*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 03 Jun 2010 11:16:31 +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/Jun/03/t1275563907lrw6sh97olh64xt.htm/, Retrieved Thu, 03 Jun 2010 13:18:31 +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/2010/Jun/03/t1275563907lrw6sh97olh64xt.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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

77 70 67 76 85 106 108 120 108 111 109 104 104 117 111 110 116 118 115 111 112 97 106 93 95 97 81 71 75 70 72 80 78 80 81 99 87 100 95 128 112 104 102 108 103 99 96 85 78 74 106 100 109 87 107 106 109 83 84 83 65 68 61 75 66 78 68 68 174 64 48 45

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.573314480838667 beta 0.0612762739836527 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 67 63 4 4 76 58.4337802241813 17.5662197758187 5 85 62.2623821010106 22.7376178989894 6 106 69.8546070036565 36.1453929963435 7 108 86.403511972476 21.5964880275239 8 120 95.3700160891765 24.6299839108235 9 108 106.940932825455 1.05906717454477 10 111 105.035507309207 5.96449269079287 11 109 106.151969335143 2.84803066485692 12 104 105.581771508089 -1.58177150808878 13 104 102.416335405109 1.58366459489058 14 117 101.121324706291 15.8786752937094 15 111 108.579677641436 2.42032235856384 16 110 108.407189267267 1.5928107327329 17 116 107.816232852183 8.18376714781692 18 118 111.291467639703 6.70853236029654 19 115 114.156603561511 0.843396438488796 20 111 113.688801129271 -2.68880112927089 21 112 111.101479551963 0.898520448036791 22 97 110.602386922525 -13.6023869225255 23 106 101.311854435472 4.68814556452767 24 93 102.672246335831 -9.67224633583125 25 95 95.4598260318778 -0.459826031877768 26 97 93.5128657387581 3.48713426124188 27 81 93.9512599693995 -12.9512599693995 28 71 84.5102995335033 -13.5102995335033 29 75 74.2742090263183 0.725790973681683 30 70 72.2253728118176 -2.22537281181764 31 72 68.4064130368351 3.59358696316488 32 80 68.0497919413389 11.9502080586611 33 78 72.9039604137127 5.0960395862873 34 80 74.007561648709 5.99243835129106 35 81 75.8355990824591 5.16440091754092 36 99 77.3703390395948 21.6296609604052 37 87 89.1047134411431 -2.10471344114313 38 100 87.1578875108047 12.8421124891953 39 95 94.2314441275182 0.768555872481755 40 128 94.4100557105232 33.5899442894768 41 112 114.585678618271 -2.58567861827107 42 104 113.930456682489 -9.93045668248864 43 102 108.715504468623 -6.71550446862338 44 108 105.107811379386 2.89218862061426 45 103 107.10995211551 -4.10995211550997 46 99 104.953279188854 -5.95327918885415 47 96 101.530658035858 -5.53065803585783 48 85 98.156036511712 -13.1560365117120 49 78 89.9474959553871 -11.9474959553871 50 74 82.012106795492 -8.01210679549206 51 106 76.0514633083575 29.9485366916425 52 100 92.9063157549265 7.09368424507348 53 109 96.9073555443104 12.0926444556896 54 87 104.199193167075 -17.1991931670749 55 107 94.0933785612837 12.9066214387163 56 106 101.701080461554 4.29891953844636 57 109 104.524885731809 4.47511426819088 58 83 107.606919330432 -24.6069193304317 59 84 93.1513467045852 -9.15134670458518 60 83 87.2351856011425 -4.23518560114248 61 65 83.9887463421642 -18.9887463421642 62 68 71.6167914849716 -3.61679148497156 63 61 67.9307409809361 -6.93074098093612 64 75 62.1012743248275 12.8987256751725 65 66 68.0934677023753 -2.09346770237528 66 78 65.4168747924803 12.5831252075197 67 68 71.5966375536399 -3.59663755363991 68 68 68.3739560812232 -0.373956081223227 69 174 66.9857472718381 107.014252728162 70 64 130.924225897852 -66.9242258978518 71 48 92.7901694014725 -44.7901694014725 72 45 65.7723835994909 -20.7723835994909 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 51.7945964112031 12.2380686036375 91.3511242187687 74 49.725917542039 3.42271836520779 96.0291167188702 75 47.6572386728749 -5.18286480304995 100.497342148800 76 45.5885598037109 -13.6807573404367 104.857876947858 77 43.5198809345468 -22.132040063258 109.171801932352 78 41.4512020653827 -30.5759253366122 113.478329467378 79 39.3825231962187 -39.0388465094208 117.803892901858 80 37.3138443270546 -47.5392604093633 122.166949063473 81 35.2451654578906 -56.090390439128 126.580721354909 82 33.1764865887265 -64.7018900215527 131.054863199006 83 31.1078077195624 -73.3809003425036 135.596515781628 84 29.0391288503984 -82.1327493535649 140.211007054362

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/1gbrk1275563789.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/1gbrk1275563789.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/2gbrk1275563789.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/2gbrk1275563789.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/382851275563789.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/03/t1275563907lrw6sh97olh64xt/382851275563789.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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