Voorspelling Prijzen Jeansbroeken - Stephanie Van Mechelen

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 27 May 2008 14:07:08 -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/May/27/t12119189363uou3qhbzmya0i4.htm/, Retrieved Tue, 27 May 2008 22:08:56 +0200

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Dataseries X:

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47,87 47,87 47,89 47,88 47,91 47,92 47,92 47,91 47,93 48,05 48,03 48,04 48,04 48,06 48,04 48,09 48,12 48,16 48,16 48,16 48,08 48,13 48,16 48,15 48,15 48,15 48,27 48,47 48,51 48,53 48,53 48,53 48,68 48,64 48,67 48,66 48,66 48,67 48,71 48,96 49,01 49,04 49,04 49,04 49,06 49,13 49,19 49,26 49,26 49,26 49,29 49,43 49,43 49,45 49,45 49,46 49,57 49,68 49,71 49,7 49,7 49,8 49,84 50,09 50,2 50,16 50,16 50,29 50,36 51,02 51,03 51,04

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.686758989105527 beta 0.135239935983842 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 48.04 47.9166870771208 0.123312922879236 14 48.06 48.0327197080609 0.0272802919391211 15 48.04 48.0490772950521 -0.00907729505211563 16 48.09 48.1167163506858 -0.0267163506857599 17 48.12 48.1506047560502 -0.0306047560502307 18 48.16 48.1877432868974 -0.0277432868973762 19 48.16 48.1850937169537 -0.0250937169537195 20 48.16 48.1827649173209 -0.0227649173209485 21 48.08 48.0948899595994 -0.0148899595994081 22 48.13 48.1289849731169 0.0010150268830742 23 48.16 48.1474333656456 0.0125666343543784 24 48.15 48.1354110398148 0.0145889601852076 25 48.15 48.2820007051115 -0.132000705111466 26 48.15 48.1708476595438 -0.0208476595438043 27 48.27 48.1165571387527 0.153442861247321 28 48.47 48.2793881633368 0.190611836663173 29 48.51 48.4706042178969 0.0393957821030995 30 48.53 48.5726268733716 -0.0426268733716171 31 48.53 48.5748065685705 -0.0448065685704577 32 48.53 48.5720630313411 -0.0420630313411294 33 48.68 48.4833217284219 0.196678271578065 34 48.64 48.6983388676371 -0.0583388676370689 35 48.67 48.7044607912358 -0.0344607912358228 36 48.66 48.6807465854872 -0.0207465854872382 37 48.66 48.7749629822466 -0.114962982246652 38 48.67 48.7291053898704 -0.0591053898703606 39 48.71 48.7182815292995 -0.00828152929945958 40 48.96 48.7820994464075 0.177900553592465 41 49.01 48.9159112490748 0.0940887509252235 42 49.04 49.0338691100597 0.00613088994034428 43 49.04 49.0772949799023 -0.0372949799022777 44 49.04 49.089731790502 -0.0497317905020296 45 49.06 49.0786790947428 -0.0186790947427511 46 49.13 49.0540186486922 0.0759813513077674 47 49.19 49.1609346963794 0.0290653036205981 48 49.26 49.1916333538096 0.0683666461904338 49 49.26 49.3331170381074 -0.0731170381074406 50 49.26 49.3528147517729 -0.0928147517728704 51 49.29 49.3509763751709 -0.0609763751709096 52 49.43 49.4491397677637 -0.0191397677636616 53 49.43 49.4135672234901 0.0164327765099159 54 49.45 49.435993930666 0.0140060693340018 55 49.45 49.4573072614544 -0.00730726145442873 56 49.46 49.4754044338477 -0.0154044338476922 57 49.57 49.4898382374646 0.0801617625354396 58 49.68 49.5639091785794 0.116090821420649 59 49.71 49.6887645101825 0.0212354898174922 60 49.7 49.7305345292593 -0.0305345292593273 61 49.7 49.7549483236664 -0.0549483236664159 62 49.8 49.7779799529632 0.0220200470368468 63 49.84 49.8728975063549 -0.0328975063549137 64 50.09 50.0150184733096 0.0749815266903937 65 50.2 50.0736081653994 0.126391834600604 66 50.16 50.1995860519914 -0.0395860519914208 67 50.16 50.2011296136076 -0.0411296136076373 68 50.29 50.2142633061215 0.0757366938784685 69 50.36 50.3510366476031 0.00896335239689705 70 51.02 50.4101067828471 0.609893217152887 71 51.03 50.9122143925053 0.117785607494660 72 51.04 51.0805565342605 -0.040556534260503 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 51.1667102378957 50.9590060677814 51.37441440801 74 51.3345495983327 51.0710996416398 51.5979995550257 75 51.4773832859804 51.1575452528444 51.7972213191163 76 51.7640147244579 51.3856748835235 52.1423545653922 77 51.8622813897004 51.4247291258134 52.2998336535875 78 51.9111840908236 51.4130426281402 52.409325553507 79 52.0062082368673 51.4453061945837 52.5671102791509 80 52.156719834895 51.5306141726582 52.7828254971317 81 52.2852994145311 51.5922943417755 52.9783044872868 82 52.5956823679039 51.8314311497854 53.3599335860224 83 52.5260264795629 51.6938969476853 53.3581560114404 84 52.5573982945171 50.6987996975868 54.4159968914474

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/1j0qa1211918821.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/1j0qa1211918821.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/2rfhg1211918821.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/2rfhg1211918821.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/3pqyd1211918821.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t12119189363uou3qhbzmya0i4/3pqyd1211918821.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=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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