Stephanie De Coninck - oef 10

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 24 May 2008 01:23:37 -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/24/t1211613897tiz2vgbw9lww3w2.htm/, Retrieved Sat, 24 May 2008 09:24:57 +0200

User-defined keywords:

eigen cijferreeks

Dataseries X:

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68,64 68,61 68,61 68,61 68,58 68,75 68,54 68,5 68,47 68,47 68,47 68,59 68,32 67,86 67,91 67,91 68,05 68,15 68,25 68,25 68,31 68,31 69,65 69,65 70,18 70,08 70,08 70,09 70,04 70,14 70,26 70,23 70,54 70,54 70,57 70,61 70,63 70,45 70,4 70,4 70,33 70,51 70,45 70,39 70,59 70,59 70,32 70,94 70,44 70,57 70,61 70,61 70,68 69,96 70,11 70,22 70,49 70,49 70,58 70,85 70,69 70,7 70,7 70,7 70,67 70,64 70,98 70,75 70,88 70,88 70,92 70,89 71,02 71,01 71,02

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 5 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.867742588299969 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 68.61 68.61 0 4 68.61 68.61 0 5 68.58 68.61 -0.0300000000000011 6 68.75 68.583967722351 0.166032277648995 7 68.54 68.7280410006995 -0.188041000699471 8 68.5 68.564869816046 -0.0648698160459986 9 68.47 68.5085795139677 -0.0385795139677043 10 68.47 68.475102426662 -0.00510242666202032 11 68.47 68.4706748337437 -0.000674833743701697 12 68.59 68.4700892517643 0.119910748235739 13 68.32 68.5741409148033 -0.254140914803344 14 67.86 68.353612019599 -0.493612019598956 15 67.91 67.9252838480962 -0.015283848096189 16 67.91 67.91202140219 -0.00202140219002445 17 68.05 67.9102673454217 0.139732654578339 18 68.15 68.0315193207755 0.118480679224518 19 68.25 68.1343300520293 0.115669947970687 20 68.25 68.2347017920699 0.0152982079300870 21 68.31 68.2479766986155 0.0620233013844853 22 68.31 68.3017969586938 0.00820304130620286 23 69.65 68.3089150869888 1.34108491301123 24 69.65 69.4726315805352 0.177368419464827 25 70.18 69.6265417119243 0.553458288075745 26 70.08 70.1068010393352 -0.0268010393351830 27 70.08 70.0835446360933 -0.00354463609333777 28 70.09 70.0804688043951 0.00953119560487892 29 70.04 70.0887394287389 -0.0487394287388838 30 70.14 70.0464461506927 0.0935538493072556 31 70.26 70.127626810036 0.132373189963957 32 70.23 70.2424926645169 -0.0124926645168983 33 70.54 70.2316522474742 0.308347752525762 34 70.54 70.4992187243474 0.0407812756525772 35 70.57 70.5346063740364 0.0353936259636214 36 70.61 70.5653189306394 0.0446810693606352 37 70.63 70.6040905974144 0.0259094025856257 38 70.45 70.6265732894753 -0.176573289475328 39 70.4 70.4733531262414 -0.0733531262413578 40 70.4 70.4097014946168 -0.0097014946167917 41 70.33 70.4012830945676 -0.0712830945676473 42 70.51 70.3394277175855 0.170572282414525 43 70.45 70.4874405514201 -0.0374405514200902 44 70.39 70.4549517904235 -0.06495179042345 45 70.59 70.3985903556867 0.191409644313310 46 70.59 70.5646846558687 0.0253153441313003 47 70.32 70.5866518581089 -0.266651858108915 48 70.94 70.3552666845785 0.584733315421516 49 70.44 70.8626646851676 -0.422664685167575 50 70.57 70.4959005372773 0.074099462722728 51 70.61 70.5601997968519 0.0498002031480809 52 70.61 70.6034135540295 0.00658644597049829 53 70.68 70.6091288937036 0.0708711062963658 54 69.96 70.6706267709169 -0.710626770916932 55 70.11 70.0539856574062 0.0560143425937838 56 70.22 70.1025916880305 0.117408311969527 57 70.49 70.2044718805468 0.285528119453161 58 70.49 70.4522367899535 0.0377632100464496 59 70.58 70.4850055355818 0.0949944644182352 60 70.85 70.5674362780102 0.282563721989789 61 70.69 70.8126288534893 -0.122628853489303 62 70.7 70.7062185747622 -0.00621857476222942 63 70.7 70.7008224526025 -0.00082245260252023 64 70.7 70.7001087754525 -0.000108775452460463 65 70.67 70.7000143863598 -0.0300143863597953 66 70.64 70.6739696250537 -0.0339696250537145 67 70.98 70.644492734686 0.335507265313979 68 70.75 70.935626677483 -0.185626677483015 69 70.88 70.7745505039064 0.105449496093613 70 70.88 70.8660535225816 0.0139464774184148 71 70.92 70.8781554749943 0.0418445250057005 72 70.89 70.914465751429 -0.0244657514289344 73 71.02 70.8932357769593 0.126764223040709 74 71.01 71.0032344919645 0.00676550803554221 75 71.02 71.0091052114184 0.0108947885816093 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 76 71.0185590834612 70.5445778147764 71.492540352146 77 71.0185590834612 70.391007669008 71.6461104979143 78 71.0185590834612 70.2682369443101 71.7688812226122 79 71.0185590834612 70.1629038683083 71.874214298614 80 71.0185590834612 70.0691864580204 71.967931708902 81 71.0185590834612 69.9839234390653 72.053194727857 82 71.0185590834612 69.9051708082523 72.13194735867 83 71.0185590834612 69.8316319643462 72.2054862025762 84 71.0185590834612 69.7623908937633 72.274727273159 85 71.0185590834612 69.6967720145553 72.340346152367 86 71.0185590834612 69.6342601308339 72.4028580360884 87 71.0185590834612 69.5744517034638 72.4626664634586

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/164mx1211613809.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/164mx1211613809.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/2hdte1211613809.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/2hdte1211613809.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/31pzh1211613809.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/24/t1211613897tiz2vgbw9lww3w2/31pzh1211613809.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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