Exponential smoothing - prijzen jeans dames - Kim Liekens

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 12:40:52 -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/t1211913763f0as1va93eeyt1w.htm/, Retrieved Tue, 27 May 2008 20:42:46 +0200

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Dataseries X:

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44,13 44,13 44,14 44,14 44,14 44,14 44,15 44,17 44,19 44,26 44,27 44,29 44,29 44,29 44,29 44,32 44,33 44,34 44,34 44,34 44,37 44,47 44,51 44,51 44,51 44,52 44,7 44,84 44,9 44,91 44,94 44,94 44,95 45,28 45,34 45,34 45,34 45,36 45,44 45,62 45,75 45,77 45,77 45,77 46,09 46,25 46,28 46,29 46,29 46,29 46,3 46,34 46,34 46,35 46,42 46,52 46,59 46,66 46,67 46,72 46,72 46,72 46,76 46,89 47,02 47,02 47,04 47,18 47,22 47,8 47,88 47,91

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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0554345114806499 gamma 0.226961583618481 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 44.29 44.1360821455646 0.153917854435385 14 44.29 44.3119882486531 -0.0219882486530594 15 44.29 44.3111790454529 -0.0211790454528895 16 44.32 44.3383445236373 -0.0183445236372748 17 44.33 44.34482465423 -0.0148246542299972 18 44.34 44.3535834613256 -0.0135834613256378 19 44.34 44.3536578284509 -0.0136578284509383 20 44.34 44.3524791104286 -0.0124791104285720 21 44.37 44.373880698356 -0.00388069835599936 22 44.47 44.4615845819808 0.00841541801923285 23 44.51 44.4953847023959 0.0146152976041023 24 44.51 44.4941282860512 0.0158717139488331 25 44.51 44.6017747283616 -0.0917747283616066 26 44.52 44.5223338901019 -0.00233389010188034 27 44.7 44.5326158133203 0.167384186679712 28 44.84 44.7504378060978 0.0895621939021751 29 44.9 44.8726682186245 0.0273317813754801 30 44.91 44.9337466748532 -0.0237466748532142 31 44.94 44.9331359147389 0.00686408526105708 32 44.94 44.9630723152294 -0.0230723152294203 33 44.95 44.9841863840214 -0.0341863840214316 34 45.28 45.050977146829 0.229022853170967 35 45.34 45.3261047074384 0.0138952925615925 36 45.34 45.3440000690773 -0.00400006907727857 37 45.34 45.4525612249642 -0.112561224964246 38 45.36 45.370575491329 -0.0105754913289928 39 45.44 45.3903992055403 0.0496007944597423 40 45.62 45.5022017493742 0.117798250625754 41 45.75 45.6656111638139 0.0843888361860508 42 45.77 45.7998275020901 -0.0298275020901144 43 45.77 45.8086933990125 -0.0386933990124589 44 45.77 45.8061034374659 -0.0361034374659184 45 46.09 45.8269096148947 0.263090385105308 46 46.25 46.2217304918789 0.0282695081211273 47 46.28 46.314035460906 -0.0340354609060398 48 46.29 46.2983734682822 -0.0083734682821941 49 46.29 46.4189795289091 -0.128979528909142 50 46.29 46.3344920667427 -0.0444920667426629 51 46.3 46.3324471881525 -0.0324471881525383 52 46.34 46.3702769810044 -0.0302769810043699 53 46.34 46.3850689182122 -0.0450689182122161 54 46.35 46.3821305842786 -0.0321305842786401 55 46.42 46.3807542743367 0.0392457256632852 56 46.52 46.4524513503818 0.0675486496182529 57 46.59 46.5793350399431 0.0106649600569284 58 46.66 46.7107800096162 -0.050780009616247 59 46.67 46.7079647570146 -0.0379647570145636 60 46.72 46.6717364439285 0.0482635560714684 61 46.72 46.836453112982 -0.116453112982015 62 46.72 46.7519460283806 -0.031946028380581 63 46.76 46.7506045782366 0.00939542176342911 64 46.89 46.8210353335481 0.0689646664518975 65 47.02 46.9310781005829 0.0889218994171372 66 47.02 47.06553479511 -0.0455347951100009 67 47.04 47.0532779655913 -0.0132779655912998 68 47.18 47.0720784094503 0.107921590549658 69 47.22 47.2415122454647 -0.0215122454646774 70 47.8 47.3419934386011 0.458006561398875 71 47.88 47.8763705114335 0.0036294885664816 72 47.91 47.9112640024059 -0.00126400240590385 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 48.0561471486564 47.8739959778825 48.2382983194303 74 48.1221938988121 47.8574042571190 48.3869835405052 75 48.1886491290919 47.8554771960401 48.5218210621437 76 48.2859304805044 47.8907040426763 48.6811569183325 77 48.3587062561167 47.9052092662277 48.8122032460058 78 48.4310026884861 47.9214156655291 48.9405897114432 79 48.4932479312096 47.9290255865006 49.0574702759186 80 48.554986044924 47.9369757478775 49.1729963419704 81 48.6408953554413 47.9692825361845 49.3125081746982 82 48.7903704125354 48.0644902158295 49.5162506092412 83 48.8667512425608 48.0876668632559 49.6458356218657 84 48.8968931528134 46.5406070256654 51.2531792799615

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/1gxf21211913641.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/1gxf21211913641.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/2lapz1211913641.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/2lapz1211913641.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/3wq541211913641.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/27/t1211913763f0as1va93eeyt1w/3wq541211913641.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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