Dennis Collin oef 10 deel 2

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 25 Jan 2009 05:50:17 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd.htm/, Retrieved Sun, 25 Jan 2009 13:50:51 +0100

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/Jan/25/t1232887851sgafbbxvzo8n9gd.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 «

1,29 1,29 1,3 1,3 1,3 1,3 1,31 1,31 1,31 1,31 1,31 1,32 1,32 1,32 1,32 1,33 1,33 1,33 1,34 1,34 1,34 1,34 1,34 1,34 1,34 1,35 1,36 1,36 1,36 1,37 1,37 1,37 1,37 1,37 1,37 1,37 1,38 1,38 1,38 1,39 1,4 1,4 1,4 1,4 1,41 1,42 1,43 1,43 1,43 1,44 1,45 1,45 1,46 1,46 1,47 1,47 1,47 1,48 1,49 1,49 1,49 1,5 1,51 1,51 1,51 1,52 1,52 1,52 1,52 1,53 1,53 1,53 1,53 1,54 1,54 1,55 1,55 1,55 1,56 1,56 1,58 1,58 1,58 1,58 1,58 1,58 1,59 1,59 1,6 1,6 1,6 1,61 1,62 1,62 1,63 1,63

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 4 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.693880469628355 beta 0.087046697378327 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 1.3 1.29 0.01 4 1.3 1.29754280472885 0.00245719527115185 5 1.3 1.30000021917251 -2.19172507698318e-07 6 1.3 1.30075246848991 -0.000752468489908953 7 1.31 1.30093729759843 0.0090627024015666 8 1.31 1.30848006934918 0.00151993065081557 9 1.31 1.31088086291148 -0.000880862911483815 10 1.31 1.31156258858657 -0.00156258858657199 11 1.31 1.31167689777435 -0.00167689777435487 12 1.32 1.31161060541820 0.00838939458179566 13 1.32 1.31903583618962 0.000964163810384111 14 1.32 1.32136707984355 -0.00136707984354878 15 1.32 1.32199814742907 -0.00199814742907023 16 1.33 1.32207064143076 0.00792935856923993 17 1.33 1.3295105712402 0.000489428759800514 18 1.33 1.33181764055815 -0.00181764055814893 19 1.34 1.33241409403866 0.00758590596133701 20 1.34 1.33999367353906 6.32646094178568e-06 21 1.34 1.34231431297440 -0.00231431297439522 22 1.34 1.34288492151731 -0.00288492151731257 23 1.34 1.34288534666746 -0.0028853466674561 24 1.34 1.34271120186611 -0.00271120186610796 25 1.34 1.34249413613976 -0.00249413613976057 26 1.35 1.34227704225059 0.007722957749412 27 1.36 1.34961585694069 0.0103841430593148 28 1.36 1.35942841841798 0.000571581582015757 29 1.36 1.36246675865857 -0.00246675865857293 30 1.37 1.36324786171512 0.00675213828487942 31 1.37 1.37083360648664 -0.000833606486641436 32 1.37 1.37310540127911 -0.00310540127911074 33 1.37 1.37361327578671 -0.00361327578671133 34 1.37 1.37355050422318 -0.00355050422318159 35 1.37 1.37331683815499 -0.00331683815499084 36 1.37 1.37304497137257 -0.00304497137257020 37 1.38 1.37277783135999 0.00722216864000713 38 1.38 1.38007107829046 -7.10782904578267e-05 39 1.38 1.38229939048672 -0.00229939048672101 40 1.39 1.38284263717688 0.0071573628231234 41 1.4 1.39038004503265 0.00961995496734902 42 1.4 1.40020724279332 -0.000207242793318629 43 1.4 1.40320302249129 -0.00320302249129223 44 1.4 1.40392662659663 -0.00392662659662824 45 1.41 1.40391096768631 0.00608903231369462 46 1.42 1.41121275645589 0.0087872435441092 47 1.43 1.42091753083987 0.0090824691601279 48 1.43 1.43137573767979 -0.0013757376797916 49 1.43 1.43449410448582 -0.00449410448581755 50 1.44 1.43517725354243 0.00482274645757341 51 1.45 1.44261647740884 0.00738352259116426 52 1.45 1.45227853860998 -0.00227853860998461 