*The author of this computation has been verified*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 21 Dec 2009 03:03:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7.htm/, Retrieved Mon, 21 Dec 2009 11:05:52 +0100

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/Dec/21/t1261389948vskc4804ohc0ca7.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:

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43.9 51 51.9 54.3 50.3 57.2 48.8 41.1 58 63 53.8 54.7 55.5 56.1 69.6 69.4 57.2 68 53.3 47.9 60.8 61.7 57.8 51.4 50.5 48.1 58.7 54 56.1 60.4 51.2 50.7 56.4 53.3 52.6 47.7 49.5 48.5 55.3 49.8 57.4 64.6 53 41.5 55.9 58.4 53.5 50.6 58.5 49.1 61.1 52.3 58.4 65.5 61.7 45.1 52.1 59.3 57.9 45 64.9 63.8 69.4 71.1 62.9 73.5 62.7 51.9 73.3 66.7 62.5 70.3

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.319439681255854 beta 0.0705399226443017 gamma 0.308746635913248 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 55.5 50.5034777049332 4.99652229506683 14 56.1 52.9309038757646 3.16909612423542 15 69.6 67.4102660445945 2.1897339554055 16 69.4 68.8274364483586 0.572563551641409 17 57.2 57.5918281764854 -0.391828176485433 18 68 69.248561695987 -1.24856169598704 19 53.3 56.1312008204423 -2.83120082044229 20 47.9 46.4814253585955 1.41857464140452 21 60.8 65.9179045817852 -5.11790458178524 22 61.7 68.8827932795695 -7.18279327956947 23 57.8 56.4544812920705 1.34551870792954 24 51.4 57.6349180982275 -6.23491809822752 25 50.5 57.3730444907888 -6.87304449078883 26 48.1 55.1563646158473 -7.05636461584727 27 58.7 64.9441678879978 -6.24416788799776 28 54 62.3658765867787 -8.36587658677867 29 56.1 48.7761673107149 7.32383268928515 30 60.4 60.5812181735006 -0.181218173500596 31 51.2 48.3280490784913 2.87195092150872 32 50.7 41.688885699362 9.01111430063799 33 56.4 60.7141894843056 -4.31418948430564 34 53.3 62.7446818597275 -9.44468185972755 35 52.6 51.6333498470826 0.966650152917438 36 47.7 50.7075133651127 -3.00751336511274 37 49.5 50.7747339240367 -1.27473392403672 38 48.5 49.9777604796206 -1.47776047962063 39 55.3 61.0194842702603 -5.71948427026027 40 49.8 57.9313000808969 -8.13130008089692 41 57.4 47.8093138730616 9.5906861269384 42 64.6 58.3507597333908 6.24924026660916 43 53 48.8096136500295 4.19038634997052 44 41.5 43.7468642303466 -2.24686423034662 45 55.9 55.0929349540346 0.80706504596536 46 58.4 57.2817254961368 1.11827450386321 47 53.5 51.7743610363699 1.72563896363014 48 50.6 50.2839122436732 0.316087756326816 49 58.5 51.9361574108268 6.56384258917316 50 49.1 53.8659092798134 -4.76590927981338 51 61.1 63.885962510168 -2.78596251016796 52 52.3 61.3344169240577 -9.03441692405772 53 58.4 54.4880109454729 3.91198905452712 54 65.5 63.0051935973981 2.49480640260189 55 61.7 51.4539162676409 10.2460837323591 56 45.1 46.563595653662 -1.46359565366196 57 52.1 60.0928581605871 -7.99285816058714 58 59.3 59.6462840826926 -0.346284082692634 59 57.9 53.6351964446657 4.26480355533431 60 45 52.613709154218 -7.61370915421795 61 64.9 52.8537509133028 12.0462490866972 62 63.8 54.0552589378758 9.74474106212422 63 69.4 70.8485591519473 -1.44855915194728 64 71.1 67.3137414561448 3.78625854385518 65 62.9 67.6864678546306 -4.78646785463059 66 73.5 74.8326800239706 -1.33268002397057 67 62.7 62.2198322090803 0.480167790919722 68 51.9 50.8106024538952 1.08939754610485 69 73.3 65.3671257035642 7.93287429643581 70 66.7 73.0028707355137 -6.30287073551372 71 62.5 65.4940084963394 -2.99400849633942 72 70.3 59.0328442493523 11.2671557506477 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 71.9384766955216 66.1375266354273 77.7394267556158 74 68.3892260677253 61.6013235595086 75.177128575942 75 81.63616829656 73.0948811584049 90.1774554347152 76 79.5133680743804 70.1295471867329 88.897188962028 77 76.5570609841261 66.4524146244619 86.6617073437904 78 87.8347188118313 75.5501329540012 100.119304669661 79 74.0646523776854 62.4505820643615 85.6787226910093 80 60.6744010060357 49.8513256550424 71.497476357029 81 79.2564786397212 64.6812395447585 93.8317177346838 82 81.6107921174738 65.6542065948934 97.567377640054 83 76.1003539510147 60.1578349976111 92.0428729044182 84 73.1360659535527 56.301878217142 89.9702536899635

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/1qld11261389785.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/1qld11261389785.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/259641261389785.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/259641261389785.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/3llyp1261389785.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/21/t1261389948vskc4804ohc0ca7/3llyp1261389785.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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