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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: Tue, 30 Nov 2010 10:31:04 +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/Nov/30/t1291112950rr8nyed0z4dkbv9.htm/, Retrieved Tue, 30 Nov 2010 11:29:14 +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/Nov/30/t1291112950rr8nyed0z4dkbv9.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 time4 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491527
beta0.177842898062282
gamma0.593783465800473


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924271071
1591339216.54046372288-83.540463722884
1694879563.6837390525-76.6837390525016
1787008755.77257036377-55.7725703637716
1896279656.62380040247-29.6238004024708
1989479350.24380475744-403.243804757440
2092839699.78239553113-416.782395531127
2188299042.42155295763-213.421552957634
2299479575.43327830275371.566721697251
2396289462.01672409177165.983275908229
2493188775.37973766809542.620262331908
2596059309.97278290418295.027217095818
2686408661.11902781597-21.1190278159702
2792148776.5991422721437.400857727909
2895679201.70519948736365.294800512638
2985478479.0693673372667.9306326627375
3091859432.78885628325-247.788856283250
3194708924.90192534264545.098074657359
3291239419.77362094013-296.773620940128
3392788925.52238256696352.477617433044
34101709886.20179988823283.798200111771
3594349707.31587557403-273.315875574028
3696559208.93777542882446.062224571177
3794299643.7278195637-214.727819563708
3887398799.42061989-60.4206198899992
3995529179.84407265357372.155927346434
4096879587.7408618339299.2591381660786
4190198700.57566008587318.424339914131
4296729546.72216589657125.277834103428
4392069533.85368355207-327.853683552074
4490699501.97079455985-432.970794559853
4597889345.86084071642442.139159283584
461031210297.645014354214.3549856457503
47101059805.95946625138299.040533748623
4898639774.7634805105288.2365194894774
4996569836.53709924992-180.537099249921
5092959093.01482721702201.985172782981
5199469752.4631185878193.536881412205
52970110014.0928950343-313.092895034275
5390499201.74857262883-152.748572628829
54101909890.0173758482299.982624151804
5597069663.5188578316242.4811421683844
5697659631.15772152543133.842278474573
57989310022.8300650879-129.830065087885
58999410693.3737308997-699.373730899686
591043310261.4366175686171.563382431439
601007310097.5384434724-24.5384434723783
61101129995.63683516307116.363164836932
6292669484.15430846739-218.154308467389
63982010077.1025414262-257.102541426164
64100979998.387521829998.6124781701055
6591159305.7422417943-190.742241794302
661041110212.5772925215198.422707478492
6796789823.26733998628-145.267339986278
68104089796.4829285558611.517071444208
691015310096.947740159156.0522598409407
701036810485.5143429546-117.514342954579
711058110584.7149952137-3.71499521370242
721059710300.0096105413296.990389458748
731068010319.3899927210360.610007278967
7497389676.3680764103361.6319235896663
75955610302.5795309447-746.5795309447


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429899787.7649000435210936.4031085544
779514.35574484688934.4570012126810094.2544884809
7810659.556369008210072.347474149911246.7652638665
7910074.72467916189478.2925554021510671.1568029215
8010472.17987525389864.4569336373411079.9028168702
8110407.44884061229786.243868411311028.6538128131
8210695.396580954210058.426994430611332.3661674777
8310867.438852322910212.362728107711522.5149765380
8410739.968678644510064.415064700911415.5222925882
8510750.567990175810052.164260742911448.9717196088
869893.847174685399170.2425691304410617.4517802403
8710074.02543693939322.91033408310825.1405397956
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/1buql1291113060.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/1buql1291113060.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/2buql1291113060.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/2buql1291113060.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/3ml7o1291113060.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291112950rr8nyed0z4dkbv9/3ml7o1291113060.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
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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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


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