Exponential smoothing triple additive

*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: Sat, 18 Dec 2010 13:01:41 +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/Dec/18/t1292677160i7aaoeaxv4xr6x1.htm/, Retrieved Sat, 18 Dec 2010 13:59:20 +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/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1.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:

Dataseries X:

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37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.380859354911949 beta 0.0316088853012832 gamma 0.733581043314767 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 80 65.9535256410256 14.0464743589744 14 42 32.4467148172594 9.55328518274057 15 54 47.1353051316088 6.86469486839122 16 66 60.5908949080094 5.40910509199063 17 81 79.7238940940242 1.27610590597584 18 63 69.423164327768 -6.42316432776798 19 137 111.487769948459 25.5122300515414 20 72 80.189065931405 -8.18906593140491 21 107 86.4563236715524 20.5436763284476 22 58 68.1223642893237 -10.1223642893237 23 36 97.1537646423697 -61.1537646423697 24 52 157.471510088703 -105.471510088703 25 79 65.8538039157979 13.1461960842021 26 77 28.6504949782513 48.3495050217487 27 54 56.0480501431283 -2.04805014312831 28 84 64.4949190767417 19.5050809232583 29 48 86.335926809278 -38.335926809278 30 96 56.1913729959147 39.8086270040853 31 83 129.66480326721 -46.6648032672097 32 66 53.9973913310618 12.0026086689382 33 61 79.6754118037346 -18.6754118037346 34 53 30.6746061226883 22.3253938773117 35 30 47.4750331631063 -17.4750331631063 36 74 103.414328539598 -29.4143285395985 37 69 94.669052063968 -25.669052063968 38 59 58.2346826816616 0.765317318338404 39 42 43.6095578051338 -1.60955780513378 40 65 61.0081831412311 3.99181685876892 41 70 49.478803349939 20.521196650061 42 100 76.7603341378024 23.2396658621976 43 63 103.965837074185 -40.9658370741847 44 105 56.501549428838 48.498450571162 45 82 81.9715413639335 0.0284586360665458 46 81 58.7674302672506 22.2325697327494 47 75 57.5054384585557 17.4945615414443 48 102 121.8113910067 -19.8113910066999 49 121 119.011021546427 1.9889784535731 50 98 106.036128029636 -8.03612802963619 51 76 87.7937238475087 -11.7937238475087 52 77 104.548576897231 -27.5485768972311 53 63 88.825394332414 -25.825394332414 54 37 99.4433230770021 -62.4433230770021 55 35 63.5759025308791 -28.5759025308791 56 23 60.3350961492459 -37.3350961492459 57 40 28.9375786540567 11.0624213459433 58 29 17.9911476535468 11.0088523464532 59 37 8.13783623184112 28.8621637681589 60 51 57.8014044626901 -6.80140446269012 61 20 67.986280314366 -47.986280314366 62 28 28.9516752372214 -0.95167523722138 63 13 9.31321056571043 3.68678943428957 64 22 22.6070517338614 -0.607051733861354 65 25 16.0505737046134 8.94942629538664 66 13 21.8230856739734 -8.82308567397342 67 16 20.9469405271601 -4.94694052716012 68 13 22.1988348561951 -9.19883485619508 69 16 23.3093821664561 -7.30938216645614 70 17 4.93082348471587 12.0691765152841 71 9 3.19217990983177 5.80782009016823 72 17 27.2017554894693 -10.2017554894693 73 25 16.6693885648016 8.33061143519844 74 14 20.4077763690549 -6.40777636905491 75 8 0.693902625599549 7.30609737440045 76 7 13.3553977851453 -6.35539778514529 77 10 8.82028766465281 1.17971233534719 78 7 3.33822505002736 3.66177494997264 79 10 8.90454913922404 1.09545086077596 80 3 10.526306643243 -7.52630664324296 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 13.1518860780322 -37.4465989189017 63.750371074966 82 6.4665766273601 -47.8972220237316 60.8303752784518 83 -2.75000728511186 -60.8467257368931 55.3467111666694 84 11.6688643515531 -50.1402534266439 73.47798212975 85 13.4546037022275 -52.0555460762892 78.9647534807443 86 7.24134529397715 -61.9656545585403 76.4483451464945 87 -3.811053389558 -76.7164471374402 69.0943403583242 88 -0.232709452868718 -76.8426607262685 76.377241820531 89 1.05592991449164 -79.2685090912678 81.3803689202511 90 -3.78144524583877 -87.8334001501263 80.2705096584488 91 -0.852758842782082 -88.6478246626031 86.942306977039 92 -3.65473445255916 -95.2106461244973 87.901177219379

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/1oqmu1292677297.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/1oqmu1292677297.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/2zz3x1292677297.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/2zz3x1292677297.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/3zz3x1292677297.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/18/t1292677160i7aaoeaxv4xr6x1/3zz3x1292677297.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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