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Exponential Smoothing Yen

*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: Fri, 24 Dec 2010 12:28:44 +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/24/t1293193617j96njaoyi5jebln.htm/, Retrieved Fri, 24 Dec 2010 13:26:57 +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/24/t1293193617j96njaoyi5jebln.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 «
126,64 126,81 125,84 126,77 124,34 124,4 120,48 118,54 117,66 116,97 120,11 119,16 116,9 116,11 114,98 113,65 115,82 117,59 118,57 118,07 114,98 114,04 115,02 114,28 115,04 116,7 119,21 118,39 116,5 115,46 117,59 117,33 116,2 116,83 118,99 118,62 121,09 122,4 123,76 125,33 123,23 122,52 123,64 124,67 124,71 122,53 124,4 125,45 125,35 124,3 127,03 128,51 128,1 128,94 129,67 129,87 131,12 132,68 132,24 133,63 129,91 127,93 131,17 130,86 133,48 134,08 136,02 132,8 132,37 133,05 132,57 130,7 130,5 129,67 127,8 126,82 126,85 128,28 128,3 126,82 125,08 128,53 130,34 131,52 132,59 131,17 132,72 133,36 132,82 132,9 130,9 129,41 128,67 129,28 130,91 131,06 130,84 131,41 133,22 132,06 132,48 134,38 135,22 134,89 136,09 136,33 136,32 137,48 136,53 136,8 138,03 137,39 137,55 136,08 134,78 133,28 133,57 134,84 133,02 133,49 133,77 134,34 134,5 134,03 135,51 136,53 135,95 134,32 132,44 133,61 13 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.996556487594152
betaFALSE
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2126.81126.640.170000000000002
3125.84126.809414602891-0.969414602891007
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334125.11124.0321428483411.07785715165878
335125.46125.1062883855270.353711614473468
336124.7125.458781989667-0.758781989667455
337124.48124.702612875195-0.222612875194756
338124.76124.4807665701970.279233429802574
339125.81124.7590384562201.05096154377965
340124.95125.806381000886-0.856381000885932
341123.66124.952948958601-1.29294895860069
342122.66123.664452285779-1.00445228577907
343119.34122.663458843907-3.32345884390716
344117.84119.351444371759-1.51144437175932
345120.97117.8452046774453.12479532255509
346117.38120.959239728541-3.57923972854105
347118.06117.3923251564090.667674843591271
348116.99118.057700853393-1.06770085339303
349115.55116.993676641134-1.44367664113439
350114.17115.554971318424-1.38497131842378
351115.32114.1747691659171.14523083408325
352112.49115.316056383415-2.82605638341528
353111.93112.499731560216-0.5697315602159
354112.08111.9319618776960.148038122304385
355111.63112.079490228889-0.449490228889303
356109.53111.631547825179-2.10154782517948
357111.35109.5372367060071.81276329399250
358110.79111.343757727108-0.553757727108263
359113.06110.7919068716032.26809312839687
360112.62113.052189793175-0.432189793174743
361110.65112.621488250914-1.97148825091448
362112.36110.656788844251.70321115574998
363113.74112.3541349712551.38586502874460
364111.73113.735227756581-2.00522775658068
365109.86111.736905026656-1.87690502665635
366109.32109.866463145744-0.5464631457439
367109.99109.3218817526220.668118247378288
368109.84109.987699326527-0.147699326526578
369111.13109.8405086044631.28949139553676
370112.43111.1255596203821.30444037961777
371111.77112.42550814337-0.655508143370113
372112.15111.7722572504240.377742749576186
373112.89112.1486992381560.741300761844386
374112.12112.887447321630-0.767447321630115
375113.1112.1226427143730.977357285627122
376111.09113.096634458062-2.00663445806198
377110.76111.096909870650-0.336909870650331
378109.59110.761160153319-1.17116015331924
379109.99109.5940329045170.395967095482803
380110.25109.9886364823940.261363517605602
381108.31110.249099991485-1.93909999148468
382108.79108.3166773148770.473322685123151
383108.14108.788370107462-0.648370107461815
384109.88108.1422326705091.73776732949138
385109.93109.8740159766420.0559840233575954
386110.46109.9298072183210.530192781678949
387109.56110.458174274579-0.898174274578793
388111.49109.5630928742571.92690712574287
389111.85111.4833646714080.366635328592409
390111.35111.848737486698-0.498737486697564
391110.95111.351717408723-0.401717408722689
392112.49110.9513833188811.53861668111941
393113.11112.4847017543710.625298245629281
394112.54113.107846777734-0.56784677773382
395112.84112.5419553874240.298044612576248
396111.5112.838973679679-1.3389736796791
397111.52111.5046107724770.0153892275229168
398111.57111.5199470070040.0500529929958873
399112.48111.5698276418980.910172358102344
400112.31112.476865810193-0.166865810193414
401113.79112.3105746044881.47942539551249
402114.01113.7849055802970.225094419702970
403113.64114.009224884573-0.369224884573271
404112.62113.641271430471-1.02127143047058
405113.27112.6235167608410.646483239159423
