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*The author of this computation has been verified*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Tue, 07 Dec 2010 18:46:49 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl.htm/, Retrieved Tue, 07 Dec 2010 19:45:33 +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/Dec/07/t1291747532g25nltqxgmqognl.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:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
13328 12873 14000 13477 14237 13674 13529 14058 12975 14326 14008 16193 14483 14011 15057 14884 15414 14440 14900 15074 14442 15307 14938 17193 15528 14765 15838 15723 16150 15486 15986 15983 15692 16490 15686 18897 16316 15636 17163 16534 16518 16375 16290 16352 15943 16362 16393 19051 16747 16320 17910 16961 17480 17049 16879 17473 16998 17307 17418 20169 17871 17226 19062 17804 19100 18522 18060 18869 18127 18871 18890 21263 19547 18450 20254 19240 20216 19420 19415 20018 18652 19978 19509 21971
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.441210707478134
beta0
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131448313934.6017628205548.398237179485
141401113700.065161968310.934838032037
151505714874.7571667774182.242833222597
161488414775.1272144314108.872785568577
171541415368.500611452345.4993885476906
181444014429.121320471610.878679528354
191490014650.1753353045249.824664695496
201507415288.8215439687-214.821543968683
211444214114.5442035144327.455796485561
221530715602.317098758-295.317098758043
231493815141.315924293-203.315924293007
241719317250.6149864358-57.6149864358413
251552815827.5545920913-299.554592091294
261476515086.2001187187-321.200118718656
271583815910.0756977178-72.0756977177753
281572315657.239289389965.7607106100913
291615016196.1788016315-46.178801631504
301548615197.004430002288.995569997956
311598615674.2870528431311.712947156899
321598316080.5997081843-97.599708184258
331569215261.0606682514430.939331748588
341649016446.492781765843.5072182342119
351568616186.3937951022-500.393795102198
361889718246.0350436742650.96495632581
371631617000.4144461031-684.414446103096
381563616077.1603957516-441.160395751614
391716316987.3162750128175.683724987248
401653416920.8154859542-386.815485954226
411651817197.5229334712-679.522933471191
421637516106.2021993499268.797800650093
431629016587.2675771981-297.267577198112
441635216496.1719754499-144.171975449859
451594315951.4267087222-8.42670872215604
461636216726.5129040676-364.512904067622
471639315982.4650081337410.534991866254
481905119087.3847334156-36.3847334156053
491674716792.3023814173-45.302381417303
501632016286.959175982633.0408240173674
511791017751.023600729158.976399271021
521696117362.832824545-401.832824545036
531748017469.35267396410.6473260359744
541704917212.4539204237-163.453920423715
551687917186.4939385994-307.493938599382
561747317176.4345396915296.565460308535
571699816902.000350364895.9996496352142
581730717524.1834199866-217.183419986577
591741817278.2273353959139.772664604061
602016920013.9498656037155.050134396297
611787117798.347540850872.6524591491543
621722617388.8246184117-162.824618411705
631906218836.8425637327225.157436267276
641780418164.4773802876-360.477380287623
651910018519.733186048580.266813952025
661852218416.8707374281105.129262571947
671806018428.9245119387-368.924511938749
681886918729.3032104639139.696789536079
691812718273.5828564744-146.582856474353
701887118613.7325810499257.267418950065
711889018776.5725247399113.427475260094
722126321509.2081618553-246.208161855302
731954719070.523441675476.47655832499
741845018707.5899661546-257.58996615461
752025420330.5966431988-76.59664319882
761924019197.847864049242.1521359508151
772021620256.4259062639-40.425906263903
781942019614.2054072447-194.205407244735
791941519229.2933470367185.706652963272
802001820058.5933914304-40.5933914304114
811865219363.3570782877-711.357078287678
821997819679.9895785808298.01042141924
831950919780.429550844-271.429550844034
842197122142.3016039647-171.301603964734


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520140.49494269219558.662634311420722.3272510726
8619157.146393898318521.198919627819793.0938681689
8720994.941653034520309.135889726421680.7474163427
8819962.3436793119230.066477737920694.6208808821
8920956.180022013120180.209497509921732.1505465163
9020245.865527139619428.534131772121063.1969225071
9120158.929763402319302.232054283821015.6274725209
9220779.840002354319885.507111443621674.1728932649
9319727.698362135118797.251332627220658.1453916431
9420922.212973264919957.002100121887.4238464298
9520572.970597423319574.205167188921571.7360276577
9623110.550699300722079.321946992624141.7794516088
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/1r8uh1291747605.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/1r8uh1291747605.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/2r8uh1291747605.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/2r8uh1291747605.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/31zt21291747605.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291747532g25nltqxgmqognl/31zt21291747605.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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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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