*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sun, 16 Aug 2009 11:12:06 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a.htm/, Retrieved Sun, 16 Aug 2009 19:12:25 +0200

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/Aug/16/t1250442741phg6kdiys3lwn0a.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 «

105,46 104,66 103,52 103,71 103,78 103,67 103,66 102,76 102 101,5 101,5 99,22 98,97 98,9 99,78 104,4 106,21 105,46 108,33 111,72 111,88 112,86 113,09 116,9 114,62 118,86 124,71 122,53 127,89 136,16 134,12 130,26 135,35 131,43 129,61 123,96 121,1 125,38 123,1 129,92 136,68 131,17 124,82 122,47 126,15 118,74 116,8 116,64 116,53 117,68 119,46 126,19 124,39 121,9 122,53 122,93 124,66 124,41 120,93 120,18 123,44 126,1 125,82 122,18 117,27 117,86 119,09 123,08 125,42 121,81 121,66 121,27 120,92 122,16 124,17 127,26 134,16 134,09 135,57 136,13 136,23 140,6 136,5 130,59 129,5 135,25 138,06 146,28 145,04 147,96 156,71 160,97 168,17 163,91 153,05 151,76

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 0.917280045034661 beta 0 gamma 1 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 98.97 98.8947702991453 0.0752297008546776 14 98.9 98.691154624911 0.208845375089126 15 99.78 99.3430186090222 0.436981390977792 16 104.4 103.844147208062 0.555852791938108 17 106.21 105.573064171128 0.636935828872225 18 105.46 104.553023652631 0.906976347369152 19 108.33 107.905685913102 0.424314086898022 20 111.72 108.270611713552 3.44938828644841 21 111.88 111.435794378665 0.444205621335371 22 112.86 111.835632953385 1.02436704661459 23 113.09 113.010558693080 0.0794413069196622 24 116.9 110.992889574380 5.90711042561983 25 114.62 116.263714711462 -1.64371471146183 26 118.86 114.494398311841 4.36560168815905 27 124.71 118.978043314963 5.73195668503654 28 122.53 128.345980127129 -5.81598012712888 29 127.89 124.236849088403 3.65315091159671 30 136.16 126.005860216351 10.1541397836490 31 134.12 137.800835169646 -3.68083516964612 32 130.26 134.650423476733 -4.39042347673256 33 135.35 130.375714679931 4.97428532006907 34 131.43 134.978895891689 -3.54889589168852 35 129.61 131.880694582748 -2.27069458274826 36 123.96 128.189357236388 -4.22935723638771 37 121.1 123.53759894468 -2.43759894468016 38 125.38 121.537158761810 3.84284123819043 39 123.1 125.654310859651 -2.5543108596509 40 129.92 126.466174992211 3.45382500778871 41 136.68 131.643337318190 5.0366626818103 42 131.17 135.219177691751 -4.04917769175128 43 124.82 132.841304446486 -8.02130444648648 44 122.47 125.650769787035 -3.18076978703509 45 126.15 123.260300471130 2.88969952886958 46 118.74 125.24629556846 -6.50629556845993 47 116.8 119.541063305537 -2.74106330553747 48 116.64 115.256245629453 1.38375437054744 49 116.53 115.901496770538 0.628503229462126 50 117.68 117.233048657135 0.446951342865049 51 119.46 117.706046585420 1.75395341458039 52 126.19 122.966788293848 3.22321170615166 53 124.39 128.063345901228 -3.67334590122805 54 121.9 122.898088902965 -0.998088902964625 55 122.53 122.990344373014 -0.460344373014479 56 122.93 123.135736319301 -0.205736319300740 57 124.66 123.976354785089 0.683645214910825 58 124.41 123.161543990656 1.24845600934395 59 120.93 124.881050447477 -3.95105044747712 60 120.18 119.827540443748 0.352459556251546 61 123.44 119.464331090754 3.97566890924568 62 126.1 123.851153298959 2.24884670104143 63 125.82 126.085109035051 -0.265109035050898 64 122.18 129.615342028465 -7.4353420284653 65 117.27 124.364538051453 -7.0945380514529 66 117.86 116.282386901976 1.57761309802395 67 119.09 118.781764622789 0.308235377211105 68 123.08 119.653220603712 3.42677939628817 69 125.42 123.899442849142 1.52055715085825 70 121.81 123.899035796484 -2.08903579648397 71 121.66 122.127024679402 -0.467024679402158 72 121.27 120.625328142817 0.644671857183454 73 120.92 120.829871016891 0.0901289831094374 74 122.16 121.509722331369 0.650277668631219 75 124.17 122.069388288146 2.10061171185360 76 127.26 127.176528364515 0.0834716354854521 77 134.16 128.850773413409 5.30922658659139 78 134.09 132.863708002254 1.22629199774627 79 135.57 134.935823020483 0.634176979517349 80 136.13 136.364224549863 -0.234224549863200 81 136.23 137.094598312399 -0.864598312399465 82 140.6 134.607750382943 5.99224961705735 83 136.5 140.382713800490 -3.88271380049025 84 130.59 135.83983328053 -5.24983328053005 85 129.5 130.591592454855 -1.09159245485546 86 135.25 130.233809749539 5.01619025046091 87 138.06 134.918211762735 3.14178823726508 88 146.28 140.813544552946 5.46645544705441 89 145.04 147.857767449152 -2.81776744915183 90 147.96 144.078232417578 3.88176758242173 91 156.71 148.537182472065 8.17281752793545 92 160.97 156.808794407796 4.16120559220406 93 168.17 161.518864039746 6.65113596025392 94 163.91 166.493247334306 -2.58324733430612 95 153.05 163.585221992929 -10.5352219929285 96 151.76 152.827040396794 -1.06704039679400 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 97 151.759561509718 144.301130001953 159.217993017484 98 152.908310290873 142.787346026331 163.029274555415 99 152.836410635105 140.620043141770 165.052778128441 100 156.042140136451 142.040520522266 170.043759750636 101 157.386821989106 141.803142420133 172.970501558079 102 156.746154046288 139.726847773807 173.765460318770 103 157.999391616204 139.656477368882 176.342305863526 104 158.442400763188 138.865163466452 178.019638059924 105 159.541446470035 138.803222407671 180.279670532399 106 157.651007701183 135.813433331558 179.488582070808 107 156.454756605306 133.570583658988 179.338929551625 108 156.143531468531 132.258576192771 180.028486744292

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/112c51250442719.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/112c51250442719.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/2nx431250442719.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/2nx431250442719.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/30xy01250442719.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Aug/16/t1250442741phg6kdiys3lwn0a/30xy01250442719.ps (open in new window)

Parameters (Session):

par2 = grey ; par3 = FALSE ; par4 = Unknown ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = Unknown ;

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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