406113.51113.2677738269460.242226173054220
407112.92113.509165891168-0.589165891168065
408113.66112.9220288000550.737971199944653
409113.14113.657458787018-0.51745878701783
410113.48113.1417818757530.338218124247391
411113.23113.478835341693-0.248835341693265
412110.56113.230856867586-2.67085686758614
413109.5110.569197128758-1.06919712875778
414109.78109.5036817935770.276318206422829
415109.49109.779048494828-0.289048494828222
416109.66109.4909953420780.169004657922173
417109.93109.6594180303640.270581969636211
418109.82109.929068247631-0.109068247630773
419108.54109.820375577864-1.28037557786379
420108.23108.544408989187-0.314408989186518
421106.19108.231082671255-2.04108267125478
422106.49106.1970284935000.292971506500166
423107.15106.4889911489830.6610088510172
424107.74107.1477238078210.592276192178844
425107.54107.737960489585-0.197960489584531
426107.07107.540681679402-0.470681679401764
427107.54107.0716207982020.468379201797788
428107.81107.5383871304080.271612869592033
429108.38107.8090646977140.570935302286017
430108.42108.3780339772040.041966022796359
431106.86108.419855489480-1.55985548947987
432106.41106.865371381729-0.45537138172935
433106.46106.4115680770020.0484319229977501
434106.84106.4598332240720.380166775927691
435107.69106.8386908909910.851309109009193
436107.04107.687068506522-0.647068506521904
437111.04107.0422281884303.99777181157036
438111.93111.0262336231710.903766376828898
439111.98111.9268878692690.0531121307305966
440112.07111.9798171077190.0901828922810637
441112.05112.069689454092-0.0196894540916333
442113.14112.0500678008791.08993219912057
443112.49113.136246804951-0.646246804950806
444113.2112.492225358890.707774641109921
445113.52113.1975627692430.322437230757203
446113.22113.518889683396-0.298889683395771
447113.85113.2210292303330.628970769667248
448113.68113.847834131352-0.167834131351725
449114.26113.6805779389130.579422061086561
450114.1114.258004752944-0.158004752944436
451114.8114.1005440913270.699455908673059
452114.98114.7975914149010.182408585098869
453115.1114.9793718737740.120628126225711
454114.21115.099584615551-0.889584615550845
455114.24114.2130632956600.0269367043403008
456113.35114.239907243124-0.889907243124426
457114.23113.3530644066320.876935593368259
458114.43114.2269802614050.203019738594890
459114.28114.429300899012-0.149300899011521
460113114.280514119498-1.28051411949795
461113.16113.0044094662560.155590533743649
462112.59113.159464222067-0.569464222066813
463113.65112.5919609571131.05803904288663
464113.18113.64635662943-0.466356629429953
465113.21113.1816059048390.0283940951609907
466113.11113.209902224581-0.099902224581058
467112.78113.110344014550-0.330344014549709
468112.57112.781137543712-0.211137543712312
469111.87112.570727054751-0.700727054751098
470111.94111.8724129623060.0675870376938406
471113.18111.9397672631971.24023273680278
472113.67113.1757292431850.494270756815311
473115.15113.6682979725171.48170202748294
474114.41115.144897740687-0.734897740686606
475112.88114.412530629487-1.53253062948708
476112.44112.885277288235-0.445277288234976
477113.48112.4415333178661.03846668213393
478112.78113.476424027097-0.69642402709701
479112.59112.782398144777-0.192398144777030
480113.31112.5906625253980.719337474601602
481113.21113.307522952482-0.0975229524822225
482112.5113.210335821497-0.710335821496727
483113.72112.5024460502141.21755394978635
484114.09113.7158073378690.374192662130881
485113.97114.088711462926-0.118711462925774
486112.5113.970408784395-1.47040878439530
487111.28112.505063370891-1.22506337089074
488111.35111.2842185209160.0657814790843787
489110.92111.349773480661-0.429773480660685
490110.73110.921479930312-0.191479930312354
491109110.730659363515-1.7306593635155


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
492109.005959546989106.671782214455111.340136879522
493109.005959546989105.710612965732112.301306128245
494109.005959546989104.972321689981113.039597403997
495109.005959546989104.349656331736113.662262762242
496109.005959546989103.800953792596114.210965301381
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/1p7rw1293193716.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/1p7rw1293193716.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/2p7rw1293193716.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/2p7rw1293193716.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/30yrh1293193716.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/24/t1293193617j96njaoyi5jebln/30yrh1293193716.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 <- 5
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')
 




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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