Double Smoothing - Gem. prijs gebakken tong of forel - Niels Braspennincx

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 18 Aug 2009 16:37:21 -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/t1250635120lvngcyyyy0quyui.htm/, Retrieved Wed, 19 Aug 2009 00:38:40 +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/t1250635120lvngcyyyy0quyui.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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15.22 15.27 15.31 15.33 15.42 15.49 15.65 15.67 15.69 15.83 15.92 15.99 15.94 15.96 16.03 16.09 16.04 16.23 16.2 16.2 16.26 16.28 16.27 16.29 16.3 16.37 16.39 16.42 16.43 16.37 16.37 16.39 16.48 16.51 16.5 16.54 16.52 16.56 16.61 16.75 16.75 16.79 16.82 16.84 17.14 17.25 17.28 17.3 17.34 17.44 17.48 17.55 17.59 17.66 17.67 17.64 17.68 17.72 17.78 17.83 17.88 18.11 18.16 18.27 18.29 18.35 18.35 18.38 18.41 18.41 18.42 18.43 18.48 18.54 18.65 18.66 18.69 18.72 18.72 18.73 18.84 18.83 18.91 18.91 18.94 18.97 19 19.08 19.18 19.24 19.23 19.25 19.3 19.33 19.35 19.35 19.31 19.47 19.7 19.76 19.9 19.97 20.1 20.26 20.44 20.43 20.57 20.6 20.69 20.93 20.98 21.11 21.14 21.16 21.32 21.32 21.48 21.58 21.74 21.75 21.81 21.89 22.21 22.37 22.47 22.51 22.55 22.61 22.58 22.85 22.93 22.98

