Nick Vermeulen Exonential smoothing model 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 09:48:16 -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/Jun/05/t1244216931hfmc38psqc5xkkl.htm/, Retrieved Fri, 05 Jun 2009 17:48:51 +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/Jun/05/t1244216931hfmc38psqc5xkkl.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:

maandelijkse verkoop auto's

Dataseries X:

» Textbox « » Textfile « » CSV «

14.620 16.005 16.683 15.487 15.684 15.962 12.000 13.769 14.031 16.078 15.827 13.149 15.969 16.628 16.670 16.487 16.883 16.201 12.168 14.010 16.556 17.404 16.435 13.123 16.744 17.410 16.484 17.103 17.301 17.301 12.843 13.748 16.904 17.342 15.476 15.424 15.988 19.244 18.715 17.780 17.160 17.349 11.171 13.438 16.713 18.369 17.067 14.055 15.500 18.475 19.423 18.686 19.646 19.733 12.605 16.616 19.156 21.348 20.049 18.020 20.262 21.789 20.603 21.928 21.025 19.346 11.786 19.082 20.127 20.217 20.385 16.653 13.065 20.275 21.776 20.260 22.523 23.033 14.133 20.110 19.682 22.197 17.212 11.784 15.467 17.002 15.952 18.767 20.605 19.809 14.233 19.311 20.827 23.388 20.181 14.344

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 0.422497061600848 beta 0.0909939654833242 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 16.683 17.39 -0.707000000000001 4 15.487 18.4491141865388 -2.96211418653884 5 15.684 18.4415717146605 -2.75757171466052 6 15.962 18.4144338655929 -2.45243386559287 7 12 18.4219328184999 -6.42193281849994 8 13.769 16.505440956064 -2.73644095606400 9 14.031 16.0408569708472 -2.00985697084721 10 16.078 15.8059842701906 0.272015729809430 11 15.827 16.545653639023 -0.718653639022998 12 13.149 16.8391396991379 -3.69013969913790 13 15.969 15.7353153791593 0.233684620840727 14 16.628 16.2982792357891 0.329720764210869 15 16.67 16.9144940910722 -0.244494091072188 16 16.487 17.2787053594341 -0.791705359434147 17 16.883 17.3812846132337 -0.498284613233697 18 16.201 17.5886768760961 -1.38767687609613 19 12.168 17.3669547236250 -5.19895472362505 20 14.01 15.3351067131389 -1.32510671313893 21 16.556 14.8890047965905 1.66699520340947 22 17.404 15.7711442500186 1.63285574998144 23 16.435 16.7016345064469 -0.266634506446856 24 13.123 16.8193450319068 -3.69634503190685 25 16.744 15.3459081250599 1.39809187494006 26 17.41 16.0786050408598 1.33139495914022 27 16.484 16.8343077629217 -0.350307762921705 28 17.103 16.8660285555143 0.236971444485693 29 17.301 17.1549833796486 0.146016620351379 30 17.301 17.4111236205358 -0.110123620535756 31 12.843 17.5548116946036 -4.71181169460362 32 13.748 15.5731559718304 -1.82515597183041 33 16.904 14.7409362669464 2.16306373305364 34 17.342 15.6768859680072 1.66511403199276 35 15.476 16.4664681647305 -0.990468164730478 36 15.424 16.0959964518442 -0.671996451844244 37 15.988 15.8342434112602 0.153756588739805 38 19.244 15.9272797272503 3.31672027274969 39 18.715 17.4841691653034 1.23083083469664 40 17.78 18.2070953462707 -0.427095346270672 41 17.16 18.2131330422129 -1.05313304221290 42 17.349 17.9141842851612 -0.565184285161223 43 11.171 17.7996641134734 -6.62866411347339 44 13.438 14.8685046404258 -1.43050464042579 45 16.713 14.0785569729848 2.63444302701516 46 18.369 15.1073180777597 3.26168192224026 47 17.067 16.5264801003672 0.540519899632798 48 14.055 16.8167392805015 -2.76173928050145 49 15.5 15.6056294691062 -0.105629469106244 50 18.475 15.5126573568552 2.96234264314479 51 19.423 16.8297807710755 2.59321922892450 52 18.686 18.0906461187292 0.595353881270832 53 19.646 18.5303074187872 1.11569258121283 54 19.733 19.2327027382628 0.500297261737202 55 12.605 19.6943291131904 -7.08932911319039 56 16.616 16.6768136353391 -0.0608136353391231 57 19.156 16.6264873333610 2.52951266663903 58 21.348 17.7678125952709 3.58018740472914 59 20.049 19.4906840167211 0.55831598327892 60 18.02 19.9582879230864 -1.93828792308639 61 20.262 19.2965671501876 0.965432849812373 62 21.789 19.8987756314555 1.89022436854452 63 20.603 20.9643748887044 -0.361374888704443 64 21.928 21.0647871328082 0.863212867191827 65 21.025 21.7157700505258 -0.690770050525792 66 19.346 21.6836433160837 -2.33764331608373 67 11.786 20.8658475097668 -9.07984750976678 68 19.082 16.8504183833403 2.23158161665973 69 20.127 17.6998272732658 2.42717272673416 70 20.217 18.725184718636 1.49181528136400 71 20.385 19.4127087574372 0.972291242562768 72 16.653 19.9181148450569 -3.26511484505695 73 13.065 18.50770300654 -5.44270300654 74 20.275 15.9680235764518 4.30697642354823 75 21.776 17.7131354005906 4.06286459940941 76 20.26 19.5113062380879 0.748693761912065 77 22.523 19.9380329294702 2.58496707052975 78 23.033 21.2399579377352 1.79304206226475 79 14.133 22.2762298907614 -8.14322989076142 80 20.11 18.801392248294 1.30860775170598 81 19.682 19.3702372467355 0.311762753264453 82 22.197 19.529903782697 2.66709621730300 83 17.212 20.7872274550166 -3.57522745501657 84 11.784 19.2697392319153 -7.4857392319153 85 15.467 15.8122844016269 -0.345284401626868 86 17.002 15.3583764062496 1.64362359375035 87 15.952 15.8079647828127 0.144035217187284 88 18.767 15.6295188649385 3.13748113506152 89 20.605 16.8364145192089 3.76858548079106 90 19.809 18.4548319794322 1.35416802056776 91 14.233 19.1052257175672 -4.8722257175672 92 19.311 16.9376752235585 2.37332477644154 93 20.827 17.9225902417305 2.90440975826947 94 23.388 19.2435462167605 4.14445378323948 95 20.181 21.2477493606671 -1.06674936066707 96 14.344 21.0092236478139 -6.66522364781392 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 18.1491165886616 12.3720431912434 23.9261899860799 98 18.1050469356232 11.7437905312065 24.4663033400399 99 18.0609772825848 11.0760819970093 25.0458725681603 100 18.0169076295464 10.3721205698262 25.6616946892666 101 17.972837976508 9.6345972158375 26.3110787371785 102 17.9287683234696 8.86577288267193 26.9917637642672 103 17.8846986704312 8.06755518845824 27.7018421524041 104 17.8406290173928 7.24156428666193 28.4396937481236 105 17.7965593643543 6.38918708815525 29.2039316405534 106 17.7524897113159 5.51162094245375 29.9933584801781 107 17.7084200582775 4.60990846731831 30.8069316492367 108 17.6643504052391 3.6849652213371 31.6437355891411

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/11zb91244216891.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/11zb91244216891.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/2jm7j1244216891.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/2jm7j1244216891.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/35qap1244216891.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244216931hfmc38psqc5xkkl/35qap1244216891.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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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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