exponential smoothing weekend aan zee

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 03:23:08 -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/t1211793852zg9xmwv9l593qcr.htm/, Retrieved Mon, 26 May 2008 11:24:12 +0200

User-defined keywords:

Dataseries X:

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104,7 104,7 104,7 104,7 106 107 107 107 107 107 107 107 107 107 107 107 107,6 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 109,9 110,6 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 114,3 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 119,01 121,27 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 123,54 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 125,24 128,35 128,35 128,35 128,35 128,35 128,35 128,35

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 3 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.0267675815717632 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 104.7 104.7 0 4 104.7 104.7 0 5 106 104.7 1.30000000000000 6 107 106.034797856043 0.965202143956702 7 107 107.060633983165 -0.060633983164891 8 107 107.059010958075 -0.0590109580745093 9 107 107.057431377441 -0.0574313774406221 10 107 107.055894078360 -0.0558940783601969 11 107 107.054397929058 -0.054397929058311 12 107 107.052941828055 -0.0529418280549123 13 107 107.051524703354 -0.0515247033538913 14 107 107.050145511654 -0.0501455116539091 15 107 107.048803237580 -0.048803237580259 16 107 107.047496892937 -0.0474968929373603 17 107.6 107.046225515981 0.553774484018746 18 109.9 107.661048719655 2.23895128034543 19 109.9 110.020980030686 -0.120980030686439 20 109.9 110.017741687846 -0.117741687846475 21 109.9 110.014590027613 -0.114590027612650 22 109.9 110.011522729701 -0.111522729701221 23 109.9 110.008537535937 -0.108537535936833 24 109.9 110.00563224859 -0.105632248590055 25 109.9 110.002804728759 -0.102804728759310 26 109.9 110.000052894796 -0.100052894796278 27 109.9 109.997374720773 -0.097374720773331 28 109.9 109.994768234992 -0.094768234992003 29 110.6 109.992231518531 0.607768481468554 30 114.3 110.708500010936 3.59149998906410 31 114.3 114.504635779858 -0.204635779858151 32 114.3 114.499158174928 -0.1991581749283 33 114.3 114.493827192235 -0.193827192235219 34 114.3 114.488638907056 -0.188638907056244 35 114.3 114.483589499724 -0.183589499724008 36 114.3 114.478675252814 -0.178675252814429 37 114.3 114.473892548410 -0.173892548409853 38 114.3 114.469237865436 -0.169237865435576 39 114.3 114.464707777068 -0.164707777067505 40 114.3 114.460298948209 -0.160298948209345 41 114.3 114.456008133037 -0.156008133037275 42 119.01 114.451832172610 4.55816782738967 43 119.01 119.283843301748 -0.273843301747789 44 119.01 119.276513178830 -0.266513178830365 45 119.01 119.269379265576 -0.259379265576072 46 119.01 119.262436309927 -0.252436309926750 47 119.01 119.255679200409 -0.245679200409114 48 119.01 119.249102962372 -0.239102962371675 49 119.01 119.242702754322 -0.232702754322332 50 119.01 119.236473864364 -0.226473864364038 51 119.01 119.230411706726 -0.220411706725798 52 119.01 119.224511818387 -0.214511818386654 53 121.27 119.21876985579 2.05123014421011 54 123.54 121.533676325997 2.00632367400253 55 123.54 123.857380758601 -0.317380758600706 56 123.54 123.848885243256 -0.308885243255546 57 123.54 123.840617132310 -0.300617132310393 58 123.54 123.832570338699 -0.292570338699406 59 123.54 123.824738938293 -0.28473893829279 60 123.54 123.817117165535 -0.277117165535387 61 123.54 123.809699409202 -0.269699409201976 62 123.54 123.802480208266 -0.262480208266311 63 123.54 123.795454247881 -0.255454247880564 64 123.54 123.788616355463 -0.248616355462573 65 123.54 123.781961496888 -0.241961496887654 66 125.24 123.775484772782 1.46451522721750 67 125.24 125.51468630359 -0.274686303590116 68 125.24 125.507333615552 -0.267333615552118 69 125.24 125.500177741191 -0.260177741190958 70 125.24 125.493213412280 -0.253213412280473 71 125.24 125.486435501612 -0.246435501612183 72 125.24 125.479839019221 -0.239839019220611 73 125.24 125.473419108710 -0.233419108709526 74 125.24 125.467171043677 -0.227171043676734 75 125.24 125.461090224234 -0.221090224234374 76 125.24 125.455172173622 -0.215172173622463 77 125.24 125.449412534913 -0.209412534913056 78 128.35 125.443807067803 2.90619293219738 79 128.35 128.631598824178 -0.281598824178502 80 128.35 128.624061104682 -0.274061104681778 81 128.35 128.616725151707 -0.266725151706567 82 128.35 128.609585564451 -0.259585564451015 83 128.35 128.602637086680 -0.252637086679727 84 128.35 128.595874602854 -0.245874602853974 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 85 128.589293134366 126.862852891432 130.315733377299 86 128.828586268731 126.354138023071 131.303034514392 87 129.067879403097 125.996859077791 132.138899728403 88 129.307172537463 125.714167906135 132.900177168791 89 129.546465671828 125.476734149762 133.616197193895 90 129.785758806194 125.269728005185 134.301789607203 91 130.025051940560 125.084463706656 134.965640174463 92 130.264345074925 124.915362033262 135.613328116589 93 130.503638209291 124.758603147685 136.248673270897 94 130.742931343657 124.611446356432 136.874416330881 95 130.982224478022 124.471853393146 137.492595562898 96 131.221517612388 124.33826477553 138.104770449246

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/14arq1211793782.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/14arq1211793782.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/23lc11211793782.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/23lc11211793782.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/3ga5g1211793782.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/26/t1211793852zg9xmwv9l593qcr/3ga5g1211793782.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

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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