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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: Thu, 09 Dec 2010 19:54:22 +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/t12919243297jcrsluy480uppw.htm/, Retrieved Thu, 09 Dec 2010 20:52:10 +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/t12919243297jcrsluy480uppw.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 «
286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881 294563
 
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
alpha0.819010626931158
beta0.422758665301198
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13292300290364.2142094021935.78579059819
14288186288573.902492723-387.902492722787
15281477281925.614863226-448.614863226423
16282656282908.10635773-252.106357730459
17280190280513.791799919-323.791799919447
18280408280915.071853821-507.071853820526
19276836279371.714756965-2535.714756965
20275216271437.9019508353778.09804916533
21274352271898.1454372972453.85456270335
22271311273003.243127755-1692.24312775541
23289802294611.713991497-4809.71399149712
24290726293722.442582664-2996.44258266373
25292300290870.7415991221429.25840087823
26278506286066.314126849-7560.31412684912
27269826268870.65195669955.348043310281
28265861266862.57855225-1001.57855225034
29269034259405.9724786369628.02752136407
30264176266934.991183153-2758.99118315341
31255198261410.676833747-6212.67683374725
32253353248565.5519825574787.44801744341
33246057246919.696978542-862.696978542139
34235372240716.675708324-5344.67570832407
35258556253663.4757150444892.52428495564
36260993259301.9029856051691.09701439535
37254663260966.662871024-6303.66287102413
38250643245400.7085304965242.29146950436
39243422241863.4189976051558.58100239461
40247105241835.7408193755269.25918062523
41248541245450.6261014233090.37389857738
42245039247131.458845871-2092.45884587118
43237080243506.884460543-6426.88446054308
44237085234381.9822133072703.01778669254
45225554231189.374598531-5635.37459853094
46226839219796.8129942227042.18700577784
47247934248560.808388502-626.808388501522
48248333251007.783076531-2674.78307653122
49246969248046.578951782-1077.57895178214
50245098241056.742037424041.25796257981
51246263237659.4345197328603.5654802678
52255765248302.9029561667462.09704383434
53264319258308.2834148936010.71658510726
54268347267442.913613978904.086386021867
55273046272525.635378617520.364621383254
56273963280186.040173054-6223.04017305386
57267430274526.164174507-7096.16417450667
58271993270078.3432711371914.65672886278
59292710297326.093400524-4616.09340052435
60295881298825.137445836-2944.13744583557
61294563298529.141743234-3966.14174323354


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
62291696.584758329283130.14362148300263.025895177
63286012.500995323272858.569618521299166.432372125
64286621.360466709268163.820250168305078.90068325
65284887.210826267260516.248895975309258.17275656
66280728.271998057249899.549587436311556.994408678
67277241.571031326239456.983668843315026.158393809
68275315.617208485230112.367695075320518.866721896
69268809.450544399215753.051026108321865.85006269
70268476.328932647207155.748675367329796.909189928
71288983.022981553219007.133580811358958.912382294
72292172.661238336213167.52619024371177.796286432
73292729.721328746204336.465964794381122.976692698
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/1fvd71291924458.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/1fvd71291924458.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/2pmcs1291924458.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/2pmcs1291924458.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/3pmcs1291924458.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t12919243297jcrsluy480uppw/3pmcs1291924458.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=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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Software written by Ed van Stee & Patrick Wessa


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