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Exponential Smoothning - OPJV

*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: Mon, 27 Dec 2010 15:21:52 +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/27/t1293463383r6e83sp0ohveq2g.htm/, Retrieved Mon, 27 Dec 2010 16:23:03 +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/27/t1293463383r6e83sp0ohveq2g.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 «
20503 22885 26217 26583 27751 28158 27373 28367 26851 26733 26849 26733 27951 29781 32914 33488 35652 36488 35387 35676 34844 32447 31068 29010 29812 30951 32974 32936 34012 32946 31948 30599 27691 25073 23406 22248 22896 25317 26558 26471 27543 26198 24725 25005 23462 20780 19815 19761 21454 23899 24939 23580 24562 24696 23785 23812 21917 19713 19282 18788 21453 24482 27474 27264 27349 30632 29429 30084 26290 24379 23335 21346 21106 24514 28353 30805 31348 34556 33855 34787 32529 29998 29257 28155 30466 35704 39327 39351 42234 43630 43722 43121 37985 37135 34646 33026 35087 38846 42013 43908 42868 44423 44167 43636 44382 42142 43452 36912 42413 45344 44873 47510 49554 47369 45998 48140 48441 44928 40454 38661 37246 36843 36424 37594 38144 38737 34560 36080 33508 35462 33374 32110 35533 35532 37903 36763 40399 44164 44496 43110 43880 43930 44327
 
