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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 08:39:13 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr.htm/, Retrieved Thu, 19 May 2011 10:36:43 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

8 8 8.2 8.5 8.7 8.7 8 8 8.3 8.5 8.7 8.6 8.3 7.9 7.9 8.1 8.3 8.1 7.4 7.3 7.7 8 8 7.7 6.9 6.6 6.9 7.5 7.9 7.7 6.5 6.1 6.4 6.8 7.1 7.3 7.2 7 7 7 7.3 7.5 7.2 7.7 8 7.9 8 8 7.9 7.9 8 8.1 8.1 8.2 8 8.3 8.5 8.6 8.7 8.7 8.5 8.4 8.5 8.7 8.7 8.6 7.9 8.1 8.2 8.5 8.6 8.5

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 4 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.947401841274992 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8.2 8 0.199999999999999 4 8.5 8.389480368255 0.110519631745003 5 8.7 8.79418687086725 -0.094186870867249 6 8.7 8.90495405598369 -0.204954055983686 7 8 8.71078020596796 -0.710780205967962 8 8 7.3373857300921 0.662614269907903 9 8.3 7.96514770945793 0.334852290542072 10 8.5 8.58238738607264 -0.0823873860726376 11 8.7 8.70433342480959 -0.00433342480958743 12 8.6 8.90022793016596 -0.300227930165956 13 8.3 8.51579143632455 -0.215791436324549 14 7.9 8.0113502322193 -0.111350232219298 15 7.9 7.50585681718834 0.394143182811663 16 8.1 7.8792687943101 0.220731205689907 17 8.3 8.28838994500756 0.0116100549924418 18 8.1 8.4993893324847 -0.399389332484704 19 7.4 7.9210071435031 -0.521007143503104 20 7.3 6.72740401643084 0.57259598356916 21 7.7 7.16988250557093 0.530117494429073 22 8 8.07211679588512 -0.0721167958851172 23 8 8.3037932106767 -0.303793210676703 24 7.7 8.01597896351475 -0.315978963514753 25 6.9 7.41661991167671 -0.516619911676712 26 6.6 6.12717325611487 0.472826743885128 27 6.9 6.2751301838757 0.6248698161243 28 7.5 7.16713299822903 0.332867001770971 29 7.9 8.08249180860653 -0.182491808606532 30 7.7 8.3095987331151 -0.6095987331151 31 6.5 7.53206377092295 -1.03206377092295 32 6.1 5.35428465403734 0.745715345962664 33 6.4 5.66077674586938 0.73922325413062 34 6.8 6.66111821794602 0.138881782053978 35 7.1 7.19269507398351 -0.0926950739835126 36 7.3 7.40487559021441 -0.104875590214411 37 7.2 7.50551626294048 -0.305516262940476 38 7 7.11606959289121 -0.116069592891215 39 7 6.80610504687004 0.193894953129961 40 7 6.98980148247929 0.010198517520708 41 7.3 6.99946357675669 0.300536423243313 42 7.5 7.5841923375076 -0.0841923375076021 43 7.2 7.70442836193165 -0.504428361931654 44 7.7 6.92653200304628 0.773467996953723 45 8 8.15931700752751 -0.159317007527514 46 7.9 8.30837978124953 -0.408379781249526 47 8 7.82148002455425 0.178519975445753 48 8 8.09061017799592 -0.09061017799592 49 7.9 8.00476592852433 -0.10476592852433 50 7.9 7.8055104949375 0.094489505062504 51 8 7.89503002601488 0.104969973985124 52 8.1 8.09447877264697 0.00552122735302873 53 8.1 8.19970959360733 -0.0997095936073276 54 8.2 8.10524454103096 0.0947554589690363 55 8 8.29501603732908 -0.295016037329084 56 8.3 7.81551730035786 0.484482699642142 57 8.5 8.5745171020647 -0.0745171020647035 58 8.6 8.70391946236213 -0.103919462362127 59 8.7 8.70546597237594 -0.00546597237594071 60 8.7 8.80028750008261 -0.100287500082615 61 8.5 8.70527493784748 -0.205274937847479 62 8.4 8.31079708376317 0.0892029162368324 63 8.5 8.29530809085304 0.204691909146957 64 8.7 8.58923358247296 0.110766417527037 65 8.7 8.89417389038951 -0.194173890389512 66 8.6 8.71021318910696 -0.110213189106959 67 7.9 8.50579701081424 -0.605797010814237 68 8.1 7.23186380732994 0.868136192670057 69 8.2 8.25433763474302 -0.0543376347430158 70 8.5 8.30285805953695 0.197141940463046 71 8.6 8.78963069692417 -0.189630696924169 72 8.5 8.70997422549595 -0.20997422549595 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 8.4110442576408 7.68450259472611 9.13758592055548 74 8.3220885152816 6.73158046301265 9.91259656755054 75 8.23313277292239 5.59625069421178 10.870014851633 76 8.14417703056319 4.30415823452714 11.9841958265992 77 8.05522128820398 2.87303106563711 13.2374115107709 78 7.96626554584478 1.31579274973631 14.6167383419532 79 7.87730980348558 -0.35764077004696 16.1122603770181 80 7.78835406112638 -2.1393622412759 17.7160703635286 81 7.69939831876717 -4.02287946232295 19.4216760998573 82 7.61044257640797 -6.0027398217152 21.2236249745311 83 7.52148683404877 -8.07428037155734 23.1172540396549 84 7.43253109168956 -10.233454400934 25.0985165843131

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/1mx3u1305794346.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/1mx3u1305794346.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/2ou4r1305794346.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/2ou4r1305794346.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/3ft761305794346.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t1305794203cmfmmwmmzvbhqfr/3ft761305794346.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=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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