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 0.980728633093982 beta 0.0666957327863417 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 15.31 15.32 -0.00999999999999801 4 15.33 15.3595386095206 -0.0295386095205714 5 15.42 15.3779830125307 0.042016987469319 6 15.49 15.4693523869480 0.0206476130520272 7 15.65 15.5411147729383 0.108885227061711 8 15.67 15.7065365413768 -0.0365365413768028 9 15.69 15.7269491473039 -0.0369491473039094 10 15.83 15.7445402397307 0.0854597602693374 11 15.92 15.8877712111323 0.0322287888676556 12 15.99 15.9809051431629 0.00909485683710365 13 15.94 16.0519458640137 -0.111945864013743 14 15.96 15.9969560587501 -0.0369560587500857 15 16.03 16.0130935915646 0.0169064084353785 16 16.09 16.0831614433864 0.00683855661361221 17 16.04 16.1438027774779 -0.103802777477863 18 16.23 16.0891452044848 0.140854795515171 19 16.2 16.2836436892374 -0.0836436892374302 20 16.2 16.2524989134944 -0.0524989134944427 21 16.26 16.2484647353831 0.0115352646168887 22 16.28 16.3079852356862 -0.0279852356861880 23 16.27 16.3269163238720 -0.0569163238719632 24 16.29 16.3137509451312 -0.0237509451312476 25 16.3 16.3315582437749 -0.0315582437748745 26 16.37 16.3396444632744 0.0303555367256330 27 16.39 16.410436868344 -0.0204368683439853 28 16.42 16.4300789233815 -0.0100789233815313 29 16.43 16.4592200450642 -0.0292200450641538 30 16.37 16.4676776253735 -0.0976776253735459 31 16.37 16.4026077625241 -0.0326077625240622 32 16.39 16.3992208900486 -0.0092208900485744 33 16.48 16.4181670508050 0.0618329491950327 34 16.51 16.510842265057 -0.00084226505699192 35 16.5 16.5419950092000 -0.0419950091999652 36 16.54 16.5300411678582 0.00995883214181248 37 16.52 16.5696913576613 -0.0496913576613132 38 16.56 16.547590566036 0.0124094339639989 39 16.61 16.5872055051191 0.0227944948809444 40 16.75 16.6384963681662 0.111503631833784 41 16.75 16.7840803206555 -0.0340803206554732 42 16.79 16.7846567145073 0.00534328549273155 43 16.82 16.8242464742492 -0.00424647424916458 44 16.84 16.8541535183854 -0.0141535183854096 45 17.14 16.8734186531588 0.266581346841246 46 17.25 17.1854457050555 0.0645542949445179 47 17.28 17.3035615657101 -0.0235615657101143 48 17.3 17.3337185070034 -0.0337185070034458 49 17.34 17.3517087036146 -0.0117087036145769 50 17.44 17.3905186734572 0.049481326542832 51 17.48 17.4925760520314 -0.0125760520314486 52 17.55 17.5329493777626 0.0170506222373561 53 17.59 17.6034937195266 -0.0134937195265827 54 17.66 17.6431997209515 0.0168002790484714 55 17.67 17.7137148274121 -0.0437148274120744 56 17.64 17.7220216312360 -0.0820216312359676 57 17.68 17.6873947867817 -0.0073947867817381 58 17.72 17.7254729294101 -0.00547292941011079 59 17.78 17.7650779060084 0.0149220939915935 60 17.83 17.8256609263878 0.00433907361222197 61 17.88 17.8761486962615 0.00385130373848597 62 18.11 17.9264100116290 0.183589988371036 63 18.16 18.1649548987916 -0.00495489879162747 64 18.27 18.2182643145049 0.0517356854950961 65 18.29 18.3305558621057 -0.0405558621057125 66 18.35 18.3496816706170 0.000318329383031113 67 18.35 18.4089147911328 -0.058914791132807 68 18.38 18.4062026534025 -0.0262026534025352 69 18.41 18.4338583193649 -0.0238583193648516 70 18.41 18.4622525582762 -0.0522525582762121 71 18.42 18.4593818925585 -0.0393818925585343 72 18.43 18.4665578713074 -0.0365578713073837 73 18.48 18.4741121830295 0.00588781697050322 74 18.54 18.5236793211477 0.0163206788522885 75 18.65 18.5845458080128 0.0654541919871505 76 18.66 18.6978803239053 -0.0378803239053127 77 18.69 18.7073939535739 -0.0173939535738796 78 18.72 18.7358614074955 -0.0158614074955281 79 18.72 18.7647943719934 -0.0447943719933797 80 18.73 18.7624219313129 -0.0324219313129213 81 18.84 18.7700627654917 0.0699372345083269 82 18.83 18.8826647879735 -0.0526647879735016 83 18.91 18.8715826709029 0.0384173290971042 84 18.91 18.9523402874399 -0.0423402874398739 85 18.94 18.9511271013324 -0.0111271013323595 86 18.97 18.9797977522564 -0.00979775225636459 87 19 19.0091312588429 -0.00913125884289556 88 19.08 19.0385211351748 0.0414788648252191 89 19.18 19.1202589586681 0.0597410413319146 90 19.24 19.2238147078611 0.0161852921388608 91 19.23 19.2857127733580 -0.0557127733579534 92 19.25 19.2734541517403 -0.0234541517402604 93 19.3 19.2912983382119 0.00870166178807352 94 19.33 19.3412478310387 -0.0112478310386948 95 19.35 19.3708965597402 -0.0208965597401516 96 19.35 19.3897156512896 -0.0397156512896260 97 19.31 19.3874805036809 -0.0774805036808708 98 19.47 19.343140252119 0.126859747881003 99 19.7 19.507500284894 0.192499715106017 100 19.76 19.7488267992252 0.0111732007747598 101 19.9 19.8130520527106 0.0869479472894206 102 19.97 19.9572790710707 0.0127209289292693 103 20.1 20.0295416084144 0.0704583915855892 104 20.26 20.1630376412105 0.0969623587894723 105 20.44 20.3288692216472 0.111130778352791 106 20.43 20.5158652871499 -0.0858652871498506 107 20.57 20.5040451865536 0.065954813446389 108 20.6 20.6454335374001 -0.0454335374001111 109 20.69 20.6746083166489 0.015391683351055 110 20.93 20.7644429078959 0.165557092104077 111 20.98 21.0123781732829 -0.0323781732829325 112 21.11 21.0640747866594 0.0459252133406345 113 21.14 21.1955697606224 -0.0555697606223831 114 21.16 21.2238908664094 -0.0638908664093876 115 21.32 21.2398720974152 0.0801279025848132 116 21.32 21.4023378582256 -0.082337858225582 117 21.48 21.4000830420475 0.0799169579524701 118 21.58 21.5621835713258 0.0178164286741840 119 21.74 21.6645457134013 0.0754542865987027 120 21.75 21.8283704492821 -0.0783704492820938 121 21.81 21.8362086186070 -0.0262086186070505 122 21.89 21.8934890722139 -0.00348907221392025 123 22.21 21.9728230138385 0.237176986161511 124 22.37 22.3036988949831 0.0663011050168869 125 22.47 22.4713286895681 -0.00132868956812970 126 22.51 22.5725450980175 -0.0625450980174911 127 22.55 22.6096337210773 -0.0596337210773115 128 22.61 22.6456769484295 -0.0356769484294546 129 22.58 22.7028816246766 -0.122881624676566 130 22.85 22.6665244399411 0.183475560058941 131 22.93 22.9426217307278 -0.0126217307277905 132 22.98 23.0255752009248 -0.0455752009248016 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 133 23.0732291665405 22.9409847934510 23.2054735396300 134 23.1655800366621 22.9741951087339 23.3569649645904 135 23.2579309067838 23.0166094153225 23.4992523982451 136 23.3502817769055 23.0631200811052 23.6374434727057 137 23.4426326470271 23.1117925451177 23.7734727489365 138 23.5349835171488 23.1616663420245 23.9083006922730 139 23.6273343872704 23.2121921096343 24.0424766649066 140 23.7196852573921 23.2630267242867 24.1763437904974 141 23.8120361275137 23.3139426831825 24.3101295718449 142 23.9043869976354 23.3647825578127 24.4439914374581 143 23.9967378677570 23.4154339171926 24.5780418183215 144 24.0890887378787 23.4658145412411 24.7123629345162

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/1gzvl1250635035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/1gzvl1250635035.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/2f6o31250635035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/2f6o31250635035.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/36q9c1250635035.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/19/t1250635120lvngcyyyy0quyui/36q9c1250635035.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

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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