*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Mon, 17 Jan 2011 08:17:23 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7.htm/, Retrieved Mon, 17 Jan 2011 09:15:02 +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/2011/Jan/17/t129525209938td2rrhmmsvcq7.htm/}, year = {2011}, } @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 = {2011}, 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:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

6715 7703 9856 8326 9269 7035 10342 11682 10304 11385 9777 8882 7897 6930 9545 9110 7459 7320 10017 12307 11072 10749 9589 9080 7384 8062 8511 8684 8306 7643 10577 13747 11783 11611 9946 8693 7303 7609 9423 8584 7586 6843 11811 13414 12103 11501 8213 7982 7687 7180 7862 8043 8340 6692 10065 12684 11587 9843 8110 7940 6475 6121 9669 7778 7826 7403 10741 14023 11519 10236 8075 8157

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' @ www.wessa.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.113673696771336 beta 0 gamma 0.687041745941993 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 7897 8033.04353241997 -136.043532419971 14 6930 7020.78799293574 -90.7879929357387 15 9545 9587.90823085265 -42.9082308526486 16 9110 9133.71624314024 -23.7162431402376 17 7459 7498.08212829965 -39.0821282996476 18 7320 7347.88711799718 -27.887117997182 19 10017 10286.1761146323 -269.176114632271 20 12307 11554.1148044881 752.885195511892 21 11072 10308.4913747681 763.508625231909 22 10749 11452.6349210914 -703.634921091387 23 9589 9803.733404871 -214.733404871011 24 9080 8938.38201277751 141.617987222487 25 7384 7874.41139417128 -490.411394171285 26 8062 6863.45002244018 1198.54997755982 27 8511 9623.0059046685 -1112.00590466849 28 8684 9061.68444169751 -377.684441697515 29 8306 7394.00248774349 911.99751225651 30 7643 7358.23379465385 284.766205346151 31 10577 10208.6829044251 368.317095574934 32 13747 12198.4337969091 1548.56620309093 33 11783 11015.6951503757 767.304849624286 34 11611 11267.6379926474 343.362007352556 35 9946 9993.27522487825 -47.2752248782454 36 8693 9342.10264062157 -649.102640621568 37 7303 7764.4653634404 -461.4653634404 38 7609 7772.73111870512 -163.73111870512 39 9423 8965.28179842135 457.718201578655 40 8584 9028.86834169099 -444.86834169099 41 7586 8113.08145946444 -527.081459464444 42 6843 7531.0107048825 -688.010704882506 43 11811 10278.5557457046 1532.44425429542 44 13414 13100.3132055348 313.686794465231 45 12103 11322.7166137701 780.283386229887 46 11501 11318.4278467755 182.572153224544 47 8213 9811.5665351329 -1598.5665351329 48 7982 8647.77384857799 -665.773848577992 49 7687 7227.59298198486 459.407018015137 50 7180 7516.56167840749 -336.561678407485 51 7862 9029.58391838196 -1167.58391838196 52 8043 8380.14685960922 -337.146859609222 53 8340 7462.42794031059 877.572059689413 54 6692 6951.24651036826 -259.246510368259 55 10065 11017.6530699823 -952.653069982258 56 12684 12734.0841470802 -50.0841470801988 57 11587 11264.0102411256 322.989758874404 58 9843 10865.6600082615 -1022.6600082615 59 8110 8279.43300262341 -169.433002623409 60 7940 7861.35410525662 78.6458947433803 61 6475 7232.74301618565 -757.743016185649 62 6121 6910.89276064295 -789.89276064295 63 9669 7790.98844082486 1878.01155917514 64 7778 7992.62037207107 -214.62037207107 65 7826 7824.37619228277 1.62380771722565 66 7403 6564.31497236196 838.685027638036 67 10741 10270.8576665589 470.142333441121 68 14023 12697.480055163 1325.51994483697 69 11519 11595.7800622879 -76.780062287924 70 10236 10316.0588405195 -80.0588405195376 71 8075 8321.69830060509 -246.698300605085 72 8157 8041.80556232065 115.194437679349 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 6882.67294212008 5886.81144868338 7878.53443555678 74 6613.47886287942 5606.28661607364 7620.67110968521 75 9288.34704542431 8246.68124624228 10330.0128446063 76 7982.17606639205 6943.46006622989 9020.89206655422 77 7969.90398755861 6919.51818824659 9020.28978687064 78 7198.1983876587 6147.98412428637 8248.41265103103 79 10596.6764380603 9462.47410836109 11730.8787677595 80 13477.4692649095 12249.0744792147 14705.8640506043 81 11398.4491660813 10223.7671071721 12573.1312249904 82 10140.9620142998 8992.5190733938 11289.4049552058 83 8077.5006144051 6975.11485836901 9179.88637044117 84 8046.11157061404 7534.21552607787 8558.0076151502

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/18usq1295252242.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/18usq1295252242.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/2hclm1295252242.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/2hclm1295252242.ps (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/374ec1295252242.png (open in new window) http://www.freestatistics.org/blog/date/2011/Jan/17/t129525209938td2rrhmmsvcq7/374ec1295252242.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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