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
alpha0.955476297029324
beta0
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132795123606.75852272734344.24147727272
142978128949.1199494997831.880050500306
153291432239.3782863910674.621713609042
163348832886.8383432057601.161656794298
173565235211.3590569555440.640943044462
183648836197.7143668685290.285633131498
193538733596.78374202711790.21625797287
203567635703.6262764101-27.6262764100757
213484433594.85502412511249.14497587493
223244734103.6334401268-1656.63344012683
233106832019.8427885528-951.842788552829
242901030318.0878989256-1308.08789892564
252981229798.662634238313.3373657617267
263095130846.5645008638104.435499136187
273297433434.7650880421-460.765088042121
283293632994.1192541694-58.1192541694181
293401234681.5657078299-669.565707829883
303294634600.4505028695-1654.45050286947
313194830208.15306171981739.84693828016
323059932185.9318239906-1586.93182399058
332769128644.1276651643-953.127665164306
342507326919.3107579642-1846.31075796425
352340624685.6678147397-1279.66781473968
362224822654.8225315389-406.822531538946
372289623055.3697087059-159.369708705879
382531723942.31008557991374.68991442011
392655827719.0438346965-1161.04383469645
402647126627.2255405919-156.225540591859
412754328193.7099027009-650.709902700863
422619828086.7602545280-1888.76025452795
432472523621.71209056971103.28790943032
442500524843.1532796539161.846720346100
452346223000.4848768039461.515123196074
462078022587.5578039234-1807.55780392343
471981520416.1714318193-601.17143181929
481976119072.4756642477688.524335752296
492145420530.6183261198923.38167388018
502389922520.40399962991378.59600037009
512493926187.9696650275-1248.96966502745
522358025056.8785554112-1476.87855541118
532456225339.4939903978-777.49399039782
542469625056.2825654625-360.282565462487
552378522184.87566767051600.12433232954
562381223839.1158344686-27.1158344685791
572191721829.240536425387.7594635747373
581971320958.1712608702-1245.17126087015
591928219377.8446889211-95.844688921119
601878818574.3986777217213.601322278340
612145319589.22037566901863.77962433104
622448222497.80182807041984.19817192957
632747426627.0170606004846.982939399564
642726427488.4116364712-224.411636471235
652734928998.8687159533-1649.86871595327
663063227900.69971618202731.30028381796
672942928070.51152559881358.48847440118
683008429421.4235997856662.576400214424
692629028075.6475578758-1785.64755787580
702437925355.2352669807-976.235266980722
712333524083.0429375168-748.042937516828
722134622670.2146411082-1324.21464110823
732110622289.1616854156-1183.16168541560
742451422291.82441756012222.17558243989
752835326597.78839183421755.21160816575
763080528279.27147913322525.72852086683
773134832353.9556648559-1005.95566485592
783455632066.09618996622489.90381003381
793385531944.13672525861910.86327474136
803478733791.8452457619995.154754238058
813252932654.8359417111-125.835941711081
822999831556.3723400160-1558.37234001595
832925729738.1218031421-481.121803142105
842815528554.6770260139-399.677026013924
853046629063.27804715831402.72195284168
863570431688.30952756264015.69047243741
873932737687.14350230991639.85649769007
883935139292.713781963158.2862180368757
894223440852.57167537301381.42832462696
904363043001.4496232287628.55037677128
914372241075.23004384332646.76995615667
924312143585.3092210899-464.309221089861
933798541003.9060254657-3018.90602546565
943713537077.400708005657.599291994411
953464636851.1359451182-2205.13594511821
963302634024.0627426539-998.062742653878
973508734041.16987183711045.83012816290
983884636441.53870739552404.46129260454
994201340795.10046553121217.89953446879
1004390841927.08350310151980.91649689853
1014286845382.8802420564-2514.88024205639
1024442343775.4067944103647.59320558967
1034416741957.24079567152209.75920432855
1044363643911.2497927933-275.249792793271
1054438241396.74829030852985.25170969150
1064214243344.0507813587-1202.05078135866
1074345241813.47487923271638.52512076731
1083691242712.6720877668-5800.67208776683
1094241338232.00150288724180.99849711277
1104534443688.44069258561655.55930741443
1114487347273.6142317984-2400.61423179836
1124751044982.16547582292527.83452417714
1134955448760.3599076388793.640092361231
1144736950454.9042462039-3085.90424620392
1154599845139.0233421756858.97665782438
1164814045691.74983120452448.25016879552
1174844145924.65758741022516.34241258985
1184492847237.4941472631-2309.49414726311
1194045444775.255316445-4321.25531644498
1203866139648.8029748707-987.802974870654
1213724640211.1356843402-2965.13568434021
1223684338727.1711439165-1884.17114391654
1233642438749.6202731522-2325.62027315225
1243759436749.2592556008844.740744399249
1253814438842.0847173858-698.08471738582
1263873738938.5896787552-201.589678755248
1273456036554.2436827262-1994.24368272619
1283608034451.54610789871628.45389210132
1293350833904.1896721675-396.189672167457
1303546232219.30674712153242.69325287851
1313337434972.4803170590-1598.48031705896
1323211032595.9925914652-485.992591465169
1333553333549.75505365121983.24494634876
1343553236841.9794586496-1309.97945864956
1353790337393.4001832024509.599816797563
1363676338243.1809707146-1480.18097071461
1374039938045.90653866352353.09346133649
1384416441079.84572544163084.15427455839
1394449641755.13460050922740.86539949083
1404311044338.0174283625-1228.01742836252
1414388040971.22572410702908.77427589295
1424393042606.17405646911323.82594353094
1434432743310.36842112311016.63157887689


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
14443482.090199228340030.888323868146933.2920745885
14545010.146661788940236.827595332149783.4657282457
14646260.800984123840459.21883475252062.3831334957
14748144.890438203341471.650148687354818.1307277193
14848419.168271034940975.653208423155862.6833336468
14949806.843244033241665.608877363857948.0776107027
15050625.00693831141841.301709949359408.7121666727
15148338.175015749738955.890748874257720.4592826252
15248125.51656088938180.616431165858070.4166906122
15346116.251686864735638.903782176256593.5995915531
15444901.367376428433917.351733614155885.3830192426
1554432732858.679278669555795.3207213305
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/1r1cw1293463307.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/1r1cw1293463307.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/2kabz1293463307.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/2kabz1293463307.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/3kabz1293463307.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293463383r6e83sp0ohveq2g/3kabz1293463307.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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