Exponential smoothing - Aardappelprijs - Kristof Vermeulen

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 01 Jun 2008 08:54:09 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4.htm/, Retrieved Sun, 01 Jun 2008 14:57:03 +0000

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No (this computation is public)

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Dataseries X:

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0,36 0,35 0,35 0,35 0,33 0,78 0,71 0,62 0,52 0,46 0,43 0,43 0,42 0,42 0,42 0,42 0,43 0,99 1,03 0,83 0,64 0,6 0,58 0,58 0,58 0,57 0,57 0,56 0,56 0,88 0,84 0,69 0,59 0,54 0,52 0,52 0,51 0,52 0,51 0,51 0,53 0,95 0,98 0,88 0,81 0,77 0,76 0,75 0,73 0,74 0,73 0,75 0,77 1,09 1,03 0,9 0,76 0,66 0,63 0,61 0,61 0,61 0,61 0,61 0,62 0,76 0,83 0,81 0,77 0,75 0,76 0,76

Text written by user:

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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.427961762367385 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 0.42 0.381454930921276 0.0385450690787244 14 0.42 0.382199148727861 0.037800851272139 15 0.42 0.388794526379802 0.0312054736201978 16 0.42 0.3946701047839 0.0253298952160997 17 0.43 0.406728202033024 0.023271797966976 18 0.99 0.93959734412076 0.0504026558792394 19 1.03 0.979169422343925 0.0508305776560753 20 0.83 0.790108400298008 0.0398915997019921 21 0.64 0.610349914875342 0.0296500851246579 22 0.6 0.57336468524232 0.0266353147576803 23 0.58 0.5557622225549 0.0242377774450997 24 0.58 0.565430478240453 0.0145695217595465 25 0.58 0.54595681178643 0.0340431882135694 26 0.57 0.537764088426115 0.0322359115738852 27 0.57 0.533243385408397 0.0367566145916034 28 0.56 0.534298474616607 0.0257015253833931 29 0.56 0.544937297239602 0.0150627027603977 30 0.88 1.24097530413189 -0.360975304131893 31 0.84 1.10582300987989 -0.265823009879894 32 0.69 0.782519629802283 -0.0925196298022835 33 0.59 0.561190565266293 0.0288094347337066 34 0.54 0.527193919172221 0.0128060808277793 35 0.52 0.505484173907298 0.0145158260927024 36 0.52 0.506115283462974 0.0138847165370256 37 0.51 0.498748023053782 0.0112519769462185 38 0.52 0.482503228831789 0.0374967711682109 39 0.51 0.484264831525809 0.0257351684741908 40 0.51 0.476774346417104 0.0332256535828961 41 0.53 0.485253417113277 0.0447465828867230 42 0.95 0.905334876300396 0.0446651236996037 43 0.98 0.983619758460618 -0.00361975846061757 44 0.88 0.849694754143913 0.0303052458560866 45 0.81 0.721782893473176 0.0882171065268239 46 0.77 0.688016580973826 0.0819834190261745 47 0.76 0.687867141438742 0.0721328585612585 48 0.75 0.710396719944856 0.0396032800551437 49 0.73 0.706536383695711 0.0234636163042891 50 0.74 0.707111221938404 0.0328887780615956 51 0.73 0.691588547422003 0.0384114525779968 52 0.75 0.687522521436921 0.062477478563079 53 0.77 0.714090169714788 0.0559098302852118 54 1.09 1.29550847595839 -0.205508475958388 55 1.03 1.24765709399755 -0.217657093997551 56 0.9 1.02111522606375 -0.121115226063751 57 0.76 0.84783376002545 -0.08783376002545 58 0.66 0.732859642537123 -0.0728596425371233 59 0.63 0.662819764731786 -0.0328197647317865 60 0.61 0.625318763951989 -0.0153187639519892 61 0.61 0.593822964334313 0.0161770356656866 62 0.61 0.597090355896929 0.0129096441030709 63 0.61 0.580669583794658 0.0293304162053424 64 0.61 0.586659170947267 0.0233408290527328 65 0.62 0.592698997731945 0.0273010022680553 66 0.76 0.917867224012115 -0.157867224012115 67 0.83 0.868328871542498 -0.038328871542498 68 0.81 0.784208067147231 0.0257919328527693 69 0.77 0.702695754012859 0.0673042459871414 70 0.75 0.663478649584249 0.0865213504157514 71 0.76 0.683141511669046 0.0768584883309538 72 0.76 0.700648368700601 0.0593516312993986 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 0.717681426740382 0.548662980728098 0.886699872752667 74 0.71110165436842 0.52785241316225 0.89435089557459 75 0.696055077058173 0.499911671762975 0.892198482353371 76 0.684401840838947 0.47558141217863 0.893222269499264 77 0.682173951961466 0.429075549849497 0.935272354073435 78 0.902654617799094 0.62153801447683 1.18377122112136 79 1.00477469986815 0.72167591638452 1.28787348335178 80 0.966953109627418 0.69137845589209 1.24252776336275 81 0.883007672372452 0.612195159617789 1.15382018512711 82 0.814610138319783 0.540192928127893 1.08902734851167 83 0.787551871519812 0.510127467963302 1.06497627507632 84 0.76 NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/1posv1212332042.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/1posv1212332042.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/2bcio1212332042.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/2bcio1212332042.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/3jpaf1212332042.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Jun/01/t1212332219dijia74dopd58g4/3jpaf1212332042.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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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