Home » date » 2009 » Jun » 07 »

exponential smoothing Filip Bosschaerts

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Sun, 07 Jun 2009 15:31:29 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla.htm/, Retrieved Sun, 07 Jun 2009 23:32:17 +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/2009/Jun/07/t12444103378wz25r0aqypssla.htm/},
    year = {2009},
}
@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 = {2009},
    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:
Filip Bosschaerts
 
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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.276932709155431
beta0
gamma0.577138618850172


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240678.2345328283-2976.23453282829
143036432460.6011739035-2096.60117390354
153260934167.0670641293-1558.06706412932
163021231322.1289976808-1110.1289976808
172996530682.1979668410-717.197966841046
182835228822.4157242163-470.415724216327
192581422246.80888994643567.19111005355
202241421276.26412146211137.73587853791
212050621938.2570672756-1432.25706727559
222880627765.74323742791040.25676257205
232222823220.1160275709-992.116027570948
241397114690.4083149259-719.408314925868
253684537684.0013503702-839.001350370214
263533830425.31761441724912.68238558284
273502234297.6190903654724.380909634558
283477732271.69458509682505.30541490321
292688732796.9696720100-5909.96967200996
302397029602.1238049251-5632.12380492505
312278023282.0051084644-502.00510846444
321735120170.7307045642-2819.73070456416
332138218664.28780394552717.7121960545
342456126672.8410937893-2111.84109378929
351740920406.1652789812-2997.16527898118
361151411434.997516417779.0024835822751
373151434599.7892408052-3085.78924080518
382707129119.1319184530-2048.13191845304
392946229315.9359011925146.064098807492
402610527873.0542625796-1768.05426257959
412239723703.117345793-1306.11734579302
422384321899.17665074871943.82334925126
432170519817.93565269281887.06434730720
441808916401.06252359131687.93747640872
452076418453.77099997182310.22900002819
462531624334.0577029644981.94229703558
471770418554.6970174236-850.697017423641
481554811461.67227175144086.32772824861
492802934415.5240158981-6386.52401589813
502938328453.8101070086929.189892991424
513643830390.79195131006047.20804868996
523203429783.34925026082250.65074973920
532267926919.0941211718-4240.09412117184
542431925658.8722276831-1339.87222768305
551800422644.5824150959-4640.58241509589
561753717336.8927377133200.107262286729
572036619237.2608736831128.73912631699
582278224236.0469846087-1454.04698460875
591916917017.30236999972151.69763000032
601380712816.0089888519990.99101114807
612974330542.2343858723-799.234385872296
622559129180.7447235738-3589.74472357377
632909632002.0862132317-2906.08621323174
642648227330.8419313555-848.841931355491
652240520899.5827813071505.41721869300
662704422440.77267399884603.22732600125
671797019694.9019632502-1724.90196325023
681873017214.72806039411515.27193960594
691968419866.8357300826-182.835730082639
701978523424.5812421143-3639.58124211433
711847917105.30419734111373.69580265894
721069812204.1821164803-1506.1821164803


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7328491.779530535823325.366781081433658.1922799902
7426187.115982280720826.252014494831547.9799500666
7530287.872775726024739.368088471435836.3774629805
7627279.927551632321549.923533495333009.9315697693
7722066.196518729116160.268324850927972.1247126074
7824483.234456872418406.473015559630559.9958981853
7917821.787533844311578.865830186024064.7092375025
8017171.452562648410766.679874926623576.2252503703
8118695.294459590512132.661225532125257.9276936489
8220861.138497040614144.353793914627577.9232001667
8317641.871478024910774.394610096824509.3483459531
8411158.52607673704143.5934102811618173.4587431928
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/1r6ao1244410284.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/1r6ao1244410284.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/2kh4t1244410284.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/2kh4t1244410284.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/3g9cs1244410284.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/07/t12444103378wz25r0aqypssla/3g9cs1244410284.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')
 




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