exponential smoothing- ihuur nietsociale woning-olivier bosiers

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 19 Aug 2009 03:43:33 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36.htm/, Retrieved Wed, 19 Aug 2009 11:44:34 +0200

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/2009/Aug/19/t1250675074yjmqar8uey12t36.htm/}, year = {2009}, } @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 = {2009}, 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:

Dataseries X:

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102,2 102,4 102,4 102,5 102,5 102,6 102,8 102,9 102,9 103,1 103,2 103,3 103,6 103,7 103,8 104 104 104,1 104,2 104,3 104,4 104,5 104,7 104,7 104,9 105 105,2 105,3 105,4 105,5 105,7 105,8 105,9 106 106,1 106,2 106,6 106,8 107 107,1 107,3 107,4 107,6 107,7 107,9 108,2 108,3 108,5 108,92 109,23 109,41 109,65 109,91 110,01 110,2 110,49 110,57 110,72 110,94 111,09 111,28 111,41 111,62 111,76 111,89 112,04 112,12 112,3 112,47 112,59 112,78 112,73 112,99 113,1 113,33 113,38 113,68 113,65 113,81 113,88 114,02 114,25 114,28 114,38 114,73 114,97 115,05 115,29 115,37 115,54 115,76 115,92 116,02 116,21 116,26 116,51

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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.846107257208812 beta 0.0470191847945091 gamma 0.383076569353457 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 103.6 102.869284019506 0.730715980494367 14 103.7 103.620358668199 0.0796413318009428 15 103.8 103.819530923376 -0.0195309233760952 16 104 104.034039230561 -0.0340392305605519 17 104 104.03487490211 -0.0348749021100048 18 104.1 104.133615423051 -0.0336154230506907 19 104.2 104.269707049563 -0.0697070495629362 20 104.3 104.343029328404 -0.0430293284039323 21 104.4 104.335813744886 0.0641862551144357 22 104.5 104.616246080153 -0.116246080152990 23 104.7 104.633729749252 0.0662702507485022 24 104.7 104.808257117621 -0.108257117620596 25 104.9 105.081542298681 -0.181542298680569 26 105 105.004477949696 -0.00447794969601034 27 105.2 105.105809878778 0.0941901212221126 28 105.3 105.400754181454 -0.100754181454008 29 105.4 105.324963794677 0.0750362053225473 30 105.5 105.502270990402 -0.00227099040216672 31 105.7 105.649967803123 0.0500321968774102 32 105.8 105.817798259421 -0.0177982594209283 33 105.9 105.829497006814 0.0705029931860253 34 106 106.098669181665 -0.0986691816651302 35 106.1 106.135313429479 -0.0353134294793875 36 106.2 106.202818306406 -0.00281830640589931 37 106.6 106.558006518396 0.0419934816037824 38 106.8 106.682564441141 0.117435558859199 39 107 106.900122973572 0.099877026428345 40 107.1 107.197390404024 -0.0973904040235993 41 107.3 107.140864687014 0.159135312986479 42 107.4 107.395636415119 0.00436358488083499 43 107.6 107.563939713598 0.0360602864022752 44 107.7 107.726706048313 -0.0267060483128603 45 107.9 107.744867751482 0.155132248518456 46 108.2 108.090845601655 0.109154398344955 47 108.3 108.329145797695 -0.0291457976945964 48 108.5 108.425621244396 0.074378755604215 49 108.92 108.879320476131 0.0406795238688886 50 109.23 109.031907870880 0.198092129119829 51 109.41 109.344968499889 0.0650315001114166 52 109.65 109.629846022794 0.0201539772058084 53 109.91 109.717627909634 0.19237209036622 54 110.01 110.023941713478 -0.0139417134775499 55 110.2 110.211787012894 -0.0117870128943025 56 110.49 110.360667396763 0.129332603237160 57 110.57 110.556058135053 0.0139418649465171 58 110.72 110.812667543877 -0.092667543876857 59 110.94 110.894900823338 0.0450991766624469 60 111.09 111.085850380536 0.00414961946357550 61 111.28 111.507141263227 -0.227141263227026 62 111.41 111.454498797205 -0.0444987972049233 63 111.62 111.557024101364 0.062975898636239 64 111.76 111.841759096411 -0.08175909641065 65 111.89 111.850743885063 0.0392561149365918 66 112.04 112.007441613573 0.0325583864265582 67 112.12 112.229960908603 -0.109960908603099 68 112.3 112.294804361104 0.00519563889550057 69 112.47 112.362629746186 0.107370253813556 70 112.59 112.682630414063 -0.0926304140631515 71 112.78 112.762523123765 0.0174768762346247 72 112.73 112.915768525520 -0.185768525519819 73 112.99 113.147052434465 -0.157052434464575 74 113.1 113.147926783101 -0.0479267831010048 75 113.33 113.237175053830 0.092824946170424 76 113.38 113.524224418429 -0.144224418428891 77 113.68 113.468619829236 0.211380170763562 78 113.65 113.759015207191 -0.109015207191050 79 113.81 113.837127504860 -0.0271275048595072 80 113.88 113.965671097104 -0.0856710971041537 81 114.02 113.944508997233 0.075491002767464 82 114.25 114.208362893174 0.041637106826002 83 114.28 114.395636229815 -0.115636229814953 84 114.38 114.405734508492 -0.0257345084923486 85 114.73 114.765810354900 -0.0358103548997093 86 114.97 114.868678191532 0.101321808467731 87 115.05 115.091395109796 -0.0413951097961984 88 115.29 115.245273664701 0.0447263352987477 89 115.37 115.370738575217 -0.0007385752172695 90 115.54 115.454643826653 0.0853561733471082 91 115.76 115.702984395919 0.0570156040805614 92 115.92 115.903123998771 0.0168760012288089 93 116.02 115.984657942668 0.0353420573318886 94 116.21 116.219760167804 -0.00976016780424516 95 116.26 116.358445224737 -0.0984452247368353 96 116.51 116.392813158478 0.117186841522269 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 116.888266642542 116.675873826554 117.10065945853 98 117.041579647035 116.744386770874 117.338772523197 99 117.177890715279 116.809827050053 117.545954380504 100 117.382485556277 116.950166844580 117.814804267973 101 117.474233041144 116.981978573018 117.966487509271 102 117.570750089386 117.021068314577 118.120431864195 103 117.750192749921 117.144380703015 118.356004796827 104 117.901975676058 117.241257461976 118.56269389014 105 117.970499911358 117.256058984311 118.684940838404 106 118.174075675467 117.405600602066 118.942550748868 107 118.316191837995 117.494319792615 119.138063883375 108 118.450737262555 116.895360912129 120.00611361298

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/1oicr1250675008.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/1oicr1250675008.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/2buh01250675008.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/2buh01250675008.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/3iacw1250675008.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250675074yjmqar8uey12t36/3iacw1250675008.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')

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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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