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R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Thu, 08 May 2008 08:39:49 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/May/08/t1210257631z2t1717n867r0s6.htm/, Retrieved Thu, 08 May 2008 16:40:36 +0200
 
User-defined keywords:
 
Dataseries X:
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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577
 
Text written by user:
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.587763292801995
beta0
gamma0


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25315256421-3269
35353654499.6017958303-963.601795830276
45240853933.2320313632-1525.23203136316
54145453036.7566303221-11582.7566303221
63827146228.8374535598-7957.83745355983
73530641551.5127082725-6245.51270827245
82641437880.6295936215-11466.6295936215
93191731140.9656263337776.034373666269
103803031597.09014512746432.90985487265
112753435378.1184237257-7844.1184237257
121838730767.6335498679-12380.6335498679
135055623490.751607622727065.2483923773
144390139398.71112323034502.28887676971
154857242044.99125858626527.00874141375
164389945881.327408587-1982.327408587
173753244716.1881235043-7184.18812350426
184035740493.5860559244-136.586055924403
193548940413.3057859434-4924.30578594343
202902737518.9796024334-8491.9796024334
213448532527.70570889981957.29429110023
224259833678.13144641948919.86855358061
233030638920.9027588329-8614.9027588329
242645133857.3791461323-7406.37914613228
254746029504.181351461517955.8186485385
265010440057.95244528210046.0475547180
276146545962.650435688515502.3495643115
285372655074.3624617758-1348.36246177580
293947754281.8445013519-14804.8445013519
304389545580.1003478158-1685.10034781577
313148144589.6602186818-13108.6602186818
322989636884.8709243269-6988.87092432685
333384232777.06913687641064.93086312362
343912033402.99640759245717.00359240761
353370236763.2412640267-3061.24126402673
362509434963.9560186210-9869.95601862104
375144229162.758169305522279.2418306945
384559442257.67870884643336.32129115356
395251844218.64589678038299.35410321974
404856449096.7015926184-532.701592618447
414174548783.5991504602-7038.59915046016
424958544646.56893707244938.43106292763
433274747549.1974398944-14802.1974398944
443337938849.0091319168-5470.00913191679
453564535633.938552884411.0614471156077
463703435640.44006546421393.55993453578
473568136459.5234413039-778.5234413039
482097236001.9359399196-15029.9359399196
495855227167.891301269431384.1086987306
505495545614.31837169109340.68162830895
516554051104.42816256114435.5718374390
525157059589.1273992139-8019.12739921391
535114554875.7786736532-3730.77867365324
544664152682.9639157114-6041.96391571136
553570449131.719309622-13427.719309622
563325341239.3987933776-7986.39879337764
573519336545.2867409521-1352.28674095211
584166835750.46223327765917.53776672238
593486539228.5737163265-4363.57371632653
602121036663.8252604342-15453.8252604342
615612627580.634038974728545.3659610253
624923144358.55233046494872.44766953506
635972347222.398216716312500.6017832837
644810354569.7930828656-6466.79308286561
654747250768.8494866113-3296.84948661135
665049748831.08237648811665.91762351191
674005949810.2476044203-9751.24760442032
683414944078.8222035187-9929.82220351866
693686038242.4372082402-1382.43720824017
704635637429.89136263298926.10863736707
713657742676.3303672401-6099.33036724014


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7239091.367866703918712.118358824059470.6173745837
7339091.367866703915452.618281795562730.1174516122
7439091.367866703912591.044220159665591.6915132481
7539091.367866703910009.692797939868173.042935468
7639091.36786670397639.4919888049270543.2437446028
7739091.36786670395435.8011997712472746.9345336365
7839091.36786670393367.7924702526974814.943263155
7939091.36786670391413.1180328870476769.6177005207
8039091.3678667039-445.0353836311778627.771117039
8139091.3678667039-2219.6942523785880402.4299857863
8239091.3678667039-3921.194540577582103.9302739852
8339091.3678667039-5557.9008425802683740.636575988
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/1q3qh1210257587.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/1q3qh1210257587.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/2m2ft1210257587.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/2m2ft1210257587.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/3erpv1210257587.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/May/08/t1210257631z2t1717n867r0s6/3erpv1210257587.ps (open in new window)


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





Copyright

Creative Commons License

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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