opg10 oef2 - volkaerts dennis

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 26 Jan 2009 14:46:42 -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/26/t1233006448onydv2m3lv9ufkx.htm/, Retrieved Mon, 26 Jan 2009 22:47:32 +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/26/t1233006448onydv2m3lv9ufkx.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 «

93,89 93,36 92,25 91,07 90,93 90,68 90,65 90,6 90,02 89,74 89,31 89,16 89,15 88,98 88,25 87,36 87,13 86,93 86,93 86,93 86,98 86,16 85,88 85,91 85,91 85,6 84,9 83,67 83,41 83,33 83,32 83,3 82,73 82,2 81,7 81,52 81,52 81,55 81,89 81,8 81,84 81,77 81,77 82,98 83,13 82,84 82,8 82,8 82,8 82,98 81,91 81,64 81,4 81,21 81,21 81,23 81,01 80,55 80,5 80,54 80,54 80,72 80,63 80,36 79,88 79,66 79,66 79,13 78,81 78,67 78,43 78,13 78,13 78,07 76,94 74,97 75 75,1 75,1 75,02 73,87 73,18 72,55 72,42 72,4 72,45 71,42 70,89 70,42 69,57 69,57 69,44 68,25 66,86 66,5 66,46

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.99995743816477 beta 0 gamma 0 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 2 93.36 93.89 -0.530000000000001 3 92.25 93.3600225577727 -1.11002255777267 4 91.07 92.2500472445972 -1.18004724459722 5 90.93 91.0700502249764 -0.140050224976378 6 90.68 90.9300059607946 -0.250005960794596 7 90.65 90.6800106407125 -0.0300106407125185 8 90.6 90.650001277308 -0.0500012773079561 9 90.02 90.6000021281461 -0.58000212814612 10 89.74 90.020024685955 -0.280024685955013 11 89.31 89.7400119183645 -0.430011918364528 12 89.16 89.3100183020964 -0.150018302096427 13 89.15 89.1600063850542 -0.0100063850542398 14 88.98 89.1500004258901 -0.170000425890109 15 88.25 88.9800072355301 -0.73000723553011 16 87.36 88.2500310704477 -0.890031070447677 17 87.13 87.3600378813558 -0.23003788135577 18 86.93 87.1300097908344 -0.200009790834386 19 86.93 86.9300085127838 -8.51278376501341e-06 20 86.93 86.9300000003623 -3.6231995181879e-10 21 86.98 86.93 0.049999999999983 22 86.16 86.9799978719083 -0.819997871908257 23 85.88 86.1600349006143 -0.280034900614311 24 85.91 85.8800119187993 0.0299880812006990 25 85.91 85.9099987236522 1.27634777413732e-06 26 85.6 85.9099999999457 -0.309999999945674 27 84.9 85.600013194169 -0.700013194168918 28 83.67 84.9000297938462 -1.23002979384623 29 83.41 83.6700523523254 -0.260052352325417 30 83.33 83.4100110683054 -0.0800110683053674 31 83.32 83.3300034054179 -0.0100034054179048 32 83.3 83.3200004257633 -0.0200004257632855 33 82.73 83.3000008512548 -0.570000851254818 34 82.2 82.7300242602823 -0.530024260282303 35 81.7 82.2000225588052 -0.500022558805242 36 81.52 81.7000212818778 -0.180021281877757 37 81.52 81.5200076620361 -7.66203612556637e-06 38 81.55 81.5200000003261 0.0299999996738904 39 81.89 81.549998723145 0.340001276855034 40 81.8 81.8899855289217 -0.0899855289216731 41 81.84 81.8000038299493 0.0399961700507419 42 81.77 81.8399982976896 -0.0699982976896081 43 81.77 81.770002979256 -2.97925602410487e-06 44 82.98 81.7700000001268 1.20999999987320 45 83.13 82.9799485001794 0.150051499820606 46 82.84 83.1299936135328 -0.289993613532772 47 82.8 82.8400123426604 -0.040012342660404 48 82.8 82.8000017029987 -1.70299874469038e-06 49 82.8 82.8000000000725 -7.24895699022454e-11 50 82.98 82.8 0.180000000000007 51 81.91 82.9799923388697 -1.06999233886967 52 81.64 81.9100455408376 -0.270045540837614 