*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 05 Jun 2010 09:58:01 +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/Jun/05/t1275731938empp36giexmc5aa.htm/, Retrieved Sat, 05 Jun 2010 11:58:59 +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/Jun/05/t1275731938empp36giexmc5aa.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 «

8027,7 8059,6 8059,5 7988,9 7950,2 8003,8 8037,5 8069 8157,6 8244,3 8329,4 8417 8432,5 8486,4 8531,1 8643,8 8727,9 8847,3 8904,3 9003,2 9025,3 9044,7 9120,7 9184,3 9247,2 9407,1 9488,9 9592,5 9666,2 9809,6 9932,7 10008,9 10103,4 10194,3 10328,8 10507,6 10601,2 10684 10819,9 11014,3 11043 11258,5 11267,9 11334,5 11297,2 11371,3 11340,1 11380,1 11477,9 11538,8 11596,4 11598,8 11645,8 11738,7 11935,5 12042,8 12127,6 12213,8 12303,5 12410,3 12534,1 12587,5 12683,2 12748,7 12915,9 12962,5 12965,9 13060,7 13099,9 13204 13321,1 13391,2 13366,9 13415,3 13324,6 13141,9 12925,4 12901,5 12973 13155

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 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.517785522407035 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8059.5 8091.5 -32.0000000000009 4 7988.9 8074.83086328297 -85.9308632829752 5 7950.2 7959.73710634711 -9.53710634711206 6 8003.8 7916.09893075492 87.7010692450795 7 8037.5 8015.10927470964 22.39072529036 8 8069 8060.40286810118 8.59713189881859 9 8157.6 8096.35433853261 61.2456614673874 10 8244.3 8216.66645535067 27.6335446493304 11 8329.4 8317.67470470288 11.7252952971194 12 8417 8408.84589285368 8.15410714632344 13 8432.5 8500.6679714822 -68.1679714821985 14 8486.4 8480.87158275686 5.52841724313839 15 8531.1 8537.63411716718 -6.53411716718256 16 8643.8 8578.9508458963 64.8491541036947 17 8727.9 8725.22879903154 2.67120096845974 18 8847.3 8810.71190822045 36.5880917795512 19 8904.3 8949.0566924364 -44.7566924364 20 9003.2 8982.882325062 20.3176749379945 21 9025.3 9092.30252299387 -67.0025229938747 22 9044.7 9079.7095866229 -35.0095866228985 23 9120.7 9080.98212952411 39.7178704758917 24 9184.3 9177.54746783736 6.75253216263627 25 9247.2 9244.64383123076 2.55616876923887 26 9407.1 9308.8673784123 98.2326215876965 27 9488.9 9519.6308076985 -30.7308076985028 28 9592.5 9585.51884038034 6.98115961965777 29 9666.2 9692.73358376101 -26.5335837610128 30 9809.6 9752.69487823199 56.9051217680135 31 9932.7 9925.55952643427 7.140473565727 32 10008.9 10052.3567602697 -43.4567602697389 33 10103.4 10106.0554789514 -2.65547895135387 34 10194.3 10199.1805103953 -4.88051039528546 35 10328.8 10287.5534527706 41.2465472293497 36 10507.6 10443.4103177753 64.1896822247163 37 10601.2 10655.4468059192 -54.2468059191506 38 10684 10720.9585951774 -36.9585951773915 39 10819.9 10784.621969666 35.2780303339641 40 11014.3 10938.788423032 75.5115769680015 41 11043 11172.2872243602 -129.287224360152 42 11258.5 11134.0441713543 124.455828645723 43 11267.9 11413.9855976062 -146.085597606203 44 11334.5 11347.7445901335 -13.2445901335304 45 11297.2 11407.4867331122 -110.286733112172 46 11371.3 11313.0818593931 58.2181406068757 47 11340.1 11417.3263697408 -77.226369740818 48 11380.1 11346.139673541 33.9603264590296 49 11477.9 11403.7238389177 74.1761610823269 50 11538.8 11539.9311812338 -1.13118123383356 51 11596.4 11600.2454719677 -3.84547196773565 52 11598.8 11655.854342256 -57.0543422560204 53 11645.8 11628.7124298454 17.0875701546029 54 11738.7 11684.5601262846 54.1398737154359 55 11935.5 11805.4929690794 130.007030920637 56 12042.8 12069.6087275012 -26.8087275011931 57 12127.6 12163.0275565269 -35.4275565269181 58 12213.8 12229.483680663 -15.6836806630254 59 12303.5 12307.5628978777 -4.06289787765309 60 12410.3 12395.1591881776 15.1408118224117 61 12534.1 12509.7988813367 24.3011186632793 62 12587.5 12646.1816487589 -58.681648758864 63 12683.2 12669.1971406005 14.0028593994521 64 12748.7 12772.1476184699 -23.4476184698869 65 12915.9 12825.5067810913 90.3932189087427 66 12962.5 13039.511081166 -77.0110811659724 67 12965.9 13046.2358582733 -80.3358582733199 68 13060.7 13008.0391139292 52.6608860707511 69 13099.9 13130.1061583338 -30.2061583338127 70 13204 13153.665846861 50.3341531389724 71 13321.1 13283.828142639 37.2718573609927 72 13391.2 13420.2269707738 -29.0269707737498 73 13366.9 13475.2972255478 -108.397225547771 74 13415.3 13394.87071149 20.4292885099549 75 13324.6 13453.8487013136 -129.248701313574 76 13141.9 13296.2255949835 -154.325594983497 77 12925.4 13033.6180361642 -108.218036164189 78 12901.5 12761.0843037751 140.415696224949 79 12973 12809.889518399 163.110481600967 80 13155 12965.8457643249 189.154235675147 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 81 13245.7870890594 13111.2101431316 13380.3640349872 82 13336.5741781188 13091.9670052511 13581.1813509865 83 13427.3612671782 13060.1061724895 13794.6163618669 84 13518.1483562376 13015.2040037588 14021.0927087165

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/1io0u1275731878.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/1io0u1275731878.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/2bfif1275731878.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/2bfif1275731878.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/3bfif1275731878.png (open in new window) http://www.freestatistics.org/blog/date/2010/Jun/05/t1275731938empp36giexmc5aa/3bfif1275731878.ps (open in new window)

Parameters (Session):

par1 = 4 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 4 ; par2 = Double ; 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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