thomas van eester- opgave 10 - eigen reeks

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 07 Jun 2009 14:09:31 -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/07/t12444055084y3e31ez43k253d.htm/, Retrieved Sun, 07 Jun 2009 22:11:48 +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/07/t12444055084y3e31ez43k253d.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 «

0.63 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 2 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.891917722178237 beta 0.0383687115475383 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 0.63 0.63 0 4 0.64 0.63 0.01 5 0.63 0.639261394559846 -0.00926139455984631 6 0.63 0.631026268978595 -0.00102626897859526 7 0.63 0.630101077143826 -0.000101077143826012 8 0.63 0.629997621267792 2.37873220787499e-06 9 0.63 0.629986520925397 1.34790746032509e-05 10 0.64 0.629985782452409 0.0100142175475909 11 0.65 0.639247583745542 0.0107524162544581 12 0.65 0.649535763874654 0.000464236125345852 13 0.65 0.650663620782754 -0.00066362078275406 14 0.65 0.650762811872663 -0.000762811872662805 15 0.65 0.650747427926749 -0.000747427926749089 16 0.66 0.650720186915284 0.00927981308471582 17 0.65 0.659953991159656 -0.00995399115965556 18 0.66 0.651692181697788 0.00830781830221183 19 0.66 0.660002711680453 -2.71168045262726e-06 20 0.66 0.660900839892478 -0.000900839892478467 21 0.66 0.660967083332408 -0.000967083332407581 22 0.68 0.660941147805916 0.0190588521940843 23 0.69 0.679428926045142 0.0105710739548579 24 0.7 0.690708064929814 0.00929193507018555 25 0.71 0.701164303302638 0.0088356966973615 26 0.71 0.711515987445574 -0.00151598744557402 27 0.7 0.712582941328218 -0.0125829413282177 28 0.7 0.703348472843767 -0.00334847284376660 29 0.7 0.702235799909176 -0.00223579990917644 30 0.7 0.702039026734599 -0.00203902673459910 31 0.71 0.701947980011541 0.00805201998845906 32 0.7 0.711132870780756 -0.0111328707807559 33 0.7 0.702825431334494 -0.0028254313344942 34 0.7 0.701830853197259 -0.00183085319725873 35 0.69 0.70166070195596 -0.0116607019559594 36 0.7 0.69232408496211 0.00767591503788945 37 0.69 0.700496822473196 -0.0104968224731956 38 0.69 0.69210175387316 -0.00210175387315992 39 0.69 0.691122470074824 -0.00112247007482424 40 0.7 0.69097821397916 0.00902178602084003 41 0.7 0.700190540833197 -0.000190540833196695 42 0.71 0.701179709465947 0.00882029053405331 43 0.71 0.710507643921458 -0.000507643921457968 44 0.71 0.711498455869633 -0.00149845586963304 45 0.72 0.711554265323994 0.0084457346760064 46 0.73 0.720768502242609 0.00923149775739096 47 0.74 0.730999493037833 0.00900050696216748 48 0.74 0.741332472002518 -0.00133247200251796 49 0.74 0.742403684403531 -0.00240368440353089 50 0.74 0.742437205232051 -0.00243720523205115 51 0.75 0.742357422850869 0.00764257714913075 52 0.75 0.751529519251956 -0.00152951925195577 53 0.76 0.752468517522694 0.00753148247730606 54 0.76 0.761746924204954 -0.00174692420495415 55 0.76 0.762689972758608 -0.00268997275860772 56 0.76 0.762699844062692 -0.00269984406269164 57 0.76 0.76260851763089 -0.00260851763088987 58 0.77 0.762509378866122 0.00749062113387833 59 0.77 0.771674182986876 -0.00167418298687572 60 0.78 0.772607442447517 0.00739255755248303 61 0.78 0.781880474614314 -0.00188047461431362 62 0.78 0.782818371951535 -0.00281837195153478 63 0.78 0.782823292457412 -0.00282329245741186 64 0.78 0.78272720631396 -0.00272720631395995 65 0.78 0.782623491376197 -0.00262349137619700 66 0.78 0.78252250120596 -0.00252250120595987 67 0.8 0.782425261593526 0.0175747384064736 68 0.8 0.800854544177748 -0.000854544177748218 69 0.8 0.802817179034695 -0.00281717903469514 70 0.81 0.802932896329556 0.00706710367044405 71 0.81 0.812106429080742 -0.00210642908074243 72 0.81 0.81302583974088 -0.00302583974088 73 0.8 0.813021662257128 -0.0130216622571281 74 0.81 0.803656409663906 0.006343590336094 75 0.81 0.811780457712896 -0.00178045771289548 76 0.81 0.81259759298126 -0.00259759298125939 77 0.8 0.81259701668681 -0.0125970166868107 78 0.82 0.803246685426001 0.0167533145739991 79 0.83 0.820647762240235 0.00935223775976457 80 0.83 0.83176773727176 -0.00176773727176049 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 0.832909114468135 0.819231331049799 0.84658689788647 82 0.835627167865348 0.816984523215701 0.854269812514994 83 0.83834522126256 0.815539684401193 0.861150758123928 84 0.841063274659773 0.814508559668482 0.867617989651064 85 0.843781328056986 0.813728582379485 0.873834073734487 86 0.846499381454198 0.813114136090087 0.87988462681831 87 0.849217434851411 0.81261398778576 0.885820881917062 88 0.851935488248624 0.812194842771008 0.89167613372624 89 0.854653541645837 0.811833774029534 0.89747330926214 90 0.85737159504305 0.811514302086305 0.903228887999794 91 0.860089648440262 0.811224184646082 0.908955112234442 92 0.862807701837475 0.810954086773179 0.91466131690177

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/13eyq1244405365.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/13eyq1244405365.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/2pptn1244405365.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/2pptn1244405365.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/3r7m61244405365.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444055084y3e31ez43k253d/3r7m61244405365.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

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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