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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: Mon, 01 Jun 2009 13:09:38 -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/01/t1243883421t2lq1ur04mz4mic.htm/, Retrieved Mon, 01 Jun 2009 21:10:21 +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/01/t1243883421t2lq1ur04mz4mic.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

5,29 5,29 5,29 5,31 5,33 5,34 5,34 5,37 5,41 5,41 5,38 5,44 5,44 5,46 5,46 5,45 5,46 5,46 5,48 5,47 5,48 5,51 5,55 5,58 5,59 5,6 5,6 5,67 5,71 5,7 5,73 5,72 5,75 5,75 5,77 5,83 5,85 5,87 5,86 5,87 5,93 5,97 5,98 5,99 5,99 6,03 6,06 6,07 6,08 6,08 6,1 6,13 6,14 6,14 6,16 6,2 6,19 6,32 6,32 6,33 6,32 6,33 6,38 6,42 6,46 6,47 6,42 6,48 6,47 6,49 6,48 6,51 6,51 6,52 6,57 6,59 6,62 6,63 6,61 6,64

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 0.999944487040144 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 5.29 5.29 0 3 5.29 5.29 0 4 5.31 5.29 0.0199999999999996 5 5.33 5.3099988897408 0.0200011102591979 6 5.34 5.32999888967917 0.0100011103208306 7 5.34 5.33999944480876 5.55191236095709e-07 8 5.37 5.33999999996918 0.0300000000308209 9 5.41 5.3699983346112 0.0400016653887976 10 5.41 5.40999777938916 2.22061084453884e-06 11 5.38 5.40999999987673 -0.0299999998767273 12 5.44 5.38000166538879 0.0599983346112118 13 5.44 5.43999666931486 3.33068514102308e-06 14 5.46 5.4399999998151 0.0200000001848961 15 5.46 5.45999888974079 1.11025920723762e-06 16 5.45 5.45999999993837 -0.00999999993836642 17 5.46 5.4500005551296 0.00999944487040505 18 5.46 5.45999944490122 5.55098782051289e-07 19 5.48 5.45999999996918 0.0200000000308158 20 5.47 5.4799988897408 -0.00999888974080143 21 5.48 5.47000055506796 0.00999944493203575 22 5.51 5.47999944490122 0.0300005550987841 23 5.55 5.50999833458039 0.0400016654196111 24 5.58 5.54999777938915 0.0300022206108466 25 5.59 5.57999833448793 0.0100016655120685 26 5.6 5.58999944477794 0.0100005552220557 27 5.6 5.59999944483958 5.55160420745437e-07 28 5.67 5.59999999996918 0.0700000000308192 29 5.71 5.66999611409281 0.0400038859071916 30 5.7 5.70999777926589 -0.00999777926588763 31 5.73 5.70000055500632 0.0299994449936811 32 5.72 5.72999833464201 -0.00999833464201494 33 5.75 5.72000055503715 0.0299994449628507 34 5.75 5.74999833464202 1.66535798395984e-06 35 5.77 5.74999999990755 0.0200000000924483 36 5.83 5.7699988897408 0.0600011102592024 37 5.85 5.82999666916078 0.0200033308392245 38 5.87 5.8499988895559 0.0200011104441025 39 5.86 5.86999888967916 -0.0099988896791583 40 5.87 5.86000055506796 0.00999944493203841 41 5.93 5.86999944490122 0.0600005550987843 42 5.97 5.92999666919159 0.0400033308084069 43 5.98 5.9699977792967 0.0100022207032984 44 5.99 5.97999944474712 0.0100005552528764 45 5.99 5.98999944483958 5.55160422521794e-07 46 6.03 5.98999999996918 0.0400000000308189 47 6.06 6.0299977794816 0.0300022205183952 48 6.07 6.05999833448794 0.0100016655120641 49 6.08 6.06999944477794 0.0100005552220557 50 6.08 6.07999944483958 5.55160420745437e-07 51 6.1 6.07999999996918 0.0200000000308185 52 6.13 6.0999988897408 0.0300011102591995 53 6.14 6.12999833454957 0.0100016654504289 54 6.14 6.13999944477795 5.55222052334159e-07 55 6.16 6.13999999996918 0.0200000000308229 56 6.2 6.1599988897408 0.0400011102591993 57 6.19 6.19999777941997 -0.00999777941997149 58 6.32 6.19000055500633 0.129999444993672 59 6.32 6.31999278334603 7.21665397129811e-06 60 6.33 6.31999999959938 0.010000000400618 61 6.32 6.32999944487038 -0.0099994448703793 62 6.33 6.32000055509878 0.00999944490121774 63 6.38 6.32999944490122 0.0500005550987828 64 6.42 6.37999722432119 0.0400027756788077 65 6.46 6.41999777932752 0.0400022206724806 66 6.47 6.45999777935833 0.0100022206416703 67 6.42 6.46999944474713 -0.0499994447471268 68 6.48 6.42000277561717 0.0599972243828315 69 6.47 6.47999666937649 -0.00999666937649213 70 6.49 6.4700005549447 0.0199994450552943 71 6.48 6.48999888977161 -0.00999888977160968 72 6.51 6.48000055506797 0.0299994449320327 73 6.51 6.50999833464202 1.66535798218348e-06 74 6.52 6.50999999990755 0.0100000000924485 75 6.57 6.5199994448704 0.0500005551296043 76 6.59 6.56999722432119 0.0200027756788090 77 6.62 6.58999888958672 0.0300011104132833 78 6.63 6.61999833454956 0.0100016654504378 79 6.61 6.62999944477795 -0.0199994447779472 80 6.64 6.61000111022838 0.0299988897716243 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 6.63999833467284 6.59006371065429 6.68993295869139 82 6.63999833467284 6.56938207223987 6.7106145971058 83 6.63999833467284 6.55351222963782 6.72648443970786 84 6.63999833467284 6.54013324463505 6.73986342471062 85 6.63999833467284 6.52834607964687 6.7516505896988 86 6.63999833467284 6.51768964366312 6.76230702568255 87 6.63999833467284 6.50789002403101 6.77210664531466 88 6.63999833467284 6.49876875000743 6.78122791933825 89 6.63999833467284 6.49020185464446 6.78979481470121 90 6.63999833467284 6.48209907795192 6.79789759139375 91 6.63999833467284 6.47439228068584 6.80560438865984 92 6.63999833467284 6.46702852528035 6.81296814406532

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/17in11243883373.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/17in11243883373.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/2s4hh1243883373.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/2s4hh1243883373.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/3ud4m1243883373.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/01/t1243883421t2lq1ur04mz4mic/3ud4m1243883373.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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=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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