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ES triple additive

*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: Wed, 29 Dec 2010 07:45:29 +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/29/t12936086027xlvdb00amt0rqw.htm/, Retrieved Wed, 29 Dec 2010 08:43:26 +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/29/t12936086027xlvdb00amt0rqw.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 «
11974 10106 12069 11412 11180 10508 11288 10928 10199 11030 11234 13747 13912 12376 12264 11675 11271 10672 10933 10379 10187 10747 10970 12175 14200 11676 11258 10872 11148 10690 10684 11658 10178 10981 10773 11665 11359 10716 12928 12317 11641 10459 10953 10703 10703 11101 11334 13268 13145 12334 13153 11289 11374 10914 11299 11284 10694 11077 11104 12820 14915 11773 11608 11468 11511 11200 11164 10960 10667 11556 11372 12333 13102 11115 12572 11557 12059 11420 11185 11113 10706 11523 11391 12634 13469 11735 13281 11968 11623 11084 11509 11134 10438 11530 11491 13093 13106 11305 13113 12203 11309 11088 11234 11619 10942 11445 11291 13281 13726 11300 11983 11092 11093 10692 10786 11166 10553 11103 10969 12090 12544 12264 13783 11214 11453 10883 10381 10348 10024 10805 10796 11907 12261 11377 12689 11474 10992 10764 12164 10409 10398 10349 10865 11630 12221 10884 12 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time24 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0855239409013859
beta0.00861805869647365
gamma0.213843782000805


