opgave 10 oef 2 Brecht Martens

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 May 2008 11:27:05 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo.htm/, Retrieved Mon, 26 May 2008 19:41:20 +0200

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Dataseries X:

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3,42 3,42 3,43 3,47 3,51 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,52 3,58 3,6 3,61 3,61 3,61 3,63 3,68 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,69 3,78 3,79 3,79 3,8 3,8 3,8 3,8 3,81 3,95 3,99 4 4,06 4,16 4,19 4,2 4,2 4,2 4,2 4,2 4,23 4,38 4,43 4,44 4,44 4,44 4,44 4,44 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,45 4,46 4,46 4,46 4,48 4,58 4,67 4,68 4,68

Text written by user:

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 6 seconds R Server 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0158617543048723 gamma 0.145558896711419 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 3.52 3.45501111111111 0.064988888888887 14 3.52 3.52402504068665 -0.00402504068665266 15 3.58 3.58104452981355 -0.00104452981354752 16 3.6 3.59852796173828 0.00147203826171927 17 3.61 3.60813464418085 0.00186535581915059 18 3.61 3.60816423199654 0.00183576800345664 19 3.61 3.60819335049757 0.00180664950242493 20 3.63 3.6282220071281 0.00177799287190261 21 3.68 3.68075020921419 -0.000750209214186892 22 3.69 3.69407164291329 -0.0040716429132881 23 3.69 3.69525705951378 -0.00525705951377997 24 3.69 3.69184033999407 -0.00184033999407296 25 3.69 3.65972781563992 0.0302721843600828 26 3.69 3.69437465225717 -0.00437465225717482 27 3.69 3.75138859593124 -0.0613885959312355 28 3.69 3.70791486510545 -0.0179148651054533 29 3.69 3.69721403725008 -0.00721403725007885 30 3.78 3.68709960996367 0.0929003900363279 31 3.79 3.77857317312525 0.0114268268747453 32 3.79 3.80875442264563 -0.0187544226456264 33 3.8 3.84095694460149 -0.0409569446014917 34 3.8 3.81364062894248 -0.0136406289424778 35 3.8 3.80467426463763 -0.00467426463762832 36 3.8 3.80126678926706 -0.00126678926705681 37 3.81 3.76916336243361 0.040836637566386 38 3.95 3.813977769812 0.136022230188005 39 3.99 4.01321865434057 -0.023218654340571 40 4 4.01035036575013 -0.0103503657501323 41 4.06 4.00976952412497 0.0502304758750283 42 4.16 4.06056626759192 0.0994337324080838 43 4.19 4.16214346102499 0.0278565389750085 44 4.2 4.212585314602 -0.0125853146019965 45 4.2 4.25488568943393 -0.05488568943393 46 4.2 4.21734843944661 -0.0173484394466081 47 4.2 4.20832326276253 -0.00832326276253426 48 4.2 4.20485790788025 -0.00485790788024598 49 4.23 4.17269751960568 0.057302480394319 50 4.38 4.23777310413742 0.142226895862578 51 4.43 4.44711240554847 -0.0171124055484722 52 4.44 4.4543409727761 -0.0143409727760968 53 4.44 4.45369683312276 -0.0136968331227632 54 4.44 4.44347957732101 -0.00347957732101456 55 4.44 4.44342438512046 -0.00342438512046428 56 4.44 4.46337006836504 -0.0233700683650380 57 4.45 4.49549937808254 -0.0454993780825435 58 4.45 4.46811101145971 -0.0181110114597063 59 4.45 4.45907373904572 -0.0090737390457214 60 4.45 4.45559648029302 -0.00559648029301751 61 4.45 4.42342437696430 0.0265756230356953 62 4.45 4.45801257963406 -0.00801257963406155 63 4.45 4.51496881939789 -0.0649688193978921 64 4.45 4.47143829994713 -0.0214382999471256 65 4.46 4.46068158423398 -0.000681584233983124 66 4.46 4.46067077311232 -0.000670773112324774 67 4.46 4.46066013347402 -0.000660133474023716 68 4.48 4.48064966259905 -0.000649662599049528 69 4.58 4.53313935781052 0.0468606421894773 70 4.67 4.59721598313683 0.0727840168631664 71 4.68 4.67962046532964 0.000379534670360115 72 4.68 4.686293152082 -0.0062931520819971 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 4.65410999831654 4.57489945967452 4.73332053695855 74 4.66238666329974 4.54947412830185 4.77529919829763 75 4.72774666161628 4.58836247830996 4.8671308449226 76 4.75060665993281 4.58839199785255 4.91282132201307 77 4.76304999158268 4.58026778280383 4.94583220036153 78 4.76549332323255 4.56370550029555 4.96728114616955 79 4.76793665488242 4.54829211776519 4.98758119199965 80 4.79037998653229 4.55376070452354 5.02699926854104 81 4.84532331818216 4.59242735447923 5.09821928188509 82 4.86359998316536 4.59499259053622 5.1322073757945 83 4.87312664814856 4.58927363945461 5.15697965684252 84 4.87931997979843 4.58061055052161 5.17802940907526

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/1pf8r1211822819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/1pf8r1211822819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/2wnke1211822819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/2wnke1211822819.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/3vmsj1211822819.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t12118236768gpiwuhkowrq1wo/3vmsj1211822819.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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