Exponential smoothing double - 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: Fri, 30 May 2008 07:34:24 -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/30/t12121545329ifzmz8fbwidxro.htm/, Retrieved Fri, 30 May 2008 13:35:32 +0000

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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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0784142333807304 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 44.14 44.13 0.00999999999999801 4 44.14 44.1407841423338 -0.000784142333806415 5 44.14 44.1407226544138 -0.000722654413841894 6 44.14 44.140665988022 -0.000665988021978592 7 44.15 44.1406137650818 0.00938623491820323 8 44.17 44.1513497794972 0.0186502205027637 9 44.19 44.1728122222403 0.0171877777596521 10 44.26 44.1941599886569 0.0658400113431128 11 44.27 44.2693227826721 0.000677217327869073 12 44.29 44.2793758861497 0.0106241138502625 13 44.29 44.3002089678927 -0.0102089678926518 14 44.29 44.2994084395017 -0.00940843950174042 15 44.29 44.2986706839309 -0.00867068393090165 16 44.32 44.2979907788976 0.0220092211024294 17 44.33 44.3297166150976 0.000283384902374451 18 44.34 44.3397388365075 0.000261163492510263 19 44.34 44.3497593154426 -0.00975931544255104 20 44.34 44.3489940462038 -0.00899404620380295 21 44.37 44.3482887849657 0.0217112150342516 22 44.47 44.3799912532484 0.090008746751586 23 44.51 44.4870492201225 0.0229507798774975 24 44.51 44.5288488879321 -0.0188488879320872 25 44.51 44.5273708668348 -0.0173708668348098 26 44.52 44.5260087436288 -0.00600874362879722 27 44.7 44.5355375726036 0.164462427396430 28 44.84 44.7284337677678 0.111566232232207 29 44.9 44.8771821483395 0.0228178516605411 30 44.91 44.9389713926848 -0.0289713926848165 31 44.94 44.9466996231375 -0.00669962313745742 32 44.94 44.9761742773252 -0.0361742773251947 33 44.95 44.9733376991006 -0.0233376991006367 34 45.28 44.9815076913168 0.298492308683201 35 45.34 45.3349137368722 0.00508626312777238 36 45.34 45.3953125722962 -0.0553125722961667 37 45.34 45.3909752793433 -0.0509752793432483 38 45.36 45.3869780918922 -0.0269780918921825 39 45.44 45.4048626254984 0.0351373745016161 40 45.62 45.4876178957829 0.132382104217065 41 45.75 45.6779985369984 0.0720014630015555 42 45.77 45.813644476522 -0.0436444765219974 43 45.77 45.8302221283542 -0.0602221283542264 44 45.77 45.8254998563268 -0.0554998563267759 45 46.09 45.8211478776402 0.268852122359831 46 46.25 46.1622297107078 0.0877702892922017 47 46.28 46.3291121506563 -0.0491121506562493 48 46.29 46.3552610590129 -0.0652610590128617 49 46.29 46.3601436631008 -0.070143663100751 50 46.29 46.3546434015322 -0.0646434015321944 51 46.3 46.3495744387579 -0.0495744387579222 52 46.34 46.3556870971474 -0.0156870971474348 53 46.34 46.3944570054507 -0.0544570054506579 54 46.35 46.390186801116 -0.040186801116036 55 46.42 46.3970355839145 0.0229644160855074 56 46.52 46.4688363209969 0.0511636790031247 57 46.59 46.5728482816628 0.0171517183371606 58 46.66 46.6441932205074 0.0158067794925785 59 46.67 46.7154326970035 -0.0454326970035339 60 46.72 46.7218701268976 -0.00187012689759314 61 46.72 46.7717234823306 -0.0517234823305941 62 46.72 46.7676676251159 -0.0476676251158565 63 46.76 46.7639298048353 -0.00392980483531602 64 46.89 46.8036216522018 0.0863783477981812 65 47.02 46.9403949441251 0.0796050558748931 66 47.02 47.0766371135548 -0.0566371135547712 67 47.04 47.0721959577145 -0.0321959577144781 68 47.18 47.0896713363723 0.0903286636276661 69 47.22 47.236754389283 -0.0167543892830011 70 47.8 47.2754406066916 0.524559393308387 71 47.88 47.8965735293805 -0.016573529380544 72 47.91 47.9752739287798 -0.0652739287797672 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 48.0001555236947 47.8192439480288 48.1810670993607 74 48.0903110473895 47.8242432386827 48.3563788560962 75 48.1804665710842 47.8419525692102 48.5189805729583 76 48.270622094779 47.864998577563 48.676245611995 77 48.3607776184737 47.89065987663 48.8308953603175 78 48.4509331421685 47.9176086841675 48.9842576001694 79 48.5410886658632 47.9450972361929 49.1370800955335 80 48.631244189558 47.9726657211762 49.2898226579398 81 48.7213997132527 48.0000143034797 49.4427851230258 82 48.8115552369475 48.0269392779606 49.5961711959344 83 48.9017107606422 48.053298144275 49.7501233770095 84 48.991866284337 48.0789891345624 49.9047434341116

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/18tcw1212154457.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/18tcw1212154457.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/2dsog1212154457.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/2dsog1212154457.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/3j8ef1212154457.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/30/t12121545329ifzmz8fbwidxro/3j8ef1212154457.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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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Software written by Ed van Stee & Patrick Wessa

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