triple exponential smoothing

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

Title produced by software: Exponential Smoothing

Date of computation: Wed, 07 May 2008 09:20:20 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/07/t12101736723ainlvetprhatg9.htm/, Retrieved Wed, 07 May 2008 17:21:16 +0200

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 'George Udny Yule' @ 72.249.76.132 Estimated Parameters of Exponential Smoothing Parameter Value alpha 0 beta 0.00123082877145252 gamma 0.371586577726775 Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 13 50556 50513.9134722223 42.0865277777484 14 43901 43929.062602657 -28.0626026570244 15 48572 48570.8367330918 1.16326690820279 16 43899 43787.1525301932 111.847469806758 17 37532 37300.9683272947 231.031672705300 18 40357 39861.1174577295 495.882542270527 19 35489 34972.7665881643 516.233411835739 20 29027 28567.9573852657 459.042614734299 21 34485 33416.9398490338 1068.06015096618 22 42598 40769.9223128019 1828.07768719806 23 30306 28174.0714432367 2131.92855676329 24 26451 24277.2622403382 2173.73775966184 25 47460 52769.341826265 -5309.34182626495 26 50104 46158.4244813910 3945.57551860905 27 61465 50811.0585526786 10653.9414473214 28 53726 46068.5031139435 7657.4968860565 29 39477 39626.6061611191 -149.606161119111 30 43895 42285.1703197836 1609.82968021640 31 31481 37404.3815601939 -5923.38156019388 32 29896 30978.3210247229 -1082.32102472293 33 33842 36053.606230555 -2211.60623055504 34 39120 43689.0010096239 -4569.0010096239 35 33702 31206.0570448197 2495.94295518028 36 25094 27324.7835805437 -2230.78358054374 37 51442 53036.2512322789 -1594.25123227890 38 45594 49864.3369507308 -4270.33695073079 39 52518 57009.7097596075 -4491.70975960753 40 48564 51153.715741004 -2589.71574100402 41 41745 41810.8040849194 -65.8040849193858 42 49585 45123.1509865956 4461.84901340444 43 32747 37443.1220428889 -4696.12204288891 44 33379 32815.9346243618 563.065375638238 45 35645 37471.5926052812 -1826.59260528124 46 37034 44231.0111260449 -7197.01112604494 47 35681 34373.3055109538 1307.69448904622 48 20972 28735.6439094178 -7763.64390941777 49 58552 54683.638438057 3868.36156194295 50 54955 50517.3266226859 4437.67337731409 51 65540 57580.4402671104 7959.55973288963 52 51570 52431.2016967365 -861.201696736542 53 51145 44026.1417354211 7118.85826457889 54 46641 49020.9037570375 -2379.90375703746 55 35704 37937.8956896019 -2233.89568960192 56 33253 35264.951725549 -2011.95172554898 57 35193 39032.6448754011 -3839.64487540111 58 41668 43796.4879570737 -2128.48795707374 59 34865 37099.016796068 -2234.01679606799 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 60 28090.5676036453 20440.2913724045 35740.843834886 61 58360.8592374866 50710.5830062458 66011.1354687274 62 54406.0960512486 46755.8198200079 62056.3722824894 63 62777.895393684 55127.6191624433 70428.1716249248 64 54350.9802707311 46700.7040394903 62001.2565019719 65 48911.2034804953 41260.9272492545 56561.4797117361 66 50376.3530298582 42726.0767986174 58026.629261099 67 39347.5996005215 31697.3233692808 46997.8758317623 68 36757.1270345181 29106.8508032774 44407.4032657589 69 39845.673941682 32195.3977104413 47495.9501729228 70 45245.3599665894 37595.0837353487 52895.6361978302 71 38508.6757054503 30858.3994742096 46158.9519366911

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/16l7y1210173618.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/16l7y1210173618.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/2o64u1210173618.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/2o64u1210173618.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/3dlxt1210173618.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/07/t12101736723ainlvetprhatg9/3dlxt1210173618.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=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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