double exponential smoothing: cijferreeks jurk: birgit teugels

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Thu, 04 Jun 2009 01:26:31 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu.htm/, Retrieved Thu, 04 Jun 2009 09:27:16 +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/2009/Jun/04/t1244100436u3j4bba85x0ktdu.htm/}, year = {2009}, } @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 = {2009}, 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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20,73 20,73 20,74 20,74 20,75 20,75 20,77 20,78 20,78 20,8 20,84 20,85 20,86 20,86 20,86 20,86 20,9 20,92 20,95 20,95 20,95 20,96 21,1 21,18 21,19 21,19 21,19 21,19 21,19 21,21 21,22 21,22 21,22 21,23 21,41 21,42 21,43 21,44 21,44 21,44 21,48 21,53 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,54 21,57 21,6 21,61 21,6 21,6 21,71 21,75 21,84 21,85 21,92 21,92 21,93 22 22 21,99 22,01 22,01 22,06 22,03 22,05 22,05 22,06 22,06 22,13 22,06 22,25 22,28 22,18

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.909175725154546 beta 0.0452112664258505 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 20.74 20.73 0.00999999999999801 4 20.74 20.7395028071109 0.000497192889074682 5 20.75 20.7403863297825 0.00961367021751869 6 20.75 20.7499535021191 4.64978809162631e-05 7 20.77 20.7508243449036 0.0191756550963795 8 20.78 20.7698751681042 0.0101248318957943 9 20.78 20.7811133836309 -0.00111338363085522 10 20.8 20.7820883207881 0.0179116792118705 11 20.84 20.8010966425737 0.0389033574263209 12 20.85 20.840789210582 0.00921078941799536 13 20.86 20.8538646259092 0.00613537409083165 14 20.86 20.8643961427418 -0.00439614274183242 15 20.86 20.8651719567356 -0.00517195673559456 16 20.86 20.8650298262701 -0.00502982627010695 17 20.9 20.8648101664355 0.0351898335644556 18 20.92 20.9026037226104 0.0173962773896434 19 20.95 20.9249348831843 0.0250651168156644 20 20.95 20.9552686676788 -0.00526866767879497 21 20.95 20.9578071431480 -0.00780714314797493 22 20.96 20.9577167858324 0.00228321416763677 23 21.1 20.9668941879325 0.133105812067502 24 21.18 21.1004836328781 0.0795163671218688 25 21.19 21.1886193745071 0.00138062549294204 26 21.19 21.2057727471715 -0.0157727471714928 27 21.19 21.2066823512542 -0.0166823512542074 28 21.19 21.2060792375717 -0.0160792375717023 29 21.19 21.2053635233746 -0.0153635233745639 30 21.21 21.2046670017393 0.00533299826065559 31 21.22 21.2230064679885 -0.00300646798851290 32 21.22 21.2336403131388 -0.0136403131388008 33 21.22 21.2340454395336 -0.0140454395336356 34 21.23 21.2335048972501 -0.00350489725014569 35 21.41 21.2424034913886 0.167596508611410 36 21.42 21.4137523824059 0.0062476175941164 37 21.43 21.438663586663 -0.00866358666300115 38 21.44 21.4496617693688 -0.00966176936876906 39 21.44 21.4593552816951 -0.0193552816951481 40 21.44 21.459440089341 -0.0194400893409963 41 21.48 21.4586487073349 0.0213512926650594 42 21.53 21.4958215042290 0.0341784957709557 43 21.54 21.5460613893967 -0.00606138939670231 44 21.54 21.559466994461 -0.0194669944610020 45 21.54 21.5598843582863 -0.0198843582862587 46 21.54 21.5591049187853 -0.0191049187852954 47 21.54 21.5582488193398 -0.0182488193398171 48 21.54 21.5574209472661 -0.0174209472661424 49 21.54 21.556629668593 -0.0166296685929872 50 21.54 21.5558742389876 -0.0158742389876316 51 21.54 21.5551531172712 -0.0151531172711650 52 21.54 21.5544647532418 -0.0144647532418496 53 21.57 21.5538076595995 0.0161923404005471 54 21.6 21.581688837225 0.0183111627750208 55 21.61 21.6122490768077 -0.00224907680766506 56 21.6 21.6240239973879 -0.0240239973878538 57 21.6 21.6150141826846 -0.015014182684574 58 21.71 21.6135787150295 0.0964212849704609 59 21.75 21.7174210650505 0.0325789349494734 60 21.84 21.7645586568586 0.0754413431414171 61 21.85 21.8537667250654 -0.00376672506537901 62 21.92 21.8708059092413 0.0491940907586716 63 21.92 21.9380179039577 -0.0180179039577446 64 21.93 21.9433817589500 -0.0133817589499685 65 22 21.9524106274281 0.0475893725719025 66 22 22.0188291291115 -0.0188291291114773 67 21.99 22.0240875702758 -0.0340875702758439 68 22.01 22.014072238033 -0.00407223803301804 69 22.01 22.0311787279607 -0.0211787279607378 70 22.06 22.0318618611886 0.0281381388114283 71 22.03 22.0785393103265 -0.0485393103264933 72 22.05 22.0535082763730 -0.00350827637304363 73 22.05 22.0692741577177 -0.0192741577176996 74 22.06 22.0699138184762 -0.00991381847617845 75 22.06 22.0786561650832 -0.018656165083204 76 22.13 22.0786833209708 0.0513166790291635 77 22.06 22.1444374595153 -0.0844374595153283 78 22.25 22.0832964301199 0.166703569880106 79 22.28 22.2573390761368 0.022660923863171 80 22.18 22.3013531219649 -0.121353121964873 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 22.2094448748729 22.125057913068 22.2938318366778 82 22.2278679404431 22.1114557235134 22.3442801573727 83 22.2462910060133 22.1029354886460 22.3896465233805 84 22.2647140715834 22.0969576298155 22.4324705133514 85 22.2831371371536 22.0924800456513 22.4737942286559 86 22.3015602027238 22.0889606335319 22.5141597719157 87 22.319983268294 22.0860780766016 22.5538884599864 88 22.3384063338642 22.0836252979042 22.5931873698241 89 22.3568293994344 22.0814608215652 22.6321979773036 90 22.3752524650046 22.0794837462667 22.6710211837425 91 22.3936755305748 22.0776197059048 22.7097313552447 92 22.4120985961450 22.0758124594188 22.7483847328711

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/1p8i11244100385.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/1p8i11244100385.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/2jeow1244100385.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/2jeow1244100385.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/3r8g71244100385.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244100436u3j4bba85x0ktdu/3r8g71244100385.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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=0, beta=0) if (par2 == 'Double') fit <- HoltWinters(x, gamma=0) 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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