Eigen reeks: prijs Exponential Smoothing

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 05 Jun 2009 13:53:01 -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/05/t1244231641pcqa8wvhfjtngpl.htm/, Retrieved Fri, 05 Jun 2009 21:54:01 +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/05/t1244231641pcqa8wvhfjtngpl.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:

» Textbox « » Textfile « » CSV «

0.58 0.58 0.59 0.6 0.6 0.61 0.62 0.61 0.62 0.62 0.62 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.63 0.64 0.63 0.63 0.63 0.63 0.63 0.64 0.65 0.65 0.65 0.65 0.65 0.66 0.65 0.66 0.66 0.66 0.66 0.68 0.69 0.7 0.71 0.71 0.7 0.7 0.7 0.7 0.71 0.7 0.7 0.7 0.69 0.7 0.69 0.69 0.69 0.7 0.7 0.71 0.71 0.71 0.72 0.73 0.74 0.74 0.74 0.74 0.75 0.75 0.76 0.76 0.76 0.76 0.76 0.77 0.77 0.78 0.78 0.78 0.78 0.78 0.78 0.78 0.8 0.8 0.8 0.81 0.81 0.81 0.8 0.81 0.81 0.81 0.8 0.82 0.83 0.83

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.886472179761465 beta 0.0337932685980229 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.59 0.58 0.01 4 0.6 0.589164289722368 0.0108357102776319 5 0.6 0.599394016480308 0.00060598351969221 6 0.61 0.600573528383315 0.00942647161668464 7 0.62 0.60985454445022 0.0101454555497803 8 0.61 0.620076845077982 -0.0100768450779816 9 0.62 0.612070768831652 0.00792923116834776 10 0.62 0.620264112576957 -0.000264112576957021 11 0.62 0.621186373067169 -0.00118637306716851 12 0.63 0.621255535358543 0.00874446464145717 13 0.63 0.630390065112912 -0.000390065112912064 14 0.63 0.63141540326519 -0.00141540326519018 15 0.63 0.631489406728742 -0.00148940672874154 16 0.63 0.631453190332364 -0.00145319033236435 17 0.63 0.631405545842613 -0.00140554584261288 18 0.63 0.631358031222423 -0.00135803122242328 19 0.63 0.631311954731659 -0.00131195473165857 20 0.64 0.631267421812464 0.00873257818753559 21 0.63 0.640388687917373 -0.0103886879173729 22 0.63 0.632248271810432 -0.00224827181043219 23 0.63 0.631256757101923 -0.00125675710192319 24 0.63 0.631106544186638 -0.00110654418663758 25 0.63 0.63105634232723 -0.00105634232722962 26 0.64 0.631018998391679 0.00898100160832072 27 0.65 0.640148522615093 0.009851477384907 28 0.65 0.650344818061202 -0.000344818061202123 29 0.65 0.651492051614606 -0.00149205161460575 30 0.65 0.651577597458647 -0.00157759745864694 31 0.65 0.651540049532173 -0.00154004953217313 32 0.66 0.651489651853689 0.00851034814631113 33 0.65 0.660603594846032 -0.0106035948460322 34 0.66 0.652455909439821 0.0075440905601788 35 0.66 0.660621639028606 -0.000621639028606125 36 0.66 0.661530054198104 -0.00153005419810348 37 0.66 0.66158734907608 -0.00158734907607960 38 0.68 0.661546301751829 0.018453698248171 39 0.69 0.679823898942633 0.0101761010573672 40 0.7 0.691068479856101 0.00893152014389886 41 0.71 0.701477334109758 0.00852266589024209 42 0.71 0.711779062175382 -0.00177906217538160 43 0.7 0.712895299910973 -0.0128952999109733 44 0.7 0.703771000327008 -0.00377100032700795 45 0.7 0.702622171409816 -0.00262217140981624 46 0.7 0.702413195522262 -0.00241319552226182 47 0.71 0.702317179347802 0.0076828206521975 48 0.7 0.711401153302326 -0.0114011533023264 49 0.7 0.703226173283415 -0.00322617328341501 50 0.7 0.702201439817833 -0.00220143981783349 51 0.69 0.702019155985391 -0.0120191559853908 52 0.7 0.692773684540031 0.00722631545996899 53 0.69 0.700805265349972 -0.0108052653499719 54 0.69 