0.42 0.419680264855018 0.000319735144982181 34 0.42 0.429680489433479 -0.00968048943347943 35 0.42 0.420572732014195 -0.000572732014194943 36 0.43 0.419753722639271 0.0102462773607287 37 0.43 0.427064772740365 0.0029352272596353 38 0.43 0.429849589197038 0.000150410802962131 39 0.44 0.43047434775478 0.00952565224521962 40 0.44 0.4393431890663 0.000656810933700125 41 0.44 0.43973955411661 0.000260445883389582 42 0.44 0.43970556418521 0.000294435814789828 43 0.44 0.439693400279331 0.000306599720668654 44 0.44 0.439691405753666 0.000308594246334448 45 0.44 0.43969131230581 0.000308687694190513 46 0.44 0.448792685318849 -0.00879268531884875 47 0.44 0.441322197324049 -0.00132219732404926 48 0.44 0.440803647806101 -0.000803647806101315 49 0.44 0.437403435882562 0.00259656411743775 50 0.44 0.439632101783063 0.000367898216937002 51 0.44 0.441299985587779 -0.00129998558777922 52 0.45 0.43951422094942 0.0104857790505797 53 0.45 0.448822331334183 0.00117766866581731 54 0.46 0.449628648490215 0.0103713515097847 55 0.46 0.458798098314803 0.00120190168519702 56 0.46 0.459621057125485 0.000378942874515287 57 0.46 0.459694988797471 0.000305011202529348 58 0.46 0.467984958925288 -0.00798495892528828 59 0.46 0.461931595366267 -0.00193159536626680 60 0.46 0.460915153179023 -0.000915153179023076 61 0.46 0.457729122223649 0.0022708777763506 62 0.47 0.459470884993879 0.0105291150061207 63 0.47 0.470253513954647 -0.000253513954647178 64 0.47 0.470496944112175 -0.000496944112174658 65 0.47 0.468982827285853 0.00101717271414709 66 0.47 0.470479286400635 -0.000479286400634993 67 0.47 0.468951686175235 0.00104831382476461 68 0.47 0.469563268506101 0.000436731493899445 69 0.47 0.469685564407063 0.000314435592936646 70 0.47 0.477241417769122 -0.00724141776912202 71 0.47 0.472411778048425 -0.00241177804842480 72 0.47 0.471052272746296 -0.00105227274629632 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.468030319355129 0.460579845756487 0.475480792953771 74 0.468448538133936 0.458370947757582 0.47852612851029 75 0.46867305570292 0.456520895843276 0.480825215562563 76 0.469119296205301 0.455195895301801 0.483042697108801 77 0.468187849483929 0.452692166546972 0.483683532420886 78 0.468617665077503 0.451693116881554 0.485542213273451 79 0.467657509931279 0.449413783062142 0.485901236800417 80 0.467253253200636 0.447777731218101 0.48672877518317 81 0.466960002792053 0.446324413573914 0.487595592010192 82 0.473543259821195 0.451807842198528 0.495278677443862 83 0.475735904352389 0.452952170713202 0.498519637991576 84 0.476692880551482 0.452905530724271 0.500480230378693

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/16tk61211737967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/16tk61211737967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/2nsx01211737967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/2nsx01211737967.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/367jt1211737967.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/25/t1211738212qeuc2k34huhw7nk/367jt1211737967.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')

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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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