exponential smoothing sigaretten

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 13:14:26 -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/Jun/01/t1212347744x2o6u9mr4xqsi9n.htm/, Retrieved Sun, 01 Jun 2008 19:15:48 +0000

IsPrivate?

No (this computation is public)

User-defined keywords:

Pieter Van den Broeck

Dataseries X:

» Textbox « » Textfile « » CSV «

3,42 3,42 3,43 3,47 3,51 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,58 3,6 3,61 3,61 3,61 3,63 3,68 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,78 3,79 3,79 3,8 3,8 3,8 3,8 3,81 3,95 3,99 4 4,06 4,16 4,19 4,2 4,2 4,2 4,2 4,2 4,23 4,38 4,43 4,44 4,44 4,44 4,44 4,44 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,46 4,46 4,46 4,48 4,58 4,67 4,68 4,68

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 5 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0133505095885232 gamma 0.182841778177839 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.52 3.45581517555378 0.0641848244462229 14 3.52 3.52380859542702 -0.00380859542701817 15 3.58 3.58088492117983 -0.00088492117983252 16 3.6 3.59836328021342 0.00163671978657876 17 3.61 3.60796895564939 0.00203104435060508 18 3.61 3.60800393057758 0.00199606942241637 19 3.61 3.60803827305581 0.00196172694419161 20 3.63 3.62806131377734 0.00193868622266313 21 3.68 3.68058615382746 -0.000586153827464297 22 3.69 3.6939388529079 -0.00393885290790008 23 3.69 3.69513643007025 -0.00513643007025255 24 3.69 3.69170921824993 -0.00170921824992520 25 3.69 3.65840160180003 0.0315983981999706 26 3.69 3.69374601018515 -0.00374601018515452 27 3.69 3.75357878779703 -0.06357878779703 28 3.69 3.70805653637266 -0.0180565363726641 29 3.69 3.69710470670963 -0.00710470670963392 30 3.78 3.68681276388549 0.0931872361145092 31 3.79 3.77771284933819 0.0122871506618125 32 3.79 3.8088315338865 -0.0188315338865013 33 3.8 3.84247400128342 -0.0424740012834248 34 3.8 3.81363378002641 -0.0136337800264061 35 3.8 3.80443826153263 -0.00443826153262661 36 3.8 3.80092262746532 -0.000922627465318904 37 3.81 3.76664304499707 0.0433569550029262 38 3.95 3.81316364541698 0.136836354583018 39 3.99 4.01877459680042 -0.0287745968004227 40 4 4.01064055664128 -0.0106405566412846 41 4.06 4.00890378862378 0.0510962113762181 42 4.16 4.05828907644146 0.101710923558538 43 4.19 4.15925767840314 0.0307423215968576 44 4.2 4.21276346876571 -0.0127634687657103 45 4.2 4.26019111284203 -0.0601911128420314 46 4.2 4.21696998416558 -0.0169699841655779 47 4.2 4.20677751344434 -0.00677751344433997 48 4.2 4.20286158827441 -0.00286158827440541 49 4.23 4.16492757082015 0.0650724291798479 50 4.38 4.2354723180376 0.144527681962399 51 4.43 4.45816783639808 -0.0281678363980777 52 4.44 4.45485694713161 -0.0148569471316131 53 4.44 4.45178434056866 -0.0117843405686591 54 4.44 4.43934482207659 0.000655177923412076 55 4.44 4.43935609444684 0.000643905553164181 56 4.44 4.463961995146 -0.0239619951460019 57 4.45 4.50336866093698 -0.0533686609369823 58 4.45 4.46781904733247 -0.0178190473324742 59 4.45 4.45702233899632 -0.00702233899632176 60 4.45 4.45287588359192 -0.00287588359192181 61 4.45 4.41268779084348 0.0373122091565152 62 4.45 4.45529936755093 -0.00529936755092919 63 4.45 4.52745566587846 -0.0774556658784604 64 4.45 4.47254845055493 -0.0225484505549263 65 4.46 4.45932974742805 0.00067025257195219 66 4.46 4.45699869883460 0.00300130116540309 67 4.46 4.45705033637724 0.00294966362276039 68 4.48 4.48179412180944 -0.00179412180944105 69 4.58 4.54186555634101 0.0381344436589872 70 4.67 4.59717232476696 0.0728276752330368 71 4.68 4.67710341619496 0.00289658380503965 72 4.68 4.68286106835216 -0.00286106835216504 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4.64059992568602 4.55862409128053 4.7225757600915 74 4.64558380173449 4.52901440415609 4.7621531993129 75 4.72595080642824 4.5808297668084 4.87107184604809 76 4.75021678722236 4.58165403249301 4.91877954195171 77 4.76073490086412 4.57149020831253 4.94997959341571 78 4.75807896584948 4.55027420653588 4.96588372516308 79 4.75544378271132 4.53032249412197 4.98056507130067 80 4.77916057239087 4.53651400875596 5.02180713602578 81 4.84565930333957 4.58415105589113 5.10716755078800 82 4.86391973579169 4.58659364198154 5.14124582960184 83 4.87064898509691 4.57863565547355 5.16266231472026 84 4.87293189698833 -0.260607629144876 10.0064714231215

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/1xo6r1212347660.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/1xo6r1212347660.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/245vi1212347660.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/245vi1212347660.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/3ehmr1212347660.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212347744x2o6u9mr4xqsi9n/3ehmr1212347660.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')

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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