53 81.4 81.6400114936338 -0.240011493633816 54 81.21 81.4000102153297 -0.190010215329664 55 81.21 81.2100080871835 -8.08718347400372e-06 56 81.23 81.2100000003442 0.0199999996558091 57 81.01 81.2299991487633 -0.219999148763307 58 80.55 81.0100093635675 -0.460009363567536 59 80.5 80.5500195788427 -0.0500195788427362 60 80.54 80.500002128925 0.0399978710749451 61 80.54 80.5399982976172 1.7023827894036e-06 62 80.72 80.5399999999276 0.180000000072440 63 80.63 80.7199923388696 -0.0899923388696493 64 80.36 80.630003830239 -0.270003830239091 65 79.88 80.3600114918585 -0.480011491858548 66 79.66 79.88002043017 -0.220020430170024 67 79.66 79.6600093644733 -9.36447329991097e-06 68 79.13 79.6600000003986 -0.530000000398573 69 78.81 79.1300225577727 -0.320022557772688 70 78.67 78.8100136207474 -0.140013620747368 71 78.43 78.6700059592366 -0.240005959236640 72 78.13 78.4300102150941 -0.300010215094105 73 78.13 78.1300127689853 -1.27689853428592e-05 74 78.07 78.1300000005435 -0.0600000005434822 75 76.94 78.0700025537101 -1.13000255371013 76 74.97 76.9400480949825 -1.97004809498250 77 75 74.9700838488624 0.0299161511375843 78 75.1 74.9999987267137 0.100001273286296 79 75.1 75.0999957437623 4.25623771604933e-06 80 75.02 75.0999999998188 -0.0799999998188525 81 73.87 75.0200034049468 -1.15000340494680 82 73.18 73.8700489462554 -0.69004894625543 83 72.55 73.1800293697496 -0.630029369749565 84 72.42 72.5500268152062 -0.130026815206222 85 72.4 72.4200055341799 -0.0200055341798731 86 72.45 72.4000008514723 0.0499991485277462 87 71.42 72.4499978719445 -1.02999787194447 88 70.89 71.4200438385997 -0.53004383859971 89 70.42 70.8900225596385 -0.470022559638522 90 69.57 70.4200200050227 -0.850020005022742 91 69.57 69.5700361784114 -3.61784113920294e-05 92 69.44 69.5700000015398 -0.130000001539813 93 68.25 69.4400055330386 -1.19000553303863 94 66.86 68.2500506488194 -1.39005064881943 95 66.5 66.8600591631067 -0.360059163106683 96 66.46 66.5000153247788 -0.0400153247787784 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 66.4600017031257 65.5931755140823 67.326827892169 98 66.4600017031257 65.2341504378777 67.6858529683736 99 66.4600017031257 64.9586573032598 67.9613461029915 100 66.4600017031257 64.7264046653147 68.1935987409367 101 66.4600017031257 64.5217854169477 68.3982179893036 102 66.4600017031257 64.3367951529982 68.5832082532531 103 66.4600017031257 64.1666788438224 68.7533245624289 104 66.4600017031257 64.0083383046345 68.9116651016168 105 66.4600017031257 63.8596215189988 69.0603818872525 106 66.4600017031257 63.7189616113907 69.2010417948606 107 66.4600017031257 63.5851757141314 69.33482769212 108 66.4600017031257 63.4573448546837 69.4626585515676

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/1g9uv1233006400.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/1g9uv1233006400.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/26avb1233006400.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/26avb1233006400.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/35ye51233006400.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jan/26/t1233006448onydv2m3lv9ufkx/35ye51233006400.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = Single ; 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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