exonential smoothing - Blazers - Wouter Dewachter

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 28 May 2008 04:12:49 -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/28/t1211969619l78fnm5u2jqrz1p.htm/, Retrieved Wed, 28 May 2008 12:13:39 +0200

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Dataseries X:

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161,79 161,79 161,85 161,77 161,86 161,89 161,89 161,89 162,18 162,43 162,58 162,57 162,57 162,57 162,44 162,79 163,15 163,23 163,23 163,23 163,38 163,71 163,73 163,73 163,73 163,73 163,93 164,27 164,57 164,73 164,73 164,76 165,75 165,86 165,99 166,13 166,13 166,13 166,15 166,45 166,48 166,51 166,51 166,51 166,58 166,82 167,35 167,5 167,5 167,6 167,72 167,29 166,98 166,98 166,98 166,98 167,63 167,83 167,85 167,87 167,87 167,96 167,7 169,25 168,79 168,77 168,77 169 168,92 169,23 169,28 169,29

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 0.792088674339765 beta 0.000643553350096742 gamma 0.0036999903249905 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 162.57 161.917409722222 0.652590277777733 14 162.57 162.435980553338 0.134019446662421 15 162.44 162.419698952207 0.0203010477933674 16 162.79 162.795852643753 -0.00585264375331462 17 163.15 163.163370642374 -0.0133706423742410 18 163.23 163.249926903731 -0.0199269037311751 19 163.23 163.250863200289 -0.0208632002891704 20 163.23 163.251047231904 -0.0210472319038786 21 163.38 163.387324765307 -0.00732476530654935 22 163.71 163.701134641943 0.00886535805713606 23 163.73 163.720689717726 0.0093102822736455 24 163.73 163.719768625538 0.0102313744619664 25 163.73 163.87008435355 -0.140084353550151 26 163.73 163.760364348663 -0.0303643486632552 27 163.93 163.613681612850 0.316318387150346 28 164.27 164.224330950272 0.045669049728474 29 164.57 164.632722961873 -0.0627229618733338 30 164.73 164.680227655419 0.049772344580731 31 164.73 164.736451635245 -0.00645163524529835 32 164.76 164.74813852739 0.0118614726100077 33 165.75 164.910597769111 0.839402230889476 34 165.86 165.895639124375 -0.0356391243746543 35 165.99 165.880456519823 0.109543480176541 36 166.13 165.959494284950 0.170505715049615 37 166.13 166.237292137517 -0.107292137516879 38 166.13 166.15429386368 -0.0242938636800147 39 166.15 166.013352261125 0.136647738874558 40 166.45 166.482052801465 -0.0320528014645731 41 166.48 166.829333704375 -0.349333704374885 42 166.51 166.650292585988 -0.140292585987766 43 166.51 166.556216921551 -0.0462169215512915 44 166.51 166.536691884141 -0.0266918841414281 45 166.58 166.669502013826 -0.0895020138255234 46 166.82 166.917874147183 -0.0978741471831768 47 167.35 166.853254298988 0.496745701011832 48 167.5 167.238981559636 0.261018440363614 49 167.5 167.588250059571 -0.0882500595710383 50 167.6 167.520398599096 0.0796014009036128 51 167.72 167.461927978226 0.258072021774154 52 167.29 168.026792349542 -0.73679234954173 53 166.98 167.815368529448 -0.835368529448488 54 166.98 167.251013348965 -0.271013348965113 55 166.98 167.052908792308 -0.0729087923084819 56 166.98 167.011684014241 -0.0316840142409376 57 167.63 167.139916639368 0.490083360631701 58 167.83 167.847085810724 -0.0170858107236143 59 167.85 167.846676561473 0.00332343852730332 60 167.87 167.840898425274 0.0291015747259848 61 167.87 168.005591427698 -0.135591427697506 62 167.96 167.899738303343 0.0602616966572214 63 167.7 167.825444129975 -0.125444129974937 64 169.25 168.084926800116 1.16507319988364 65 168.79 169.380005206888 -0.590005206887895 66 168.77 169.010690647766 -0.240690647765604 67 168.77 168.837029183226 -0.0670291832256567 68 169 168.800768715091 0.199231284908791 69 168.92 169.112701247907 -0.192701247906655 70 169.23 169.278699398062 -0.0486993980623822 71 169.28 169.253294053690 0.0267059463102157 72 169.29 169.266097655836 0.0239023441644122 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 169.426583951341 168.83655114721 170.016616755472 74 169.428389281117 168.675499038626 170.181279523609 75 169.306296279952 168.419825676588 170.192766883317 76 169.666275163672 168.663729338761 170.668820988583 77 170.036708840292 168.930070733496 171.143346947089 78 170.134846881687 168.932981824095 171.336711939278 79 170.151937479338 168.861746228513 171.442128730163 80 170.168979196005 168.796029953869 171.541928438140 81 170.322704125917 168.871612029975 171.773796221859 82 170.641450501419 169.116121162256 172.166779840581 83 170.654703203403 169.058497148905 172.250909257901 84 170.646363355463 168.982211626098 172.310515084829

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/1nebp1211969563.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/1nebp1211969563.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/20gb21211969563.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/20gb21211969563.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/35hpz1211969563.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/28/t1211969619l78fnm5u2jqrz1p/35hpz1211969563.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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