Exponential Smoothing Goudkoers Brussel

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 20 May 2011 06:19:33 +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/20/t13058721655llv3399k11piof.htm/, Retrieved Fri, 20 May 2011 08:16:09 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KEYWORD: KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

32819 32700 32242 32810 33865 32226 31077 31293 30236 30160 32436 30695 27525 26434 25739 25204 24977 24320 22680 22052 21467 21383 21777 21928 21814 22937 23595 20830 19650 19195 19644 18483 18079 19178 18391 18441 18584 20108 20148 19394 17745 17696 17032 16438 15683 15594 15713 15937 16171 15928 16348 15579 15305 15648 14954 15137 15839 16050 15168 17064 16005 14886 14931 14544 13812 13031 12574 11964 11451 11346 11353 10702 10646 10556 10463 10407 10625 10872 10805 10653 10574 10431 10383 10296 10872 10635 10297 10570 10662 10709 10413 10846 10371 9924 9828

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 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.7808136475473 beta 0.040561130325825 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 27525 31358.874732906 -3833.874732906 14 26434 27197.8825910096 -763.882591009551 15 25739 25821.2895271255 -82.2895271254602 16 25204 25114.9541306425 89.0458693575347 17 24977 24931.9698936418 45.0301063582083 18 24320 24285.6270157917 34.3729842083449 19 22680 22733.0931941151 -53.0931941150629 20 22052 22554.7914222584 -502.791422258426 21 21467 20786.8103882778 680.189611722151 22 21383 21000.8924940857 382.107505914311 23 21777 23445.7046297082 -1668.70462970819 24 21928 20231.8656440667 1696.13435593329 25 21814 17409.2652438228 4404.73475617721 26 22937 20488.9363630364 2448.06363696365 27 23595 22006.3393366433 1588.6606633567 28 20830 22931.8478594936 -2101.84785949362 29 19650 21248.7379665465 -1598.73796654655 30 19195 19484.725111246 -289.725111246014 31 19644 17817.8377355082 1826.16226449177 32 18483 19225.7119192389 -742.711919238936 33 18079 17739.4878990857 339.512100914253 34 19178 17821.236250045 1356.76374995496 35 18391 20807.438705644 -2416.43870564398 36 18441 17953.4797374407 487.520262559286 37 18584 14948.7817700932 3635.21822990683 38 20108 17142.2737328237 2965.72626717628 39 20148 19035.4455343074 1112.55446569259 40 19394 18925.156313981 468.843686019038 41 17745 19585.8294210866 -1840.8294210866 42 17696 18138.3159405732 -442.315940573171 43 17032 17029.8344763194 2.16552368057819 44 16438 16606.4550023145 -168.455002314546 45 15683 15980.0245178406 -297.024517840551 46 15594 15941.761680242 -347.761680241987 47 15713 16870.0670596217 -1157.06705962173 48 15937 15775.8901210466 161.109878953383 49 16171 13335.8605545791 2835.13944542092 50 15928 14862.1591865244 1065.84081347562 51 16348 14909.7764618431 1438.2235381569 52 15579 14967.0875748674 611.912425132628 53 15305 15292.159061967 12.8409380329704 54 15648 15716.1959526223 -68.1959526222818 55 14954 15126.7495756887 -172.749575688729 56 15137 14653.3494573534 483.650542646583 57 15839 14652.5169707735 1186.48302922649 58 16050 15953.065649406 96.9343505939833 59 15168 17256.8803628696 -2088.88036286957 60 17064 15900.2194087451 1163.78059125491 61 16005 15037.1170064064 967.882993593596 62 14886 14866.4103154479 19.5896845520765 63 14931 14294.3662643574 636.633735642563 64 14544 13634.9267262377 909.073273762297 65 13812 14160.3861779665 -348.3861779665 66 13031 14372.8385288407 -1341.83852884072 67 12574 12813.8894900441 -239.889490044112 68 11964 12477.7047619744 -513.704761974364 69 11451 11866.353210407 -415.353210407 70 11346 11640.7991209495 -294.799120949516 71 11353 12110.6828020543 -757.682802054263 72 10702 12499.5784613486 -1797.57846134858 73 10646 9180.68064850036 1465.31935149964 74 10556 9105.6924858139 1450.3075141861 75 10463 9746.49827189377 716.50172810623 76 10407 9172.14345001842 1234.85654998158 77 10625 9649.68642771466 975.313572285339 78 10872 10693.1983367089 178.801663291084 79 10805 10626.5257435152 178.474256484846 80 10653 10633.6460739117 19.3539260883153 81 10574 10553.6111783373 20.3888216627056 82 10431 10802.0543132899 -371.0543132899 83 10383 11215.8641475573 -832.864147557331 84 10296 11420.6702388144 -1124.67023881438 85 10872 9466.22647251288 1405.77352748712 86 10635 9463.42332375689 1171.57667624311 87 10297 9838.89405343477 458.105946565227 88 10570 9281.35500988771 1288.64499011229 89 10662 9850.67040216997 811.329597830034 90 10709 10693.0253062951 15.9746937049349 91 10413 10595.4550488185 -182.455048818514 92 10846 10370.7605878589 475.239412141114 93 10371 10746.2330825674 -375.233082567447 94 9924 10686.7595721945 -762.759572194485 95 9828 10767.8819375799 -939.881937579938 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 96 10896.1615946547 8345.25879715902 13447.0643921503 97 10481.1279444666 7194.39012473529 13767.8657641979 98 9391.43658261147 5462.11176144348 13320.7614037795 99 8720.72826878065 4200.66157476705 13240.7949627943 100 7998.01520620099 2919.63679649375 13076.3936159082 101 7426.18424767718 1811.07781199214 13041.2906833622 102 7404.68188952917 1267.70090322331 13541.662875835 103 7194.61025294456 546.127195052268 13843.0933108368 104 7205.78028154333 53.0292030595483 14358.5313600271 105 6957.95968357163 -694.108818315014 14610.0281854583 106 7052.60894591557 -1095.53769880071 15200.7555906319 107 7660.71488590755 -981.583756336501 16303.0135281516

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/1d97i1305872371.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/1d97i1305872371.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/2ylea1305872371.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/2ylea1305872371.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/36kun1305872371.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/20/t13058721655llv3399k11piof/36kun1305872371.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')

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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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