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DOUBLE MULTIPLICATIEF MODEL - LAURA VERBEEK

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Thu, 04 Jun 2009 04:54:08 -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/04/t1244112892cibpadqx5u6csad.htm/, Retrieved Thu, 04 Jun 2009 12:54:52 +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/04/t1244112892cibpadqx5u6csad.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937
 
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
alpha0.940153707491614
beta0.00064617126624545
gamma0


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3982810073-245
4992410018.5135040882-94.5135040882033
51037110105.4500282521265.549971747883
61084610531.0628858462314.937114153763
71041311003.2985728707-590.298572870655
81070910624.114966018484.885033981629
91066210879.7592980704-217.759298070419
101057010850.7391504510-280.739150450972
111029710762.3377119973-465.337711997287
121063510500.1025587032134.89744129684
131087210802.262660382969.7373396170697
141029611043.2046163435-747.204616343482
151038310515.6416365650-132.641636564989
161043110565.7817408768-134.781740876790
171057410613.8279382358-39.8279382358469
181065310751.1211097033-98.1211097033247
191080510833.5501312895-28.5501312894867
201087210981.3692219516-109.369221951580
211062511053.1395030552-428.139503055188
221040710824.9566276596-417.956627659563
231046310606.0933115385-143.093311538509
241055610645.5568318907-89.5568318907499
251064610735.2984662666-89.2984662665986
261070210825.2287551958-123.228755195796
271135310883.1844956848469.815504315238
281134611498.9784085249-152.978408524928
291145111529.1573807744-78.1573807743516
301196411629.6321390286334.367860971364
311257412118.1471613238455.85283867623
321303112721.1536665542309.846333445776
331381213187.0798463185624.920153681498
341454413949.6034854990594.396514500952
351493114683.7913082057247.208691794338
361488615091.7193915560-205.719391556016
371600515073.7004835230931.299516477016
381706416125.2198821118938.78011788824
391516817184.3425050657-2016.34250506574
401605015463.970709257586.029290742999
411583916190.5844185262-351.584418526210
421513716035.4835351872-898.483535187188
431495415365.6675906678-411.667590667834
441564815153.2833730648494.716626935238
451530515793.3401785581-488.340178558137
461557915508.875816881470.1241831186053
471634815749.4963958001598.503604199923
481592816487.2384375367-559.2384375367
491617116136.185268890634.8147311093562
501593716343.6545391543-406.654539154317
511571316135.8277954767-422.827795476715
521559415912.5388368879-318.538836887879
531568315787.1040169241-104.104016924099
541643815863.2076447418574.79235525816
551703216577.9274004043454.072599595715
561769617179.4278794590516.572120541041
571774517840.0013325710-95.0013325710424
581939417925.54402299721468.45597700279
592014819481.8689869877666.131013012273
602010820284.2898362675-176.289836267482
611858420294.5985046982-1710.59850469817
621844118861.3820009425-420.38200094254
631839118640.9119444631-249.911944463052
641917818580.5581220149597.441877985082
651807919317.2100834256-1238.21008342565
661848318327.3148346403155.685165359722
671964418647.9899506419996.010049358109
681919519759.3046982474-564.304698247426
691965019403.3409357577246.659064242271
702083019809.95760667251020.04239332753
712359520944.29315781072650.70684218925
722293723613.3142414538-676.314241453827


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7323154.013257294621844.888414844624463.1380997447
7423330.551614667721533.169617057425127.9336122780
7523507.089972040721327.797473077225686.3824710042
7623683.628329413721179.629453571526187.6272052559
7723860.166686786721068.631798439626651.7015751339
7824036.705044159720984.281900337127089.1281879823
7924213.243401532820920.239957341327506.2468457242
8024389.781758905820872.33635046227907.2271673496
8124566.320116278820837.655493695428294.9847388622
8224742.858473651820814.064008754428671.6529385493
8324919.396831024820799.945204232929038.8484578167
8425095.935188397920794.039279975929397.8310968198
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/1nlf01244112842.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/1nlf01244112842.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/22vfs1244112842.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/22vfs1244112842.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/3mich1244112842.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/04/t1244112892cibpadqx5u6csad/3mich1244112842.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; 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=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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