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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 18:58:12 +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/t1291921560tsznq7qpa2kpnk0.htm/, Retrieved Thu, 09 Dec 2010 20:06:03 +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/t1291921560tsznq7qpa2kpnk0.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 time2 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.536600454094031
beta0.263284283989488
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
390848462622
497438264.640688512821478.35931148718
585878735.66450867045-148.664508670448
697318312.623514324861418.37648567514
795638930.84348372447632.156516275527
899989216.4875636356781.5124363644
994379692.68697652683-255.686976526827
10100389576.20164956657461.798350433433
1199189909.961437568688.03856243132213
12925210001.3691930512-749.36919305116
1397379580.48187268725156.518127312745
1490359667.80674077051-632.806740770515
1591339242.17756038402-109.177560384018
1694879082.1035976795404.896402320495
1787009255.08509954843-555.085099548429
1896278834.51852003769792.481479962315
1989479249.01734710991-302.017347109908
2092839033.53905896064249.460941039357
2188299149.22772981819-320.227729818191
2299478913.979918651631033.02008134837
2396289550.8289902548577.1710097451469
2493189685.67161789349-367.671617893486
2596059529.8674072464375.1325927535745
2686409622.28675458404-982.286754584044
2792149008.51843377425205.481566225750
2895679061.13725380796505.862746192044
2985479346.40826437574-799.408264375745
3091858818.3310843829366.668915617105
3194708967.77387073751502.226129262488
3291239260.91045679034-137.910456790341
3392789191.065682256886.9343177432002
34101709254.1546629221915.845337077903
3594349891.42689759714-457.426897597144
3696559727.17605699355-72.1760569935541
3794299759.4540697591-330.454069759107
3887399606.45393941927-867.453939419269
3995529042.74687298564509.253127014365
4096879289.72794432052397.272055679479
4190199532.74590867513-513.745908675128
4296729214.3299856008457.670014399195
4392069481.83520568856-275.835205688560
4490699316.77161677336-247.771616773358
4597889131.7621683921656.237831607894
46103129524.55687492438787.443125075615
471010510099.00515855535.99484144474991
48986310254.9748803441-391.974880344085
49965610142.0162587647-486.016258764743
5092959909.93135916443-614.931359164435
5199469521.79399882013424.206001179868
5297019751.18939116352-50.1893911635161
5390499718.93332034497-669.933320344973
54101909259.47522365417930.524776345828
5597069790.2867817039-84.286781703895
5697659764.642089632020.357910367982186
5798939784.46834279044108.531657209560
5899949877.6738637055116.326136294494
59104339991.49628376845441.503716231551
601007310342.1841088014-269.184108801443
611011210273.4866061468-161.486606146831
62926610239.7650522699-973.765052269862
6398209632.60248218784187.397517812156
64100979674.99550840211422.004491597889
6591159902.8988906469-787.898890646902
66104119370.254421664051040.74557833595
6796789965.89634427613-287.896344276134
68104089807.91485390067600.085146099334
691015310211.2037436048-58.2037436048467
701036810253.0315805367114.968419463297
711058110404.0262407872176.973759212795
721059710613.2955757884-16.2955757883610
731068010716.5542839099-36.5542839098653
74973810803.7778268849-1065.7778268849
75955610188.1480924889-632.148092488906


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
769715.8953574698605.8465242503310825.9441906876
779582.85357593338241.7970472397210923.9101046269
789449.81179439767829.54402233711070.0795664582
799316.770012861917377.2076089400411256.3324167838
809183.728231326226890.7987958145311476.6576668379
819050.686449790536374.6211157110511726.75178387
828917.644668254845831.791150460712003.4981860490
838784.602886719155264.6294541780612304.5763192602
848651.561105183454674.9196131330212628.2025972339
858518.519323647764064.0749709494412972.9636763461
868385.477542112073433.2464734664413337.7086107577
878252.435760576382783.3937475073913721.4777736454
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/1uris1291921089.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/1uris1291921089.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/2uris1291921089.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/2uris1291921089.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/35i0d1291921089.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291921560tsznq7qpa2kpnk0/35i0d1291921089.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Double ; 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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