Exponential smoothing omzet product x

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 30 Jul 2010 13:35:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei.htm/, Retrieved Fri, 30 Jul 2010 15:37:05 +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/2010/Jul/30/t1280497021uo7er8nrfl7omei.htm/}, year = {2010}, } @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 = {2010}, 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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56 55 54 52 72 71 56 46 47 47 48 50 44 38 33 33 52 54 39 22 31 31 38 42 41 31 36 34 51 47 31 19 30 33 36 40 32 25 28 29 55 55 40 38 44 41 49 59 61 47 43 39 66 68 63 68 67 59 68 78 82 70 62 68 94 102 100 104 103 93 110 114 120 102 95 103 122 139 135 135 137 130 148 148 145 128 131 133 146 163 151 157 152 149 172 167 160 150 160 165 171 179 171 176 170 169 194 196 188 174 186 191 197 206 197 204 201 190 213 213

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.653714754766023 beta 0.0529159338485531 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 44 53.1428952991453 -9.14289529914532 14 38 41.0687479080939 -3.06874790809392 15 33 33.8175397197737 -0.817539719773748 16 33 32.6763659327989 0.323634067201063 17 52 51.0423894140582 0.95761058594183 18 54 52.5226449616744 1.47735503832563 19 39 38.0604363504120 0.93956364958796 20 22 28.0708335569269 -6.07083355692687 21 31 24.6634288432478 6.33657115675216 22 31 28.6694551976919 2.33054480230812 23 38 31.0956343846045 6.90436561539552 24 42 37.667289698764 4.332710301236 25 41 31.416643046307 9.5833569536930 26 31 34.4910323904657 -3.49103239046567 27 36 28.5322448681684 7.46775513183162 28 34 34.2779806135972 -0.277980613597194 29 51 53.5249638002933 -2.52496380029329 30 47 53.8428273489417 -6.84282734894171 31 31 34.4017908131469 -3.40179081314695 32 19 19.6428349077232 -0.642834907723216 33 30 24.7643105872425 5.23568941275745 34 33 27.3093812665780 5.69061873342196 35 36 34.278103235232 1.72189676476797 36 40 37.1542705357469 2.84572946425313 37 32 32.2812411328842 -0.281241132884190 38 25 24.5697506826620 0.430249317337953 39 28 25.2950956294347 2.70490437056531 40 29 25.4061617053032 3.59383829469679 41 55 46.701156742188 8.29884325781202 42 55 53.2689503961012 1.73104960389878 43 40 41.5904110003053 -1.59041100030529 44 38 29.9996727347889 8.00032726521112 45 44 44.1346471304973 -0.134647130497271 46 41 44.4685044366325 -3.46850443663246 47 49 44.9005504224267 4.09944957757329 48 59 50.6274577258272 8.3725422741728 49 61 49.3830786942564 11.6169213057436 50 47 51.2060666636596 -4.20606666365965 51 43 51.03797926002 -8.03797926002 52 39 45.4121877876488 -6.41218778764881 53 66 62.4273413023145 3.57265869768548 54 68 64.0997120763742 3.90028792362581 55 63 53.232584846858 9.767415153142 56 68 53.3241672320863 14.6758327679137 57 67 70.1733260239246 -3.17332602392462 58 59 68.4285043070775 -9.42850430707755 59 68 68.4411291716005 -0.441129171600537 60 78 73.3784826571987 4.62151734280127 61 82 71.3747092448876 10.6252907551124 62 70 67.6051093852206 2.39489061477937 63 62 71.1884931498553 -9.1884931498553 64 68 66.0970456716028 1.90295432839717 65 94 93.0166363767962 0.983363623203758 66 102 94.0313323050989 7.96866769490114 67 100 88.9177300284861 11.0822699715139 68 104 92.6763138447618 11.3236861552382 69 103 102.145016234787 0.854983765213376 70 93 101.998622743614 -8.99862274361436 71 110 106.550471988825 3.44952801117455 72 114 117.06491965552 -3.06491965552 73 120 113.130132834069 6.8698671659308 74 102 104.940289415024 -2.94028941502401 75 95 101.725076612879 -6.72507661287882 76 103 102.870264031926 0.129735968074158 77 122 129.036354549051 -7.03635454905111 78 139 127.674052119625 11.3259478803749 79 135 126.396184761247 8.60381523875284 80 135 129.095267284779 5.90473271522131 81 137 131.686012913669 5.31398708633077 82 130 131.486272887244 -1.48627288724373 83 148 145.963429417610 2.03657058239031 84 148 153.953234341842 -5.95323434184226 85 145 152.125556798794 -7.12555679879358 86 128 131.460430191638 -3.46043019163804 87 131 126.647429488925 4.35257051107536 88 133 137.844007656779 -4.84400765677859 89 146 158.541174712991 -12.5411747129909 90 163 160.012459729354 2.98754027064592 91 151 152.126151540346 -1.12615154034631 92 157 146.978514090095 10.0214859099047 93 152 151.646837280606 0.35316271939422 94 149 145.268660755636 3.73133924436351 95 172 163.976400570918 8.02359942908225 96 167 172.920210430047 -5.92021043004689 97 160 170.516252894801 -10.5162528948008 98 150 148.594556534751 1.40544346524877 99 160 149.527095093708 10.4729049062915 100 165 161.610819985528 3.38918001447223 101 171 185.380362895994 -14.3803628959942 102 179 191.318722250232 -12.3187222502323 103 171 171.764514435572 -0.764514435571698 104 176 170.488597391204 5.51140260879649 105 170 168.479652970861 1.52034702913903 106 169 163.693707946539 5.30629205346131 107 194 184.631257883462 9.36874211653821 108 196 189.386296686954 6.61370331304585 109 188 193.778398973095 -5.77839897309511 110 174 179.440103835476 -5.44010383547618 111 186 179.158623217924 6.84137678207557 112 191 186.410841616174 4.58915838382612 113 197 204.848473566369 -7.8484735663692 114 206 216.033667724240 -10.0336677242397 115 197 202.316256529717 -5.31625652971738 116 204 200.422573536797 3.57742646320298 117 201 195.884934298969 5.11506570103097 118 190 195.001892640157 -5.00189264015745 119 213 210.492982524096 2.50701747590352 120 213 209.456406982977 3.54359301702263 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 121 207.092155244158 194.83616965225 219.348140836066 122 196.390141896129 181.511526378341 211.268757413917 123 203.847727131254 186.530975858222 221.164478404285 124 205.540964359967 185.892588125736 225.189340594198 125 216.206117278357 194.290389530211 238.121845026503 126 231.571257682240 207.426886537931 255.715628826548 127 226.199640682604 199.848686708472 252.550594656737 128 231.197991442581 202.651100964909 259.744881920253 129 225.067414671224 194.327104315254 255.807725027195 130 217.373502862963 184.436328866192 250.310676859733 131 238.943930823285 203.801980289545 274.085881357025 132 236.750011493138 199.391961074474 274.108061911802

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/18ehp1280496945.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/18ehp1280496945.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/28ehp1280496945.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/28ehp1280496945.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/3j5ha1280496945.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jul/30/t1280497021uo7er8nrfl7omei/3j5ha1280496945.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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