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EP huwelijken

*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: Sun, 19 Dec 2010 09:10:15 +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/19/t1292749851klh6e0sgh2jmkuw.htm/, Retrieved Sun, 19 Dec 2010 10:10:55 +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/19/t1292749851klh6e0sgh2jmkuw.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 «
3111 3995 5245 5588 10681 10516 7496 9935 10249 6271 3616 3724 2886 3318 4166 6401 9209 9820 7470 8207 9564 5309 3385 3706 2733 3045 3449 5542 10072 9418 7516 7840 10081 4956 3641 3970 2931 3170 3889 4850 8037 12370 6712 7297 10613 5184 3506 3810 2692 3073 3713 4555 7807 10869 9682 7704 9826 5456 3677 3431 2765 3483 3445 6081 8767 9407 6551 12480 9530 5960 3252 3717 2642 2989 3607 5366 8898 9435 7328 8594 11349 5797 3621 3851
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time14 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0542570100641665
beta0.283078288759594
gamma0.116511788416041


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1328863172.61591880342-286.615918803420
1433183601.67714478930-283.677144789304
1541664469.99916116335-303.999161163349
1664016687.63278151257-286.632781512572
1792099455.88959542425-246.889595424251
1898209986.17744970616-166.177449706160
1974707000.87552063784469.124479362156
2082079429.87344895766-1222.87344895766
2195649658.86987123-94.8698712299956
2253095593.52795703516-284.527957035157
2333852852.90070252401532.099297475992
2437062990.62870447873715.371295521275
2527332111.45560415150621.544395848497
2630452581.64411728009463.355882719906
2734493491.26169114149-42.2616911414862
2855425732.0330961723-190.033096172294
29100728518.417190042641553.58280995736
3094189191.4471642279226.552835772094
3175166339.64977701391176.35022298610
3278408673.6324442214-833.632444221395
33100819107.07559970299973.924400297012
3449565154.27312701868-198.273127018681
3536412585.083238086211055.91676191379
3639702856.245201754581113.75479824542
3729312079.28557135330851.714428646704
3831702639.00395224852530.99604775148
3938893592.08861308461296.911386915395
4048505935.7001656046-1085.70016560460
4180378952.58149824644-915.581498246444
42123709394.456500996042975.54349900396
4367126887.73140463225-175.73140463225
4472978997.36906805863-1700.36906805863
45106139640.14386624884972.856133751164
4651845615.28545410394-431.285454103941
4735063225.24033444513280.759665554873
4838103502.40003118403307.599968815970
4926922682.127104567779.8728954322337
5030733177.20036459539-104.200364595387
5137134076.64206853947-363.642068539467
5245556228.53302238142-1673.53302238142
5378079219.7065091506-1412.70650915059
541086910043.1783269151825.821673084949
5596827019.364041816862662.63595818314
5677049105.38524825445-1401.38524825445
57982610053.9196966447-227.919696644676
5854565785.7198752894-329.719875289396
5936773457.73749286559219.262507134413
6034313711.66523589019-280.665235890187
6127652794.78019547489-29.780195474892
6234833242.63521532672240.364784673284
6334454104.97920284696-659.979202846962
6460816064.6983415972916.3016584027127
6587679170.49558019488-403.495580194878
66940710305.0863486525-898.086348652549
6765517373.35774277617-822.35774277617
68124808752.173145909233727.82685409077
69953010116.7820668269-586.78206682692
7059605820.85665060883139.143349391169
7132523588.96971608293-336.969716082926
7237173759.25150851769-42.2515085176901
7326422888.22963902416-246.229639024164
7429893356.06612789128-367.066127891278
7536074078.87215693946-471.872156939456
7653666118.83459955378-752.834599553784
7788989120.34775997593-222.347759975934
78943510196.7547545344-761.754754534351
7973287269.3483047619958.6516952380098
8085949199.46249746765-605.46249746765
81113499789.089600828041559.91039917196
8257975658.15533845046138.844661549545
8336213342.31278029526278.687219704742
8438513556.45278074215294.547219257849


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852664.38053932047808.6007670206984520.16031162025
863119.195879499531258.924629658164979.4671293409
873842.94114803061975.997982207935709.88431385328
885877.366055959034001.160742907317753.57136901075
898989.562400993627101.1125792905310878.0122226967
9010033.39316231598129.3472934664711937.4390311652
917264.214992371235340.880640088989187.54934465349
929143.564196499577196.9413161707211090.1870768284
9310039.54021752838065.3587865285412013.7216485281
945678.319162711983672.080165809517684.55815961445
953379.156885986581336.175427932435422.13834404073
963584.447713094961499.896891585345668.99853460458
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/1jdgd1292749800.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/1jdgd1292749800.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/2jdgd1292749800.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/2jdgd1292749800.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/3cmxy1292749800.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/19/t1292749851klh6e0sgh2jmkuw/3cmxy1292749800.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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Software written by Ed van Stee & Patrick Wessa


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