Home » date » 2010 » Dec » 09 »

ES triple additive

*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: Thu, 09 Dec 2010 16:33:47 +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/09/t1291912459sjh3y2xuefxyyvp.htm/, Retrieved Thu, 09 Dec 2010 17:34:23 +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/09/t1291912459sjh3y2xuefxyyvp.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 «
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 31956 29506 34506 27165 26736 23691 18157 17328 18205 20995 17382 9367 31124 26551 30651 25859 25100 25778 20418 18688 20424 24776 19814 12738 31566 30111 30019 31934 25826 26835 20205 17789 20520 22518 15572 11509 25447 24090 27786 26195 20516 22759 19028 16971 20036 22485 18730 14538
 
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'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.352911347621157
beta0
gamma0.797570196930633


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132802926890.14449786331138.85550213675
142938328873.9145686606509.08543133935
153643836198.8066350815239.193364918538
163203432052.0340619628-18.0340619627750
172267922785.8580109783-106.858010978282
182431924450.2933137790-131.293313779031
191800422477.4384542722-4473.43845427217
201753717382.2329683339154.767031666121
212036619775.4987175057590.5012824943
222278224048.8316950087-1266.83169500866
231916915781.60745510653387.39254489350
241380714840.1200971726-1033.12009717260
252974327729.30375636852013.69624363149
262559129696.7915852829-4105.79158528287
272909635253.7502605778-6157.75026057778
282648228716.6689708834-2234.66897088342
292240518622.37538915053782.62461084946
302704421646.84221941935397.15778058068
311797019384.0653540573-1414.06535405733
321873017757.1578342543972.842165745667
331968420664.0134286921-980.013428692135
341978523424.5269491807-3639.52694918066
351847916721.99035521351757.00964478651
361069812923.7018793200-2225.70187932005
373195626964.46761542344991.53238457656
382950626824.60836230092681.39163769914
393450633717.8279667315788.172033268536
402716531656.7383293261-4491.73832932611
412673623871.41629582182864.58370417816
422369127405.1544197002-3714.15441970022
431815718411.6292002137-254.629200213651
441732818425.7795423136-1097.77954231358
451820519594.0231543635-1389.02315436350
462099520837.6212331827157.37876681731
471738218260.2008622619-878.20086226186
48936711476.4447580411-2109.44475804115
493112429283.04362351421840.95637648576
502655126839.0498850930-288.049885093045
513065131707.2318474280-1056.23184742796
522585926270.2766784284-411.276678428389
532510023721.58354358461378.41645641538
542577823335.55868847092442.44131152914
552041818300.22217040792117.77782959211
561868818716.473143196-28.4731431959917
572042420111.7766901771312.22330982293
582477622753.85985484022022.14014515975
591981420300.0737134258-486.073713425802
601273813019.2604494312-281.260449431165
613156633509.842892375-1943.84289237502
623011128631.37334160931479.62665839066
633001933726.9307613903-3707.93076139034
643193427687.02143038274246.97856961734
652582627705.9375968030-1879.93759680296
662683526719.1443852706115.855614729368
672020520695.1709973326-490.170997332618
681778919083.3700614636-1294.37006146361
692052020207.7571916433312.242808356743
702251823732.3329632771-1214.33296327708
711557218841.8730147381-3269.87301473814
721150910684.3292315165824.670768483455
732544730707.1508400117-5260.15084001175
742409026425.1665064646-2335.16650646464
752778627497.1488837408288.851116259248
762619526973.2669903791-778.266990379092
772051622056.6239717962-1540.62397179622
782275922219.6045190107539.39548098926
791902816032.33365550812995.66634449186
801697115235.67824318341735.32175681665
812003618258.44868709851777.55131290155
822248521512.2848027183972.71519728168
831873016332.79757588492397.20242411511
841453812288.41743491712249.5825650829


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8529673.738526913125065.267938322434282.2091155038
8628757.701504505223870.665780901533644.737228109
8732008.042524699326857.485742986137158.5993064126
8830831.483608251925430.247438676936232.719777827
8925796.048453015720155.262234996231436.8346710352
9027576.227859581621705.658368018433446.7973511448
9122466.276222584716374.584901354928557.9675438144
9219961.954056251113656.890999388126267.0171131142
9322394.104376195515882.657751297728905.5510010932
9424605.247650769517893.760919294431316.7343822446
9519817.654090357012911.919433954526723.3887467596
9614851.08760526587756.4214297144621945.7537808172
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/1xuxn1291912424.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/1xuxn1291912424.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/2xuxn1291912424.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/2xuxn1291912424.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/3q3ep1291912424.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291912459sjh3y2xuefxyyvp/3q3ep1291912424.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')
 




Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by