*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Fri, 28 May 2010 14:31:39 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr.htm/, Retrieved Fri, 28 May 2010 16:33:51 +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/2010/May/28/t12750572302pyp8nsrkw0rwpr.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:

KDGP2W61

Dataseries X:

» Textbox « » Textfile « » CSV «

41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.298636158049011 beta 0 gamma 0.619823384767296 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 37702 40443.7037927351 -2741.70379273505 14 30364 31996.9844988044 -1632.98449880435 15 32609 33561.8688751679 -952.86887516793 16 30212 30629.3187017367 -417.31870173672 17 29965 29937.6615078748 27.3384921251818 18 28352 28050.12836337 301.871636629967 19 25814 21460.4140757306 4353.5859242694 20 22414 20567.6048431308 1846.39515686924 21 20506 21231.3911255919 -725.391125591916 22 28806 27004.3573666691 1801.64263333094 23 22228 22474.1539274377 -246.153927437736 24 13971 13911.1543908325 59.8456091675198 25 36845 36937.4508844866 -92.4508844865995 26 35338 29763.8786486656 5574.12135133435 27 35022 33776.7264539928 1245.27354600721 28 34777 31733.4363755032 3043.56362449683 29 26887 32268.6259188965 -5381.62591889647 30 23970 28885.1259418206 -4915.12594182057 31 22780 22498.7957062659 281.20429373407 32 17351 19299.8958105312 -1948.89581053121 33 21382 17712.2596481312 3669.74035186876 34 24561 25896.3275058556 -1335.32750585557 35 17409 19539.0897327482 -2130.08973274819 36 11514 10546.5034871906 967.49651280944 37 31514 33777.6507673379 -2263.65076733789 38 27071 28419.0617150119 -1348.06171501192 39 29462 28482.8512417911 979.148758208943 40 26105 27141.8424179566 -1036.84241795661 41 22397 22795.8623682015 -398.862368201477 42 23843 21103.1934223411 2739.80657765889 43 21705 19261.8603927031 2443.13960729689 44 18089 15739.1196211125 2349.8803788875 45 20764 17877.7965872684 2886.20341273161 46 25316 23652.0603236637 1663.93967633631 47 17704 17845.0117841157 -141.011784115715 48 15548 10793.0241261994 4754.97587380063 49 28029 33750.5998189922 -5721.59981899219 50 29383 27757.368586067 1625.63141393296 51 36438 29720.8993216367 6717.10067836331 52 32034 29217.055281909 2816.94471809096 53 22679 26299.2991948781 -3620.29919487807 54 24319 25009.0402644495 -690.040264449468 55 18004 22014.4633783915 -4010.46337839154 56 17537 16523.9015942899 1013.09840571007 57 20366 18496.5183944649 1869.48160553511 58 22782 23435.8076544214 -653.807654421384 59 19169 16151.9443704819 3017.05562951808 60 13807 12171.4619609295 1635.53803907052 61 29743 29643.0658184312 99.9341815688058 62 25591 28582.3560621918 -2991.3560621918 63 29096 31380.4596235772 -2284.45962357716 64 26482 26492.9417286765 -10.9417286764692 65 22405 19932.2668132161 2472.73318678387 66 27044 21735.4548384755 5308.54516152455 67 17970 19088.8124421773 -1118.81244217734 68 18730 16645.6535555293 2084.34644447074 69 19684 19310.4721237642 373.527876235796 70 19785 22706.0868862811 -2921.08688628111 71 18479 16340.9360090158 2138.06399098422 72 10698 11497.3792236086 -799.379223608617 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 27574.2684090769 22373.7296416929 32774.807176461 74 25139.8637104647 19712.3756604663 30567.351760463 75 29138.5975825404 23493.2765469672 34783.9186181136 76 25921.6495209015 20066.5942131785 31776.7048286246 77 20443.9496087595 14386.4174612339 26501.4817562851 78 22741.4791274721 16488.02258088 28994.9356740643 79 15715.4013080137 9271.9750578012 22158.8275582261 80 14998.8429807904 8370.88968405255 21626.7962775282 81 16297.470360516 9489.99006560895 23104.9506554231 82 18149.2956282438 11166.9026983552 25131.6885581324 83 14855.8096389228 7702.7799249366 22008.8393529089 84 8096.77929892456 777.089609396782 15416.4689884523

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/1wcwh1275057095.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/1wcwh1275057095.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/274dk1275057095.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/274dk1275057095.ps (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/374dk1275057095.png (open in new window) http://www.freestatistics.org/blog/date/2010/May/28/t12750572302pyp8nsrkw0rwpr/374dk1275057095.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=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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