53 1.46 1.45509866050784 0.00490133949216065 54 1.46 1.46319680051637 -0.0031968005163725 55 1.47 1.46548271257107 0.00451728742893054 56 1.47 1.47339412376743 -0.00339412376742532 57 1.47 1.47561095616083 -0.00561095616082552 58 1.48 1.47595067008162 0.00404932991838014 59 1.49 1.48323804738405 0.0067619526159457 60 1.49 1.49281608255782 -0.00281608255782362 61 1.49 1.49557801479144 -0.00557801479143771 62 1.5 1.49608658407814 0.00391341592185745 63 1.51 1.50341744210006 0.00658255789994211 64 1.51 1.51299795212982 -0.00299795212982357 65 1.51 1.51574965704245 -0.00574965704245223 66 1.52 1.51624472835394 0.00375527164606027 67 1.52 1.52356190246725 -0.0035619024672473 68 1.52 1.52558669344984 -0.00558669344983964 69 1.52 1.52586908521197 -0.00586908521196827 70 1.53 1.52560103807966 0.0043989619203435 71 1.53 1.53272348562799 -0.00272348562799318 72 1.53 1.53473930738579 -0.00473930738578709 73 1.53 1.53507013561406 -0.005070135614061 74 1.54 1.53486517238833 0.00513482761166628 75 1.54 1.54205137744268 -0.00205137744268025 76 1.55 1.54412731195485 0.00587268804514696 77 1.55 1.55205631112614 -0.00205631112613647 78 1.55 1.55435933143005 -0.00435933143005185 79 1.56 1.55480102729135 0.00519897270864855 80 1.56 1.56218906168580 -0.00218906168579602 81 1.58 1.56431846397204 0.0156815360279579 82 1.58 1.57979508981960 0.000204910180397588 83 1.58 1.58454516383136 -0.0045451638313585 84 1.58 1.58572472634685 -0.0057247263468525 85 1.58 1.58574003998015 -0.00574003998014727 86 1.58 1.58539802934889 -0.00539802934888645 87 1.59 1.58496729222481 0.00503270777518838 88 1.59 1.59207821544097 -0.00207821544096998 89 1.6 1.59412948369701 0.00587051630299285 90 1.6 1.60205080087231 -0.00205080087231280 91 1.6 1.60435180238658 -0.00435180238657606 92 1.61 1.60479333501119 0.00520666498881384 93 1.62 1.61218178404944 0.00781821595056109 94 1.62 1.62185455756436 -0.00185455756436070 95 1.63 1.62470356716721 0.00529643283278647 96 1.63 1.63283441390549 -0.00283441390549433 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 1.63515222628142 1.62530346020719 1.64500099235564 98 1.63943678310921 1.62710048498946 1.65177308122896 99 1.64372133993700 1.62900528179991 1.65843739807409 100 1.64800589676479 1.63095185705266 1.66505993647692 101 1.65229045359258 1.63290680864488 1.67167409854028 102 1.65657501042037 1.63485114428438 1.67829887655635 103 1.66085956724816 1.63677326396718 1.68494587052913 104 1.66514412407595 1.63866574876819 1.69162249938371 105 1.66942868090374 1.64052371334773 1.69833364845975 106 1.67371323773153 1.64234388792790 1.70508258753515 107 1.67799779455932 1.64412407374308 1.71187151537556 108 1.68228235138711 1.64586280383569 1.71870189893853

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/1xfa11232887810.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/1xfa11232887810.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/26auz1232887810.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/26auz1232887810.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/3ysyu1232887810.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/25/t1232887851sgafbbxvzo8n9gd/3ysyu1232887810.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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