*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 18 May 2011 14:34:54 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65.htm/, Retrieved Wed, 18 May 2011 16:30:58 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

31.900 31.815 31.075 31.070 31.300 31.410 30.310 31.440 31.355 31.380 31.975 31.905 32.565 32.780 32.850 32.910 32.910 33.755 34.130 34.330 34.120 33.600 33.715 33.535 33.745 34.295 33.940 34.245 34.395 33.640 33.890 33.905 33.930 33.975 33.880 33.800 33.165 33.660 33.545 33.590 33.810 33.720 33.660 33.915 34.265 34.175 33.735 33.855 34.210 33.950 33.130 32.195 33.160 33.255 32.260 31.795 31.875 31.985 31.835 32.200 32.275 32.515 32.700 32.680 32.135 31.460 30.755 31.090 31.270 31.110 30.835 31.025 30.800 30.790

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 3 seconds R Server 'Gwilym Jenkins' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.956867038068198 beta 0.00845972160096074 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 31.075 31.73 -0.655000000000005 4 31.07 31.0129499772333 0.057050022766699 5 31.3 30.9776989608723 0.322301039127687 6 31.41 31.1988668705993 0.211133129400686 7 30.31 31.3153709583438 -1.00537095834381 8 31.44 30.2597040771112 1.18029592288885 9 31.355 31.3049840840989 0.0500159159011311 10 31.38 31.2691412788866 0.110858721113399 11 31.975 31.2924143308485 0.682585669151457 12 31.905 31.8682794682632 0.0367205317367691 13 32.565 31.8264347910645 0.738565208935519 14 32.78 32.4621407102088 0.317859289791251 15 32.85 32.6978600191215 0.152139980878481 16 32.91 32.7762395308556 0.133760469144356 17 32.91 32.838115061727 0.0718849382730014 18 33.755 32.8413658329097 0.913634167090315 19 34.13 33.6574544075908 0.472545592409183 20 34.33 34.0553050399388 0.274694960061218 21 34.12 34.2660625323925 -0.146062532392541 22 33.6 34.0730286981104 -0.473028698110383 23 33.715 33.5633026309837 0.151697369016318 24 33.535 33.6525843095367 -0.117584309536703 25 33.745 33.4832474010771 0.261752598922882 26 34.295 33.6790043191087 0.615995680891338 27 33.94 34.2187111452878 -0.278711145287815 28 34.245 33.9000463817694 0.34495361823064 29 34.395 34.180938213733 0.21406178626701 30 33.64 34.3383167596403 -0.698316759640278 31 33.89 33.6170175941449 0.272982405855096 32 33.905 33.8273323300427 0.0776676699573144 33 33.93 33.8513855395987 0.0786144604013046 34 33.975 33.8769810723168 0.0980189276831638 35 33.88 33.9219375466022 -0.0419375466022345 36 33.8 33.8326348066217 -0.0326348066217079 37 33.165 33.7519693787213 -0.586969378721328 38 33.66 33.1361280541142 0.523871945885752 39 33.545 33.5874548312372 -0.0424548312371869 40 33.59 33.4965385179673 0.0934614820327297 41 33.81 33.536432599493 0.273567400507019 42 33.72 33.7508785790267 -0.0308785790267478 43 33.66 33.673760279063 -0.0137602790629714 44 33.915 33.6129105289797 0.302089471020295 45 34.265 33.8567323562686 0.408267643731364 46 34.175 34.2054574338478 -0.0304574338477721 47 33.735 34.1341343982063 -0.399134398206314 48 33.855 33.7068056030729 0.14819439692706 49 34.21 33.8043972992533 0.405602700746726 50 33.95 34.1515778010873 -0.201577801087261 51 33.13 33.9161355567788 -0.78613555677876 52 32.195 33.1149856314946 -0.91998563149459 53 33.16 32.1783118555314 0.981688144468627 54 33.255 33.0692336303626 0.185766369637413 55 32.26 33.200067840927 -0.940067840927028 56 31.795 32.246018716886 -0.451018716886004 57 31.875 31.7562736603592 0.118726339640805 58 31.985 31.8126599379128 0.172340062087159 59 31.835 31.9217424825531 -0.0867424825531025 60 32.2 31.7822153145465 0.417784685453455 61 32.275 32.128835458899 0.146164541101015 62 32.515 32.2167344171749 0.298265582825053 63 32.7 32.4525882575478 0.247411742452179 64 32.68 32.6417844899949 0.0382155100050952 65 32.135 32.6311170911344 -0.496117091134444 66 31.46 32.105148455985 -0.645148455985037 67 30.755 31.4313542539015 -0.676354253901494 68 31.09 30.7222252805346 0.367774719465402 69 31.27 31.0151659786476 0.254834021352433 70 31.11 31.2021002832427 -0.092100283242651 71 30.835 31.0563190513748 -0.221319051374799 72 31.025 30.7851010997613 0.239898900238735 73 30.8 30.9571493439271 -0.157149343927085 74 30.79 30.7480031137003 0.0419968862996711 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 75 30.7297533045358 29.8762686867608 31.5832379223107 76 30.6713180591696 29.4852657034614 31.8573704148778 77 30.6128828138034 29.1649767257345 32.0607889018723 78 30.5544475684371 28.8818247764431 32.2270703604312 79 30.4960123230709 28.6223740049487 32.3696506411932 80 30.4375770777047 28.3796441021824 32.4955100532271 81 30.3791418323385 28.1494635547661 32.6088201099109 82 30.3207065869723 27.9291072727673 32.7123059011774 83 30.2622713416061 27.7166810820029 32.8078616012093 84 30.2038360962399 27.5108065466281 32.8968656458517 85 30.1454008508737 27.31044443164 32.9803572701074 86 30.0869656055075 27.1147888838497 33.0591423271652

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/1np3g1305729291.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/1np3g1305729291.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/26dbd1305729291.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/26dbd1305729291.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/3tloh1305729291.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/18/t13057290555s95ac4p5o03a65/3tloh1305729291.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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