*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 25 Jan 2010 13:15:08 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m.htm/, Retrieved Mon, 25 Jan 2010 21:16:04 +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/2010/Jan/25/t12644505589jw94c49ex8047m.htm/}, year = {2010}, } @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 = {2010}, 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:

KDGP2W62

Dataseries X:

» Textbox « » Textfile « » CSV «

5789 6333 6901 5813 6504 5619 5867 6084 5258 5601 5081 4678 5463 5546 6810 6407 5985 5119 5904 5034 4922 6083 4365 4464 4557 5885 5286 6017 5376 5935 6276 5510 5998 5193 4602 5326 5307 5014 6153 6441 5584 6427 6062 5589 6216 5809 4989 6706 7174 6122 8075 6292 6337 8576 6077 5931 6288 7167 6054 6468 6403 6927 7914 7728 8701 8522 6481 7502 7778 7424 6941 8574 9171 7718 9083 7164 8213 8124 7075 7026 7390 7778 6203 6905 7087 6495 7664 6516 6322 7828 6708 6717 5707 8063 6315 5893 6914 7319 6615 7341 6210 7408 6168 5878 6834 6211 5982 6973

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 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.227226293087861 beta 0.00400719516398090 gamma 0.468268628242811 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 5463 5564.62030934466 -101.620309344661 14 5546 5645.370230533 -99.3702305330025 15 6810 6947.82867380658 -137.828673806577 16 6407 6473.49533036791 -66.4953303679094 17 5985 6018.63991562603 -33.6399156260304 18 5119 5155.82803312001 -36.8280331200131 19 5904 5607.62182296341 296.378177036587 20 5034 5908.09839262955 -874.098392629551 21 4922 4944.12993792744 -22.1299379274387 22 6083 5218.77152118562 864.228478814378 23 4365 4889.35761956567 -524.357619565667 24 4464 4405.36579053152 58.6342094684833 25 4557 5120.96749380307 -563.967493803075 26 5885 5084.51720181596 800.48279818404 27 5286 6500.28623857647 -1214.28623857647 28 6017 5842.51903868147 174.480961318528 29 5376 5488.01101343521 -112.011013435206 30 5935 4680.0453282685 1254.9546717315 31 6276 5525.22771223572 750.772287764278 32 5510 5497.85968270902 12.1403172909777 33 5998 5036.32253345798 961.677466542022 34 5193 5886.82285300407 -693.82285300407 35 4602 4696.88212709086 -94.8821270908611 36 5326 4519.87855823765 806.121441762346 37 5307 5206.21138924348 100.78861075652 38 5014 5862.86548180036 -848.86548180036 39 6153 6167.51037641228 -14.5103764122814 40 6441 6297.004497691 143.995502309000 41 5584 5803.71369864202 -219.71369864202 42 6427 5424.4526546247 1002.54734537530 43 6062 6040.77316263407 21.2268373659344 44 5589 5575.87746116157 13.1225388384264 45 6216 5443.4791066912 772.520893308798 46 5809 5646.23803220823 162.761967791771 47 4989 4839.22847908395 149.771520916050 48 6706 5043.28937991882 1662.71062008118 49 7174 5694.40843060607 1479.59156939393 50 6122 6358.08576395324 -236.085763953241 51 8075 7254.01794292782 820.98205707218 52 6292 7681.66551547145 -1389.66551547145 53 6337 6614.10719025756 -277.107190257564 54 8576 6672.8638747727 1903.1361252273 55 6077 7154.25202246334 -1077.25202246334 56 5931 6376.98248550287 -445.982485502868 57 6288 6428.93049316508 -140.930493165078 58 7167 6191.21066920885 975.789330791152 59 6054 5469.68382585193 584.316174148069 60 6468 6377.11893836784 90.8810616321607 61 6403 6589.49810437552 -186.498104375516 62 6927 6254.52454015845 672.475459841549 63 7914 7774.53806132073 139.461938679266 64 7728 7221.93899691618 506.061003083815 65 8701 6966.45053014664 1734.54946985336 66 8522 8359.83831051347 162.161689486527 67 6481 7276.77058106426 -795.770581064257 68 7502 6766.5726491668 735.427350833205 69 7778 7238.94888090384 539.051119096164 70 7424 7585.31733620368 -161.317336203680 71 6941 6337.61620357216 603.383796427842 72 8574 7143.82737920431 1430.17262079569 73 9171 7581.82794222258 1589.17205777742 74 7718 7968.311187041 -250.311187041008 75 9083 9318.25292636613 -235.252926366129 76 7164 8737.87363004178 -1573.87363004178 77 8213 8431.35671139932 -218.356711399318 78 8124 8836.0324898033 -712.032489803305 79 7075 7163.79785863682 -88.7978586368235 80 7026 7375.32200042453 -349.322000424528 81 7390 7531.14629362274 -141.146293622739 82 7778 7469.69768740157 308.302312598425 83 6203 6595.34870468105 -392.348704681050 84 6905 7424.91832742048 -519.918327420483 85 7087 7435.72618656723 -348.726186567232 86 6495 6797.93282439275 -302.932824392748 87 7664 7937.71647368105 -273.716473681052 88 6516 6981.53634082563 -465.536340825629 89 6322 7347.30617119082 -1025.30617119082 90 7828 7340.32445446061 487.675545539393 91 6708 6309.53217276756 398.467827232438 92 6717 6519.05061806593 197.949381934065 93 5707 6845.19391198431 -1138.19391198431 94 8063 6699.15604276166 1363.84395723834 95 6315 5907.39682102024 407.60317897976 96 5893 6818.06315412562 -925.063154125619 97 6914 6781.4279857217 132.572014278303 98 7319 6298.26054744564 1020.73945255436 99 6615 7732.32433212231 -1117.32433212231 100 7341 6548.57837227765 792.421627722353 101 6210 6987.14737327979 -777.147373279788 102 7408 7590.3860097346 -182.386009734596 103 6168 6385.39907855026 -217.399078550256 104 5878 6379.84234581784 -501.842345817840 105 6834 6057.93455901892 776.065440981076 106 6211 7241.26909505805 -1030.26909505805 107 5982 5651.11627772225 330.883722277754 108 6973 6027.16018506365 945.839814936346 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 109 6795.91081526721 5948.80138045065 7643.02025008377 110 6593.11322302713 5687.94898724789 7498.27745880638 111 6988.19548846407 6011.10222787822 7965.28874904992 112 6744.92964029036 5724.19533930152 7765.6639412792 113 6439.51385370796 5383.41362636948 7495.61408104644 114 7420.66942208264 6239.22384896921 8602.11499519606 115 6253.9760871294 5121.71885400941 7386.23332024938 116 6192.25563919212 5015.95653394146 7368.55474444279 117 6444.65176732062 5193.64392100921 7695.65961363203 118 6782.10826614538 5445.2047534634 8119.01177882736 119 5899.22713435604 4626.97034888777 7171.4839198243 120 6416.53131944743 5316.10183786378 7516.96080103108

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/18p2b1264450506.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/18p2b1264450506.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/2nee71264450506.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/2nee71264450506.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/3jqyl1264450506.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jan/25/t12644505589jw94c49ex8047m/3jqyl1264450506.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Triple ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Triple ; 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=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) 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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