Opgave 10, oefening 2, stap 1, Sara Vandenberghe

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 03 Jun 2009 12:02:06 -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/03/t1244052174qjzs0atfyk6be3g.htm/, Retrieved Wed, 03 Jun 2009 20:02:58 +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/03/t1244052174qjzs0atfyk6be3g.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 «

1.54 1.55 1.53 1.55 1.55 1.53 1.54 1.54 1.54 1.53 1.53 1.53 1.54 1.53 1.53 1.54 1.55 1.53 1.53 1.53 1.53 1.52 1.54 1.53 1.52 1.54 1.53 1.54 1.54 1.53 1.54 1.54 1.52 1.52 1.57 1.6 1.59 1.6 1.6 1.62 1.61 1.61 1.62 1.61 1.62 1.61 1.62 1.61 1.61 1.58 1.57 1.57 1.66 1.66 1.67 1.68 1.66 1.66 1.64 1.61 1.58 1.57 1.54 1.61 1.65 1.6 1.57 1.56 1.55 1.54 1.51 1.5 1.5 1.49 1.47 1.47 1.49 1.49 1.49 1.51 1.49 1.48 1.46 1.46 1.45 1.45 1.44 1.47 1.47 1.45 1.43 1.44 1.38 1.4 1.37 1.41

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.871955057656946 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 1.54 1.54198183760684 -0.00198183760683746 14 1.53 1.53060050087884 -0.000600500878837451 15 1.53 1.53042362769714 -0.000423627697144102 16 1.54 1.54040097998079 -0.000400979980792471 17 1.55 1.54956474672192 0.000435253278075587 18 1.53 1.52904100461584 0.000958995384159333 19 1.53 1.53439060875473 -0.00439060875473141 20 1.53 1.53090893184159 -0.000908931841587135 21 1.53 1.53046312072199 -0.000463120721986066 22 1.52 1.51998937019621 1.06298037854113e-05 23 1.54 1.51992870883746 0.0200712911625434 24 1.53 1.53694337594374 -0.00694337594374494 25 1.52 1.54056536982035 -0.0205653698203523 26 1.54 1.51315690137134 0.0268430986286596 27 1.53 1.53693226129687 -0.00693226129687274 28 1.54 1.54123727752034 -0.0012372775203362 29 1.54 1.54977890583157 -0.00977890583157404 30 1.53 1.52041593855789 0.00958406144210544 31 1.54 1.53260122291511 0.00739877708488579 32 1.54 1.53984517173109 0.000154828268906115 33 1.52 1.54038399547908 -0.0203839954790761 34 1.52 1.51260079881467 0.00739920118533322 35 1.57 1.52155130586795 0.0484486941320454 36 1.6 1.55985070152463 0.0401492984753724 37 1.59 1.60279116361905 -0.0127911636190485 38 1.6 1.58823186819566 0.0117681318043423 39 1.6 1.59453777054044 0.00546222945956454 40 1.62 1.61037943953537 0.009620560464632 41 1.61 1.62729490228819 -0.0172949022881905 42 1.61 1.59385765391898 0.0161423460810186 43 1.62 1.61148165312713 0.008518346872868 44 1.61 1.61877426547366 -0.00877426547366467 45 1.62 1.60889742826991 0.0111025717300854 46 1.61 1.61212660094679 -0.00212660094678907 47 1.62 1.61802721661031 0.00197278338969276 48 1.61 1.61473901119763 -0.0047390111976322 49 1.61 1.61176012622651 -0.00176012622651056 50 1.58 1.60996409321522 -0.0299640932152201 51 1.57 1.57907393198475 -0.0090739319847546 52 1.57 1.58277317474318 -0.0127731747431823 53 1.66 1.5767159179454 0.083284082054601 54 1.66 1.63526049420743 0.0247395057925683 55 1.67 1.65940461576852 0.0105953842314785 56 1.68 1.66629407979396 0.0137059202060354 57 1.66 1.67856408266441 -0.0185640826644127 58 1.66 1.65423133734559 0.00576866265441289 59 1.64 1.66754117346871 -0.027541173468715 60 1.61 1.63765871275093 -0.02765871275093 61 1.58 1.61507630924480 -0.0350763092447965 62 1.57 1.58061868662197 -0.0106186866219724 63 1.54 1.56927173000321 -0.0292717300032113 64 1.61 1.55488573130020 0.0551142686998036 65 1.65 1.62032292007223 0.0296770799277715 66 1.6 1.62462826281198 -0.0246282628119749 67 1.57 1.60391482562331 -0.0339148256233128 68 1.56 1.57239167544802 -0.0123916754480164 69 1.55 1.55777373713827 -0.00777373713827134 70 1.54 1.54596537314623 -0.00596537314622814 71 1.51 1.54477850136042 -0.0347785013604167 72 1.5 1.50857036567293 -0.00857036567292657 73 1.5 1.50168235722839 -0.00168235722838839 74 1.49 1.49947443484001 -0.00947443484001242 75 1.47 1.48673678648549 -0.0167367864854910 76 1.47 1.49408589551868 -0.0240858955186849 77 1.49 1.48720699716346 0.00279300283653927 78 1.49 1.46111710843304 0.0288828915669626 79 1.49 1.48587389554641 0.00412610445359118 80 1.51 1.49027665727288 0.0197233427271204 81 1.49 1.50425287513230 -0.0142528751323048 82 1.48 1.48702654586020 -0.00702654586020324 83 1.46 1.48122500381848 -0.0212250038184849 84 1.46 1.46019072808465 -0.000190728084646707 85 1.45 1.46149136166068 -0.0114913616606809 86 1.45 1.44973269211848 0.000267307881524737 87 1.44 1.44455949820267 -0.00455949820267088 88 1.47 1.46158563910019 0.00841436089981151 89 1.47 1.48648721069436 -0.0164872106943592 90 1.45 1.44692652056119 0.0030734794388132 91 1.43 1.44600867885574 -0.0160086788557352 92 1.44 1.43485196191626 0.00514803808374298 93 1.38 1.43176868631815 -0.0517686863181535 94 1.4 1.38275555065545 0.0172444493445538 95 1.37 1.39629918490625 -0.0262991849062546 96 1.41 1.37353378393304 0.0364662160669642 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 1.40535063638563 1.36424286833719 1.44645840443407 98 1.40511755592638 1.35057720406483 1.45965790778794 99 1.39909323344458 1.33382876096191 1.46435770592725 100 1.42175628890104 1.34729654974155 1.49621602806053 101 1.43613239565264 1.35349430429667 1.51877048700862 102 1.41345245971136 1.32337551743302 1.50352940198971 103 1.40741130820603 1.31046463772439 1.50435797868767 104 1.41292245036190 1.30956163426250 1.51628326646130 105 1.39806241822527 1.28866287667233 1.50746195977820 106 1.40302603340278 1.28790409335983 1.51814797344572 107 1.39595774069404 1.27538468206771 1.51653079932037 108 1.40416083916084 1.27837266859712 1.52994900972456

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/19mig1244052124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/19mig1244052124.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/2bamt1244052124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/2bamt1244052124.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/3fy0e1244052124.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/03/t1244052174qjzs0atfyk6be3g/3fy0e1244052124.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=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')

Copyright

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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