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Exponentional Smoothing - Nieuwe personenwagens - Alexander De Houwer

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Mon, 25 Jan 2010 14:46:18 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza.htm/, Retrieved Mon, 25 Jan 2010 22:47:44 +0100
 
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/Jan/25/t1264456060j2x45u3ttf7wyza.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 «
68897 38683 44720 39525 45315 50380 40600 36279 42438 38064 31879 11379 70249 39253 47060 41697 38708 49267 39018 32228 40870 39383 34571 12066 70938 34077 45409 40809 37013 44953 37848 32745 43412 34931 33008 8620 68906 39556 50669 36432 40891 48428 36222 33425 39401 37967 34801 12657 69116 41519 51321 38529 41547 52073 38401 40898 40439 41888 37898 8771 68184 50530 47221 41756 45633 48138 39486 39341 41117 41629 29722 7054 56231 34418 34568 29789 30630 35502 33091 27630 33520
 
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'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.391420833329359
beta0
gamma0.570171376485047


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024970721.3266559829-472.326655982892
143925339691.492306051-438.492306051041
154706047477.3180922313-417.31809223134
164169741877.6819068300-180.681906830039
173870838567.1700543144140.829945685604
184926748956.837972369310.162027630977
193901839926.8693283814-908.869328381443
203222835086.3714151689-2858.37141516886
214087039921.6311039019948.36889609805
223938335647.17825753963735.82174246039
233457131025.58419383343545.41580616663
241206612151.3362798722-85.3362798721682
257093870852.666644189885.3333558102022
263407740052.8523714584-5975.85237145841
274540945678.5874004602-269.58740046015
284080940218.8875217193590.112478280738
293701337321.6434689092-308.643468909242
304495347594.1354162223-2641.13541622234
313784836985.9703876026862.029612397411
323274532162.1728653753582.82713462468
334341239665.30700893763746.69299106237
343493137453.4070986882-2522.40709868816
353300830316.14208916392691.85791083609
3686209847.94311404445-1227.94311404445
376890668161.2547706059744.745229394146
383955635516.35040995884039.64959004124
395066947042.40367354383626.59632645623
403643243406.0623377924-6974.06233779241
414089137236.17937536623654.82062463385
424842848250.6920479249177.307952075083
433622239961.3031925521-3739.30319255215
443342533239.5664472244185.433552775576
453940141684.9962653044-2283.99626530438
463796734937.21618393583029.78381606419
473480131782.51523782613018.4847621739
481265710082.01572935142574.98427064861
496911670568.3842417824-1452.38424178238
504151938206.79106399763312.20893600245
515132149304.78172247482016.21827752518
523852941359.7354517122-2830.73545171221
534154740499.80004292361047.19995707643
545207349286.95816388652786.04183611346
553840140659.6398822971-2258.63988229705
564089835879.32735890285018.6726410972
574043945359.7092782919-4920.70927829195
584188839423.71683563932464.28316436071
593789836043.74644452721854.25355547282
60877113733.6503905962-4962.65039059618
616818469872.1572568186-1688.15725681855
625053039071.564860803511458.4351391965
634722152908.4566398564-5687.45663985639
644175640266.16560956431489.83439043573
654563342443.01320131823189.98679868184
664813852672.271164776-4534.27116477599
673948639429.153455326756.8465446733244
683934138080.35740540081260.64259459915
694111742640.8579964992-1523.85799649917
704162940597.01509117631031.98490882370
712972236444.7364522787-6722.73645227875
7270548412.0001831816-1358.00018318159
735623167097.673087001-10866.6730870010
743441837266.2125947004-2848.21259470037
753456839553.6556024449-4985.65560244493
762978929676.5440656061112.455934393929
773063031904.2004350705-1274.20043507054
783550237705.8080904286-2203.80809042857
793309126967.97441165476123.02558834527
802763028411.3177316676-781.317731667645
813352031206.34633940332313.65366059672


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8231551.448674322324741.451857518138361.4454911265
8324304.384592471216991.290531290831617.4786536516
84764.600984153938-7019.140587253798548.34255556167
8556682.367001068248454.85699176164909.8770103754
8633886.709801125225238.171828956942535.2477732936
8736547.321756950227497.321913921145597.3215999793
8830390.715952451820956.322211377839825.1096935257
8932093.192702091822289.465178113741896.9202260698
9038070.980283296227911.336516549648230.6240500428
9131085.127836243620581.621299377941588.6343731094
9227736.022764146716899.559426287338572.4861020060
9331910.813216274420751.322825779043070.3036067698
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/15tzb1264455975.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/15tzb1264455975.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/2wjvq1264455975.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/2wjvq1264455975.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/3ng2w1264455975.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jan/25/t1264456060j2x45u3ttf7wyza/3ng2w1264455975.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=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')
 




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