Opgave 10-2 - Consumptieprijzen pakketreizen - Chloë De Rijck

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 16 Jan 2009 07:07:31 -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/16/t1232114947ew5hztryhjohrfo.htm/, Retrieved Fri, 16 Jan 2009 15:09:20 +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/16/t1232114947ew5hztryhjohrfo.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 «

105,6 110,2 104,9 102,9 102,6 103,6 107,8 106,6 106 105,2 107,9 107,5 107,5 113,3 107,8 104,5 105,1 104,2 106,6 103,8 107,7 106,4 110 113,2 113,9 112 113,9 113,1 111,7 110,7 113,5 114 112,7 112,2 115,8 118,4 118,8 123,9 118 120,2 118,7 119,8 124,8 121,3 120,2 118,3 129,6 130,2 127,19 133,1 129,12 123,28 123,36 124,13 126,96 127,14 123,7 123,67 130,19 134,01 124,96 129,96 128,32 132,38 126,25 128,91 131,42 129,44 126,86 126,71 131,63 132,78 126,61 132,84 123,14 128,13 125,49 126,48 130,86 127,32 126,56 126,64 129,26 126,47 135,38 135,5 132,22 122,62 125,16 128,5 133,86 128,87 125,07 125,25 132,16 130,24

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 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.208653452026953 beta 0.135928514801665 gamma 0.144824151716476 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 107.5 106.576308760684 0.923691239316184 14 113.3 112.844873595554 0.455126404446062 15 107.8 107.607745700872 0.192254299128066 16 104.5 104.354554674865 0.145445325135029 17 105.1 104.979055241780 0.120944758220134 18 104.2 103.914373910481 0.285626089518516 19 106.6 109.008821488077 -2.40882148807660 20 103.8 107.172744393442 -3.37274439344178 21 107.7 105.598217169639 2.10178283036056 22 106.4 105.088079616920 1.31192038307984 23 110 107.967009829966 2.03299017003442 24 113.2 107.995719983242 5.20428001675758 25 113.9 109.493761570337 4.40623842966316 26 112 116.732364194594 -4.73236419459447 27 113.9 110.532687046408 3.36731295359249 28 113.1 108.176634554609 4.92336544539111 29 111.7 110.170784062969 1.52921593703110 30 110.7 109.834285509665 0.86571449033454 31 113.5 115.172891517895 -1.67289151789539 32 114 113.832690817859 0.167309182141238 33 112.7 114.177418506156 -1.47741850615607 34 112.2 113.281628386918 -1.08162838691824 35 115.8 116.127572854054 -0.327572854054125 36 118.4 116.344039818516 2.05596018148393 37 118.8 117.321267971373 1.47873202862695 38 123.9 123.046221735355 0.853778264645186 39 118 119.243343752074 -1.24334375207384 40 120.2 116.275786594317 3.92421340568275 41 118.7 117.816323139809 0.883676860191187 42 119.8 117.394634343926 2.40536565607441 43 124.8 122.932766705450 1.86723329454969 44 121.3 122.811740874061 -1.51174087406100 45 120.2 122.839629412424 -2.63962941242441 46 118.3 121.935733616598 -3.63573361659770 47 129.6 124.451768836218 5.14823116378203 48 130.2 126.355847387362 3.84415261263807 49 127.19 127.9626496001 -0.772649600100024 50 133.1 133.404983124011 -0.30498312401059 51 129.12 129.345879697500 -0.225879697500488 52 123.28 127.437607809812 -4.15760780981222 53 123.36 126.968918556119 -3.60891855611925 54 124.13 125.682348349915 -1.55234834991494 55 126.96 130.118887597700 -3.15888759769963 56 127.14 128.205213479842 -1.06521347984237 57 123.7 127.852993205802 -4.15299320580236 58 123.67 126.132231869226 -2.46223186922607 59 130.19 129.546163611634 0.643836388366424 60 134.01 129.879521311687 4.13047868831259 61 124.96 130.543665569088 -5.58366556908798 62 129.96 134.42602440002 -4.46602440002013 63 128.32 128.780018790534 -0.460018790534349 64 132.38 125.637900043535 6.7420999564651 65 126.25 127.081099647821 -0.83109964782112 66 128.91 126.263354868017 2.64664513198268 67 131.42 131.164529521225 0.255470478774669 68 129.44 130.072678784374 -0.632678784374292 69 126.86 129.338555499994 -2.47855549999376 70 126.71 128.090158747334 -1.38015874733365 71 131.63 132.045748662242 -0.415748662241555 72 132.78 132.487464365655 0.292535634345285 73 126.61 131.058510508721 -4.44851050872084 74 132.84 135.159009132355 -2.31900913235461 75 123.14 130.334189151014 -7.19418915101356 76 128.13 126.335465801779 1.79453419822060 77 125.49 125.461177887789 0.0288221122108894 78 126.48 124.828592523827 1.65140747617325 79 130.86 128.827000368689 2.03299963131099 80 127.32 127.633600256416 -0.313600256415839 81 126.56 126.392905128636 0.167094871364441 82 126.64 125.535851270326 1.10414872967354 83 129.26 129.904223453292 -0.64422345329163 84 126.47 130.156856472641 -3.68685647264132 85 135.38 127.018788281587 8.36121171841295 86 135.5 134.063994588630 1.43600541136965 87 132.22 129.598306660567 2.62169333943251 88 122.62 129.090621782214 -6.47062178221364 89 125.16 126.467761450972 -1.30776145097161 90 128.5 125.882685631961 2.61731436803927 91 133.86 130.294195227650 3.56580477234968 92 128.87 129.362988061814 -0.49298806181406 93 125.07 128.346168357144 -3.27616835714363 94 125.25 126.986614866068 -1.73661486606794 95 132.16 130.589865253157 1.57013474684348 96 130.24 131.046618437654 -0.806618437653555 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 130.062784015298 124.369193041398 135.756374989198 98 134.505063640771 128.653735231408 140.356392050133 99 129.770247209067 123.726985301821 135.813509116313 100 127.493757833897 121.223347830058 133.764167837736 101 126.816485376104 120.283394375182 133.349576377026 102 126.994981823671 120.163958754473 133.82600489287 103 130.935716094095 123.772268005701 138.099164182490 104 128.660829449433 121.131568694351 136.190090204515 105 127.307386475152 119.380258013804 135.234514936500 106 126.780260054706 118.424666996682 135.135853112730 107 131.146489594850 122.333338676713 139.959640512988 108 130.980361074005 121.682049433254 140.278672714757

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/17k3f1232114848.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/17k3f1232114848.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/2h0f91232114848.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/2h0f91232114848.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/3skj31232114848.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/16/t1232114947ew5hztryhjohrfo/3skj31232114848.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')

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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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