sven van roy - tweede zittijd - oefening 10 - exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 12 Aug 2008 11:56:58 -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/12/t1218564013okbgbp8ivq6y3r8.htm/, Retrieved Tue, 12 Aug 2008 18:00:13 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0.22 0.22 0.2 0.21 0.21 0.19 0.19 0.18 0.18 0.19 0.18 0.17 0.17 0.17 0.18 0.2 0.2 0.2 0.22 0.23 0.25 0.25 0.27 0.29 0.3 0.31 0.33 0.31 0.33 0.33 0.35 0.37 0.47 0.45 0.45 0.4 0.34 0.35 0.34 0.35 0.36 0.37 0.36 0.35 0.36 0.33 0.3 0.28 0.28 0.28 0.3 0.32 0.32 0.3 0.3 0.31 0.33 0.34 0.31 0.33 0.35 0.38 0.4 0.32 0.29 0.3 0.3 0.32 0.32 0.32 0.32 0.32 0.33 0.31 0.33 0.35 0.37 0.37 0.38 0.42 0.42 0.49 0.45 0.41 0.4 0.42 0.47 0.49 0.47 0.52 0.56 0.57 0.61 0.52 0.5 0.5

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 0.83737132434265 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.17 0.134891830662001 0.0351081693379985 14 0.17 0.161389029111555 0.00861097088844537 15 0.18 0.173910336936671 0.00608966306332939 16 0.2 0.193490203311895 0.00650979668810495 17 0.2 0.192888339035334 0.00711166096466626 18 0.2 0.190719486221453 0.00928051377854672 19 0.22 0.208212716898111 0.0117872831018890 20 0.23 0.21711978540548 0.0128802145945200 21 0.25 0.235649258661315 0.0143507413386849 22 0.25 0.237296882407610 0.0127031175923895 23 0.27 0.257805345885542 0.0121946541144582 24 0.29 0.276715473621816 0.0132845263781843 25 0.3 0.263269548564177 0.0367304514358226 26 0.31 0.28145180020167 0.0285481997983298 27 0.33 0.314109284432197 0.0158907155678029 28 0.31 0.353827019841738 -0.0438270198417379 29 0.33 0.307629975437068 0.0223700245629319 30 0.33 0.313584387247704 0.0164156127522964 31 0.35 0.343767091826548 0.00623290817345185 32 0.37 0.34758302428794 0.0224169757120602 33 0.47 0.378889826561482 0.0911101734385179 34 0.45 0.435653961626064 0.0143460383739363 35 0.45 0.465059653523729 -0.0150596535237292 36 0.4 0.467182926739026 -0.0671829267390257 37 0.34 0.380628044534449 -0.0406280445344492 38 0.35 0.330121590745779 0.0198784092542206 39 0.34 0.354137170417545 -0.0141371704175446 40 0.35 0.358765416588651 -0.0087654165886506 41 0.36 0.35262622047609 0.0073737795239101 42 0.37 0.343733272995158 0.0262667270048416 43 0.36 0.382092491501809 -0.0220924915018093 44 0.35 0.364675206780122 -0.0146752067801224 45 0.36 0.372599752807644 -0.0125997528076440 46 0.33 0.337340719319497 -0.00734071931949676 47 0.3 0.340424742763661 -0.0404247427636607 48 0.28 0.309817961589425 -0.0298179615894248 49 0.28 0.265887004812966 0.0141129951870344 50 0.28 0.272150079304594 0.00784992069540646 51 0.3 0.280123802536317 0.0198761974636835 52 0.32 0.311876638534903 0.00812336146509651 53 0.32 0.322143195592592 -0.00214319559259202 54 0.3 0.309446099328076 -0.00944609932807572 55 0.3 0.308314099477698 -0.00831409947769773 56 0.31 0.303198202666792 0.00680179733320813 57 0.33 0.326978205973748 0.00302179402625158 58 0.34 0.307655516355138 0.0323444836448624 59 0.31 0.337909363988388 -0.0279093639883883 60 0.33 0.319302701106274 0.0106972988937265 61 0.35 0.314291089935469 0.0357089100645311 62 0.38 0.336075406788497 0.0439245932115032 63 0.4 0.377084470172998 0.0229155298270017 64 0.32 0.413669055208418 -0.0936690552084178 65 0.29 0.337111311878162 -0.0471113118781621 66 0.3 0.286378036561886 0.0136219634381139 67 0.3 0.304664249982951 -0.00466424998295129 68 0.32 0.305053346260721 0.0149466537392786 69 0.32 0.33546157062212 -0.0154615706221201 70 0.32 0.305401729476662 0.0145982705233380 71 0.32 0.31111761684922 0.00888238315077972 72 0.32 0.329853826495010 -0.00985382649500954 73 0.33 0.311461194829065 0.0185388051709350 74 0.31 0.319991437024553 -0.00999143702455285 75 0.33 0.312142136339367 0.0178578636606329 76 0.35 0.322902099726687 0.0270979002733129 77 0.37 0.354701911122237 0.0152980888777633 78 0.37 0.365621940036056 0.00437805996394414 79 0.38 0.374083648065445 0.00591635193455547 80 0.42 0.388372650073959 0.0316273499260407 81 0.42 0.431510554189102 -0.0115105541891018 82 0.49 0.405635752400648 0.084364247599352 83 0.45 0.465159441092324 -0.0151594410923237 84 0.41 0.464074201691166 -0.0540742016911657 85 0.4 0.411377434924934 -0.0113774349249343 86 0.42 0.387630784830203 0.0323692151697968 87 0.47 0.421309490428734 0.0486905095712662 88 0.49 0.457908296043178 0.0320917039568217 89 0.47 0.494619389743961 -0.0246193897439614 90 0.52 0.469298203302501 0.0507017966974992 91 0.56 0.518716010149651 0.0412839898503494 92 0.57 0.572487699832381 -0.00248769983238140 93 0.61 0.58343673930615 0.0265632606938496 94 0.52 0.60181635141335 -0.0818163514133499 95 0.5 0.503511218308032 -0.00351121830803225 96 0.5 0.505386933158921 -0.00538693315892069 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 0.500244807850297 0.441404210307417 0.559085405393177 98 0.490928884086753 0.413537074346859 0.568320693826647 99 0.50089856543236 0.409973832972971 0.591823297891749 100 0.493265748239046 0.389786192803369 0.596745303674722 101 0.493710125559384 0.377864868635846 0.609555382482922 102 0.500915877098268 0.374078854151079 0.627752900045456 103 0.505742465306385 0.367280078269962 0.644204852342808 104 0.516653543810259 0.365866518325424 0.667440569295094 105 0.532604577676636 0.379160460875459 0.686048694477813 106 0.512349331268763 0.355761667461297 0.668936995076228 107 0.495537218062569 0.330091495530655 0.660982940594482 108 0.5 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/1nxw91218563812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/1nxw91218563812.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/2rxxk1218563812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/2rxxk1218563812.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/3mzd11218563812.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Aug/12/t1218564013okbgbp8ivq6y3r8/3mzd11218563812.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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