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Exponential Smoothing - Nieuwe geregistreerde domeinnamen - Dorien Dhanis

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Tue, 02 Jun 2009 08:47:22 -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/02/t12439540958rpufezk29qgyrf.htm/, Retrieved Tue, 02 Jun 2009 16:48:15 +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/02/t12439540958rpufezk29qgyrf.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 «
8166 7102 6047 5854 5764 5209 5616 5597 6251 7024 7237 9230 9016 8201 7630 7107 6820 6082 6019 6576 8086 8323 7842 9077 10737 10176 10416 9807 9565 10439 9115 9535 10790 11340 11196 12132 12013 12692 13330 11926 11356 11221 9999 11772 12543 14176 2924 2322 15557 13381 13145 12448 12178 11836 9815 12382 12662 12767 13136 13533 17808 15892 16830 14444 15550 15092 16364 14314 15874 17846 18504 15130 19845 18137 18898 19573 17368 18938 16713 16379 19139 21461 19796 16668
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.105286354127589
beta0.0235096656309281
gamma0.357989297961511


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1390168341.80493621812674.195063781877
1482017692.67196296991508.32803703009
1576307185.70804867018444.291951329816
1671076705.98981801135401.010181988650
1768206491.20256411012328.797435889876
1860825880.20373488518201.796265114823
1960196305.59531317355-286.595313173545
2065766256.22444562094319.775554379063
2180866996.0256132291089.974386771
2283237952.29768025301370.702319746989
2378428221.85319754435-379.853197544355
24907710443.1061170463-1366.10611704635
251073710364.0481378173372.951862182706
26101769455.23607663357720.763923366427
27104168816.912071469271599.08792853073
2898078315.30030146621491.69969853380
2995658117.625424429321447.37457557068
30104397407.058812030123031.94118796988
3191158042.873774447611072.12622555239
3295358383.909636833351151.09036316665
33107909764.11289270041025.8871072996
341134010678.1728122877661.827187712335
351119610732.2865452781463.713454721888
361213213374.3400349670-1242.34003496704
371201314077.9301818921-2064.93018189214
381269212753.1348944739-61.1348944738565
391333012165.01465368311164.98534631695
401192611360.2052048910565.794795109046
411135610932.0496986903423.950301309724
421122110472.1212611640748.878738836045
43999910156.8138772920-157.813877291954
441177210423.51206771621348.48793228377
451254311998.1757629573544.824237042711
461417612852.92234478671323.07765521327
47292412883.0602369135-9959.06023691351
48232214014.7344942861-11692.7344942861
491555713296.02552951192260.97447048808
501338113018.8754885759362.124511424125
511314512823.4629621890321.537037811015
521244811686.6052026555761.394797344487
531217811194.8802035217983.119796478302
541183610861.2585869274974.741413072567
55981510242.7440794549-427.744079454931
561238210938.61806919591443.38193080409
571266212245.5709638898416.429036110152
581276713305.1729213711-538.172921371066
59131369269.79717294483866.20282705521
601353311083.93302865452449.06697134546
611780817593.1192915399214.880708460139
621589216238.0010641410-346.001064141023
631683015907.0315156117922.968484388324
641444414739.3692059401-295.369205940066
651555014097.88735548081452.11264451923
661509213713.96970941461378.03029058543
671636412425.78332474843938.21667525159
681431414557.304094364-243.304094364014
691587415581.7613180096292.238681990364
701784616515.60129634391330.39870365611
711850413330.0267619585173.97323804201
721513015075.559811257254.4401887427684
731984521975.8139573879-2130.81395738792
741813719841.2262186486-1704.22621864859
751889819799.9595923961-901.959592396102
761957317704.36343489581868.63656510418
771736817836.6883887206-468.688388720642
781893817104.46076277441833.5392372256
791671316506.8408255114206.15917448861
801637916963.8004058771-584.800405877104
811913918322.5238356449816.476164355106
822146119844.71503019051616.28496980948
831979617477.81128146792318.18871853211
841666817208.5259236055-540.52592360555


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8524162.008317781222257.255614406826066.7610211557
8622108.864035972620154.537068126924063.1910038183
8722553.635861858520536.068354483524571.2033692335
8821244.516667771519186.749291923123302.2840436198
8920299.304786996718200.366564336122398.2430096573
9020344.440857405718185.777439963722503.1042748476
9118839.837776162016664.361128245321015.3144240787
9219033.154843759216792.883732822321273.4259546961
9321147.646796792318765.943936307223529.3496572775
9423044.750018386220516.789057077125572.7109796953
9520422.613411341017966.384704637822878.8421180443
9618823.655907277617310.632395259720336.6794192954
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/1w4b31243954036.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/1w4b31243954036.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/2nxnb1243954036.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/2nxnb1243954036.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/34s651243954036.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t12439540958rpufezk29qgyrf/34s651243954036.ps (open in new window)


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