0.692528660323049 -0.00252866032304933 55 0.69 0.691513284842829 -0.00151328484282931 56 0.7 0.691352678317844 0.00864732168215643 57 0.7 0.70045821282786 -0.000458212827860405 58 0.71 0.701478217726296 0.00852178227370437 59 0.71 0.710714023719756 -0.000714023719755819 60 0.71 0.711741154781944 -0.00174115478194403 61 0.72 0.711805603320063 0.0081943966799366 62 0.73 0.72092311966053 0.00907688033947007 63 0.74 0.73109484743492 0.00890515256507995 64 0.74 0.741381113122175 -0.00138111312217459 65 0.74 0.742507516724857 -0.00250751672485694 66 0.74 0.742560277712423 -0.0025602777124234 67 0.75 0.742489569844225 0.00751043015577502 68 0.75 0.751571252729267 -0.00157125272926661 69 0.76 0.752555206699366 0.00744479330063397 70 0.76 0.76175465677435 -0.00175465677435016 71 0.76 0.762746486399902 -0.00274648639990160 72 0.76 0.76277681073222 -0.00277681073222025 73 0.76 0.76269706904472 -0.00269706904472 74 0.77 0.762607220607092 0.00739277939290839 75 0.77 0.77168320606552 -0.00168320606551986 76 0.78 0.772663159456334 0.00733684054366612 77 0.78 0.781858921435934 -0.00185892143593436 78 0.78 0.782847208925227 -0.00284720892522661 79 0.78 0.782874113802748 -0.00287411380274794 80 0.78 0.782791069024107 -0.00279106902410720 81 0.78 0.782698029655867 -0.00269802965586652 82 0.78 0.7826066427847 -0.00260664278470057 83 0.8 0.78251818117546 0.0174818188245400 84 0.8 0.800761281135636 -0.000761281135635894 85 0.8 0.802809574967513 -0.00280957496751277 86 0.81 0.802957947447208 0.007042052552792 87 0.81 0.81205047095595 -0.00205047095595046 88 0.81 0.813021299797461 -0.00302129979746135 89 0.8 0.813041007428625 -0.0130410074286245 90 0.81 0.803787856242209 0.006212143757791 91 0.81 0.811788183856672 -0.00178818385667145 92 0.81 0.812642875359234 -0.00264287535923347 93 0.8 0.812660734553821 -0.0126607345538209 94 0.82 0.803418765274025 0.0165812347259753 95 0.83 0.820595708849878 0.00940429115012165 96 0.83 0.831692214008382 -0.00169221400838204 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 0.83290128274742 0.819525552674947 0.846277012819892 98 0.83561045212709 0.817467507815744 0.853753396438437 99 0.838319621506761 0.816197085581957 0.860442157431566 100 0.841028790886432 0.815339264447321 0.866718317325543 101 0.843737960266103 0.814735838647774 0.872740081884432 102 0.846447129645774 0.814303054357237 0.87859120493431 103 0.849156299025445 0.813990570917623 0.884322027133266 104 0.851865468405116 0.813765537417332 0.8899653993929 105 0.854574637784786 0.813605239311874 0.895544036257699 106 0.857283807164457 0.813493281310758 0.901074333018157 107 0.859992976544128 0.813417430572848 0.906568522515408 108 0.862702145923799 0.813368316693895 0.912035975153703

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/1wy9s1244231576.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/1wy9s1244231576.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/2u5qn1244231576.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/2u5qn1244231576.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/35kgh1244231576.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/05/t1244231641pcqa8wvhfjtngpl/35kgh1244231576.ps (open in new window)

Parameters (Session):

par1 = 12 ;

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=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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