*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 31 May 2010 20:29:45 +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/May/31/t1275337831r18zpwocgzb0jaq.htm/, Retrieved Mon, 31 May 2010 22:30:31 +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/May/31/t1275337831r18zpwocgzb0jaq.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

1 1 3 3 1 1 -2 1 1 -1 -4 -2 -1 -5 -4 -5 0 -2 -4 -6 -2 -2 -2 1 -2 0 -1 2 3 2 3 4 5 5 4 5 6 4 6 6 3 5 5 5 3 5 5 6 6 5 4 4 0 2 3 3 2 3 5 6 6 5 4 7 5 6 5 6 5 6 6 6 6

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 0.427178567563865 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 -1 1.35890151515151 -2.35890151515151 14 -5 -3.27377065511514 -1.72622934488486 15 -4 -2.5945121672831 -1.40548783271690 16 -5 -4.02823977972488 -0.97176022027512 17 0 0.514978414695782 -0.514978414695782 18 -2 -1.91334266015361 -0.0866573398463941 19 -4 -4.90869415179142 0.908694151791417 20 -6 -1.18718615234217 -4.81281384765783 21 -2 -2.70145041106951 0.701450411069507 22 -2 -3.77680582925175 1.77680582925175 23 -2 -5.64279246027286 3.64279246027286 24 1 -1.92000292849439 2.92000292849439 25 -2 -0.815536271769387 -1.18446372823061 26 0 -4.58410561169167 4.58410561169167 27 -1 -1.02547966381930 0.0254796638192989 28 2 -1.59948015861429 3.59948015861429 29 3 5.15812836103317 -2.15812836103317 30 2 2.27324033745255 -0.273240337452547 31 3 -0.231656744617019 3.23165674461702 32 4 1.20476867980059 2.79523132019941 33 5 6.09918700935527 -1.09918700935527 34 5 4.87062450823519 0.129375491764812 35 4 3.36976808037334 0.630231919626659 36 5 5.39162698075596 -0.391626980755959 37 6 2.73030984685418 3.26969015314582 38 4 4.16881973408876 -0.168819734088759 39 6 3.08581919561187 2.91418080438813 40 6 5.7930739991211 0.206926000878902 41 3 7.80337453365337 -4.80337453365337 42 5 4.86819829684822 0.131801703151781 43 5 4.54400666057947 0.455993339420527 44 5 4.54473433075936 0.455265669240639 45 3 6.20876319934777 -3.20876319934777 46 5 4.78278189494878 0.217218105051216 47 5 3.60635124525436 1.39364875474564 48 6 5.36898277665246 0.631017223347541 49 6 5.24179825423168 0.75820174576832 50 5 3.63780196209796 1.36219803790204 51 4 4.97482818702663 -0.97482818702663 52 4 4.47000812582455 -0.470008125824545 53 0 3.32112938065024 -3.32112938065024 54 2 3.84611122637495 -1.84611122637495 55 3 2.8627014955762 0.137298504423799 56 3 2.7268727375774 0.273127262422599 57 2 2.21426171745076 -0.214261717450755 58 3 4.02994278494165 -1.02994278494165 59 5 2.99463642265813 2.00536357734187 60 6 4.58172772949405 1.41827227050595 61 6 4.8636957107426 1.1363042892574 62 5 3.76719874277495 1.23280125722505 63 4 3.71025072648220 0.289749273517804 64 7 4.03480280402931 2.96519719597069 65 5 2.72018678626889 2.27981321373111 66 6 6.48269327847014 -0.482693278470141 67 5 7.21784607675214 -2.21784607675214 68 6 6.1537556538837 -0.153755653883697 69 5 5.1796025474472 -0.179602547447201 70 6 6.542849672042 -0.542849672041998 71 6 7.45430758632294 -1.45430758632294 72 6 7.22720303786996 -1.22720303786996 73 6 6.21756336344099 -0.217563363440993 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 74 4.59799868233956 0.787740974744536 8.4082563899346 75 3.47422400272556 -0.669125158557696 7.61757316400881 76 5.20755531200641 0.755968994037727 9.65914162997509 77 2.23366796905158 -2.50615262041647 6.97348855851963 78 3.43986419232116 -1.57164034168503 8.45136872632735 79 3.38728050246528 -1.88191831408965 8.65647931902021 80 4.45296162244616 -1.06190325734946 9.96782650224179 81 3.52968398139548 -2.22036063725076 9.27972860004171 82 4.76157772670089 -1.21439847727130 10.7375539306731 83 5.38282675822359 -0.810845017424619 11.5764985338718 84 5.9070615940509 -0.496909715884875 12.3110329039867 85 6 -0.607581025799065 12.6075810257991

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/1fay41275337781.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/1fay41275337781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/2fay41275337781.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/2fay41275337781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/3fay41275337781.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/31/t1275337831r18zpwocgzb0jaq/3fay41275337781.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=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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