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ES monthly births

*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 19:17:18 +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/t1291922517q82lxrciyhztdpn.htm/, Retrieved Thu, 09 Dec 2010 20:21:58 +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/t1291922517q82lxrciyhztdpn.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'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.118633222491809
beta0.177842898062907
gamma0.593783465793253


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1397379768.09802350428-31.0980235042771
1490359094.8206924271-59.8206924270944
1591339216.54046372284-83.5404637228421
1694879563.68373905242-76.6837390524197
1787008755.77257036365-55.7725703636497
1896279656.62380040231-29.6238004023144
1989479350.24380475726-403.24380475726
2092839699.78239553077-416.782395530772
2188299042.42155295708-213.421552957079
2299479575.43327830206371.566721697942
2396289462.01672409119165.983275908815
2493188775.37973766758542.620262332422
2596059309.97278290412295.027217095883
2686408661.11902781626-21.1190278162594
2792148776.59914227257437.400857727431
2895679201.70519948799365.294800512012
2985478479.0693673379467.9306326620626
3091859432.78885628384-247.788856283843
3194708924.90192534563545.098074654368
3291239419.77362094319-296.773620943191
3392788925.52238256834352.477617431659
34101709886.2017998858283.798200114197
3594349707.31587557335-273.315875573349
3696559208.93777542572446.062224574276
3794299643.72781956288-214.727819562881
3887398799.42061989147-60.420619891469
3995529179.84407265206372.155927347936
4096879587.740861833399.2591381667062
4190198700.5756600874318.424339912604
4296729546.72216590022125.277834099783
4392069533.85368355153-327.853683551533
4490699501.9707945651-432.970794565092
4597889345.86084071632442.139159283677
461031210297.64501435314.3549856469581
47101059805.95946625441299.040533745587
4898639774.763480507488.2365194925878
4996569836.53709925205-180.537099252051
5092959093.01482721878201.985172781224
5199469752.46311858526193.536881414742
52970110014.0928950339-313.09289503392
5390499201.74857262777-152.74857262777
54101909890.01737584943299.982624150571
5597069663.5188578340742.4811421659306
5697659631.15772153098133.842278469023
57989310022.8300650853-129.830065085269
58999410693.3737308994-699.37373089942
591043310261.436617568171.563382432012
601007310097.5384434705-24.5384434705411
61101129995.63683516516116.363164834836
6292669484.1543084668-218.154308466797
63982010077.1025414236-257.102541423639
64100979998.3875218314398.6124781685721
6591159305.7422417942-190.7422417942
661041110212.5772925192198.422707480755
6796789823.26733998655-145.267339986553
68104089796.48292855706611.517071442942
691015310096.947740158956.0522598411408
701036810485.514342959-117.514342959017
711058110584.7149952119-3.71499521191436
721059710300.0096105402296.990389459754
731068010319.389992721360.610007278996
7497389676.3680764116361.6319235883657
75955610302.5795309453-746.579530945288


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7610362.08400429869787.7649000431310936.4031085541
779514.355744847738934.4570012135210094.2544884819
7810659.556369005610072.347474147211246.765263864
7910074.72467916239478.2925554024410671.1568029222
8010472.17987524989864.456933633111079.9028168666
8110407.44884061119786.243868409811028.6538128123
8210695.396580956310058.426994432211332.3661674803
8310867.438852321810212.36272810611522.5149765376
8410739.968678641710064.415064697211415.5222925861
8510750.567990172710052.164260738811448.9717196067
869893.847174684659170.242569128510617.4517802408
8710074.02543694359322.9103340858210825.1405398013
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/1rigp1291922233.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/1rigp1291922233.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/2c2in1291922234.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/2c2in1291922234.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/3c2in1291922234.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/09/t1291922517q82lxrciyhztdpn/3c2in1291922234.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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