Single Exponential smoothing

*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: Wed, 08 Dec 2010 11:08:02 +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/08/t1291806453cdgulkk41ezxwn7.htm/, Retrieved Wed, 08 Dec 2010 12:07:40 +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/08/t1291806453cdgulkk41ezxwn7.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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9700 9081 9084 9743 8587 9731 9563 9998 9437 10038 9918 9252 9737 9035 9133 9487 8700 9627 8947 9283 8829 9947 9628 9318 9605 8640 9214 9567 8547 9185 9470 9123 9278 10170 9434 9655 9429 8739 9552 9687 9019 9672 9206 9069 9788 10312 10105 9863 9656 9295 9946 9701 9049 10190 9706 9765 9893 9994 10433 10073 10112 9266 9820 10097 9115 10411 9678 10408 10153 10368 10581 10597 10680 9738 9556

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 0.158806071444759 beta FALSE gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 9081 9700 -619 3 9084 9601.6990417757 -517.699041775693 4 9743 9519.48529076058 223.51470923942 5 8587 9554.980783645 -967.980783645009 6 9731 9401.25955816033 329.740441839675 7 9563 9453.62434232534 109.375657674656 8 9998 9470.99386083234 527.006139167657 9 9437 9554.68563542083 -117.685635420828 10 10038 9535.99644199417 502.003558005834 11 9918 9615.71765489236 302.282345107637 12 9252 9663.72192658602 -411.721926586017 13 9737 9598.33798489722 138.662015102776 14 9035 9620.3583547743 -585.358354774309 15 9133 9527.39989406523 -394.399894065233 16 9487 9464.7667963105 22.2332036894968 17 8700 9468.29756404406 -768.297564044064 18 9627 9346.28724619765 280.712753802352 19 8947 9390.86613583344 -443.866135833439 20 9283 9320.37749855436 -37.3774985543641 21 8829 9314.44172484851 -485.441724848513 22 9947 9237.35063160995 709.649368390048 23 9628 9350.04725990723 277.952740092771 24 9318 9394.18784260867 -76.1878426086678 25 9605 9382.08875063213 222.911249367866 26 8640 9417.48841042509 -777.488410425089 27 9214 9294.01853037165 -80.0185303716498 28 9567 9281.31110192054 285.688898079456 29 8547 9326.68023347992 -779.680233479925 30 9185 9202.86227861785 -17.8622786178457 31 9470 9200.02564032349 269.974359676507 32 9123 9242.89920777453 -119.899207774533 33 9278 9223.85848561852 54.1415143814793 34 10170 9232.45648681951 937.543513180486 35 9434 9381.34408895622 52.6559110437756 36 9655 9389.70616732743 265.293832672569 37 9429 9431.83643867268 -2.83643867268438 38 8739 9431.38599499018 -692.385994990182 39 9552 9321.43089520242 230.569104797580 40 9687 9358.04666893186 328.953331068142 41 9019 9410.28645512746 -391.286455127456 42 9672 9348.14779037912 323.852209620882 43 9206 9399.57748751772 -193.577487517716 44 9069 9368.83620720488 -299.83620720488 45 9788 9321.22039706178 466.779602938224 46 10312 9395.34783203494 916.65216796506 47 10105 9540.9177617108 564.082238289207 48 9863 9630.49744594527 232.502554054732 49 9656 9667.42026315557 -11.4202631555727 50 9295 9665.60665602897 -370.606656028971 51 9946 9606.75206893373 339.247931066269 52 9701 9660.62670011213 40.3732998878731 53 9049 9667.03822525858 -618.03822525858 54 10190 9568.89000270257 621.109997297426 55 9706 9667.52604130844 38.4739586915566 56 9765 9673.63593954118 91.3640604588218 57 9893 9688.14510705388 204.854892946116 58 9994 9720.6773078189 273.322692181107 59 10433 9764.08261080088 668.917389199121 60 10073 9870.31075350068 202.689246499323 61 10112 9902.49903646133 209.500963538667 62 9266 9935.7690614448 -669.7690614448 63 9820 9829.4056680215 -9.40566802150715 64 10097 9827.9119908337 269.088009166302 65 9115 9870.64480044229 -755.644800442289 66 10411 9750.64381827639 660.356181723611 67 9678 9855.51238925018 -177.512389250178 68 10408 9827.32234408059 580.677655919415 69 10153 9919.5374813929 233.462518607103 70 10368 9956.6127468025 411.38725319751 71 10581 10021.9435403252 559.056459674764 72 10597 10110.725100402 486.274899598 73 10680 10187.9485068494 492.051493150648 74 9738 10266.0892714251 -528.089271425135 75 9556 10182.2254888580 -626.225488857985 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 10082.7770791339 9200.11000863375 10965.444149634 77 10082.7770791339 9189.04915834539 10976.5049999224 78 10082.7770791339 9178.12353470454 10987.4306235632 79 10082.7770791339 9167.32829602245 10998.2258622453 80 10082.7770791339 9156.65888281559 11008.8952754522 81 10082.7770791339 9146.11099530065 11019.4431629671 82 10082.7770791339 9135.68057314564 11029.8735851221 83 10082.7770791339 9125.36377720688 11040.1903810609 84 10082.7770791339 9115.15697301867 11050.3971852491 85 10082.7770791339 9105.0567158346 11060.4974424331 86 10082.7770791339 9095.05973704572 11070.4944212220 87 10082.7770791339 9085.16293182374 11080.391226444

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/1rwas1291806479.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/1rwas1291806479.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/2knsd1291806479.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/2knsd1291806479.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/3knsd1291806479.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/08/t1291806453cdgulkk41ezxwn7/3knsd1291806479.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=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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