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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: Fri, 24 Dec 2010 10:05:21 +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/24/t1293185408bg2mg2yiddangc2.htm/, Retrieved Fri, 24 Dec 2010 11:10:09 +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/24/t1293185408bg2mg2yiddangc2.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 «
9700 9081 9084 9743 8587 9731 9563 9998 9437 10038 9918 9252 9737 9035 9133 9487 8700 9627 8947 9283 8829 9947 9628 9318 9605 8640 9214 9567 8547 9185 9470 9123 9278 10170 9434 9655 9429 8739 9552 9687 9019 9672 9206 9069 9788 10312 10105 9863 9656 9295 9946 9701 9049 10190 9706 9765 9893 9994 10433 10073 10112 9266 9820 10097 9115 10411 9678 10408 10153 10368 10581 10597 10680 9738 9556
 
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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633081220547
beta0.177857467177405
gamma0.5937606815085


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206438525-59.8206438524921
1591339216.54027552891-83.5402755289124
1694879563.6832928337-76.6832928337008
1787008755.77177456493-55.7717745649261
1896279656.62261533747-29.6226153374682
1989479350.24224745979-403.242247459786
2092839699.77990897321-416.779908973213
2188299042.4175918722-213.417591872209
2299479575.42770895528371.572291044724
2396289462.01040501833165.989594981666
2493188775.37320289687542.626797103134
2596059309.96768879984295.032311200162
2686408661.11582635564-21.1158263556354
2792148776.59763276738437.402367232617
2895679201.70534380874365.294656191258
2985478479.071365477767.9286345223063
3091859432.79251990023-247.792519900235
3194708924.91458754528545.085412454724
3291239419.78785425682-296.787854256820
3392788925.53326165975352.46673834025
34101709886.2024401871283.797559812900
3594349707.32333142966-273.323331429661
3696559208.93877176675446.061228233255
3794299643.73599787529-214.73599787529
3887398799.4357954875-60.4357954874995
3995529179.84953180272372.150468197282
4096879587.748296431399.2517035687033
4190198700.58905330985318.410946690148
4296729546.74142131195125.25857868805
4392069533.8599186699-327.859918669908
4490699501.99459678781-432.99459678781
4597889345.86760799596442.132392004038
461031210297.647652282614.3523477174276
47101059805.97469658919299.025303410814
4898639774.7594553185788.2405446814264
4996569836.5490668885-180.549066888509
5092959093.02527743563201.974722564371
5199469752.46004416102193.539955838984
52970110014.0963668069-313.096366806853
5390499201.74952137105-152.749521371048
54101909890.02447533174299.975524668256
5597069663.5287347837642.4712652162380
5697659631.17664908248133.823350917515
57989310022.8239980114-129.823998011401
58999410693.3752773111-699.375277311072
591043310261.4369351175171.563064882548
601007310097.5339138071-24.5339138070922
61101129995.64352685936116.356473140644
6292669484.15197570541-218.151975705412
63982010077.0938250165-257.093825016538
64100979998.390460116198.6095398839061
6591159305.73915852747-190.739158527469
661041110212.5669742498198.433025750250
6796789823.26417307528-145.264173075282
68104089796.48237564632611.517624353677
691015310096.942566585956.057433414142
701036810485.5241309133-117.524130913331
711058110584.7066133174-3.70661331736665
721059710300.0046737778296.99532622221
731068010319.3889237420360.611076258041
7497389676.3721946804161.6278053195856
75955610302.5828340882-746.582834088236


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08555931139787.7658812375510936.4052373851
779514.36163888498934.4621917131810094.2610860566
7810659.551959584410072.342060445911246.7618587228
7910074.73012016489478.2964894773110671.1637508523
8010472.17197759209864.4467995052611079.8971556787
8110407.44976107679786.2415776256311028.6579445278
8210695.407185713610058.433156512111332.381214915
8310867.439758852310212.357699186511522.5218185182
8410739.964142714810064.402840546511415.5254448832
8510750.562795536410052.149371485211448.9762195877
869893.84903239089170.2324824399510617.4655823417
8710074.04222420759322.9126966727210825.1717517423
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/1o6d51293185116.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/1o6d51293185116.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/2zfc81293185116.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/2zfc81293185116.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/3zfc81293185116.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293185408bg2mg2yiddangc2/3zfc81293185116.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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