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131391213713.8616452992198.138354700845
141237612237.3748762257138.625123774269
151226412165.60880813698.3911918640042
161167511602.390961559772.6090384403142
171127111232.521640134338.4783598656832
181067210718.4700223933-46.4700223932668
191093311477.5357001490-544.535700148968
201037910900.3534880909-521.353488090906
211018710028.3946463998158.605353600167
221074710858.3304646311-111.330464631134
231097011042.4315850731-72.4315850730854
241217513542.9311052669-1367.93110526689
251420013640.9564500248559.043549975173
261167612182.5195771599-506.519577159881
271125812046.0567129745-788.056712974529
281087211399.6776304375-527.677630437483
291114810969.0456721942178.954327805764
301069010447.7502384579242.249761542109
311068411131.6761360110-447.676136010969
321165810564.94953303621093.05046696383
33101789962.85854052486215.141459475144
341098110743.7122117321237.287788267908
351077310964.3623258355-191.362325835509
361166513200.3882447923-1535.38824479229
371135913659.8373938020-2300.83739380203
381071611745.2439716718-1029.24397167176
391292811505.44234027381422.55765972615
401231711097.09416418641219.90583581364
411164110953.4479311061687.552068893927
421045910487.7424564449-28.7424564449175
431095311013.0887608071-60.088760807077
441070310780.6078504390-77.607850438977
45107039905.65607107289797.343928927112
461110110739.99996871361.000031290003
471133410886.8640933975447.135906602451
481326812914.5948218803353.405178119687
491314513387.2146794904-242.214679490446
501233411900.1876435763433.812356423736
511315312268.8911989637884.108801036253
521128911778.3830384783-489.383038478321
531137411386.7072670123-12.7072670123343
541091410722.7817716782191.218228321803
551129911262.716082515336.283917484745
561128411037.0284580154246.971541984607
571069410363.1534911704330.846508829552
581107711074.14391161672.85608838331063
591110411208.8309473176-104.830947317561
601282013172.2274431405-352.227443140535
611491513468.70394112521446.29605887484
621177312260.2115706604-487.211570660364
631160812639.4505119112-1031.45051191124
641146811716.3583354729-248.358335472936
651151111438.525321691472.4746783086248
661120010821.839395187378.160604812998
671116411347.6771776742-183.677177674197
681096011144.4301184834-184.430118483384
691066710449.7956701136217.204329886375
701155611086.5765484987469.423451501318
711137211240.1011649544131.898835045560
721233313175.5322214937-842.532221493697
731310213781.5929641904-679.592964190426
741111512011.4189219817-896.418921981742
751257212247.1704316818324.829568318222
761155711592.1481751232-35.1481751232022
771205911394.3852842205664.61471577951
781142010887.6514050885532.348594911535
791118511316.4508788237-131.450878823749
801111311117.206795526-4.20679552599358
811070610516.3438401836189.656159816444
821152311199.8875532506323.112446749357
831139111274.5827522382116.417247761758
841263413017.811776959-383.811776958994
851346913694.9826878066-225.982687806641
861173511921.5511117760-186.551111776020
871328112457.7071262035823.292873796512
881196811776.1598943288191.840105671192
891162311736.0593158455-113.059315845545
901108411137.7844347606-53.7844347605842
911150911387.0482233904121.951776609572
921113411234.9481636655-100.94816366546
931043810664.2398866485-226.239886648505
941153011338.5235486798191.476451320154
951149111361.6543837804129.345616219622
961309313008.290274709784.7097252902804
971310613756.8640629284-650.864062928398
981130511954.9616424890-649.961642489032
991311312648.7791076034464.220892396606
1001220311812.5882983158390.411701684201
1011130911729.5415219505-420.541521950521
1021108811116.0302103273-28.0302103272807
1031123411401.3508410301-167.350841030146
1041161911180.1941898230438.805810177049
1051094210630.8191108987311.180889101328
1061144511432.820484584912.1795154150514
1071129111428.4038341983-137.403834198294
1081328113043.2375723240237.76242767598
1091372613660.908776141765.0912238583114
1101130011920.7947327492-620.794732749246
1111198312835.3927377838-852.392737783768
1121109211871.5978580237-779.597858023662
1131109311528.4705977143-435.470597714348
1141069210988.9983638023-296.998363802333
1151078611222.4310004773-436.431000477263
1161116611094.960274474371.0397255257194
1171055310487.065380071265.9346199287847
1181110311207.3310314392-104.331031439227
1191096911161.3222154438-192.32221544381
1201209012842.4083353394-752.408335339358
1211254413338.4832797733-794.483279773329
1221226411386.9468133375877.053186662453
1231378312381.68072965251401.31927034755
1241121411623.8528924113-409.852892411323
1251145311378.901318110974.098681889076
1261088310909.7218021862-26.7218021862172
1271038111138.8354157542-757.835415754245
1281034811082.7110859067-734.711085906678
1291002410403.9087196856-379.908719685563
1301080511051.4210219283-246.421021928287
1311079610974.6214978413-178.62149784127
1321190712545.930308905-638.930308905003
1331226113042.1446174628-781.14461746276
1341137711417.2983454144-40.2983454144105
1351268912434.0955471457254.904452854324
1361147411221.1889642829252.811035717121
1371099211125.1895708322-133.189570832175
1381076410616.0526039754147.947396024572
1391216410714.74702813371449.25297186628
1401040910851.1457581461-442.145758146078
1411039810266.2058348480131.794165152029
1421034910983.4200440787-634.420044078666
1431086510886.2447473934-21.2447473933717
1441163012380.6622302628-750.662230262773
1451222112839.0926009216-618.092600921605
1461088411372.7701024268-488.77010242679
1471201912408.3127903861-389.312790386075
1481102111138.7981807552-117.798180755239
1491079910934.2426618679-135.242661867938
1501042310478.5305294948-55.530529494763
1511048410812.7722607621-328.7722607621
1521045010424.396961658625.6030383414291
15399069989.204556255-83.2045562550065
1541104910535.5426932424513.457306757588
1551128110654.6424414418626.357558558153
1561248512060.4760347732424.523965226803
1571284912644.8756468006204.124353199360
1581138011274.3060916889105.693908311061
1591207912380.7212565589-301.721256558851
1601136611172.4406195528193.559380447236
1611132810991.9785115000336.021488499970
1621044410593.3824404453-149.382440445264
1631085410867.3182072975-13.3182072974505
1641043410576.6085687239-142.608568723932
1651013710107.015110470229.9848895298455
1661099210781.0602411463210.939758853718
1671090610897.48910092668.51089907344976
1681236712211.6804503702155.319549629827
1691437112730.42598182571640.57401817425
1701169511464.9870234456230.012976554448
1711154612503.9823220540-957.982322054046
1721092211337.566526828-415.566526828008
1731067011133.5560544401-463.55605444014
1741025410571.7517609036-317.751760903628
1751057310857.8698415874-284.869841587413
1761023910518.4263887194-279.426388719361
1771025310070.5561374226182.443862577447
1781117610792.8120522472383.187947752767
1791071910884.2984910501-165.298491050124
1801181712212.1182532878-395.118253287785


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18112973.615548451611906.417772251714040.8133246516
18211290.19516570110219.034260965412361.3560704366
18312075.200096066511000.023034459713150.3771576733
18411095.492627884510016.246399792012174.7388559770
18510916.65051543579833.2821374659312000.0188934055
18610422.35785389249334.8143762255111509.9013315592
18710741.66947079089649.8979843725411833.4409572090
18810427.45159639909331.3992399776811523.5039528204
18910093.80388060388993.4178476090511194.1899135986
19010839.58236415839734.8099094208411944.3548188958
19110790.6247282349681.4131745443811899.8362819236
19212087.347838830210973.644583336713201.0510943237
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/1oe3h1293608705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/1oe3h1293608705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/2oe3h1293608705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/2oe3h1293608705.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/3g5kk1293608705.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t12936086027xlvdb00amt0rqw/3g5kk1293608705.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')
 




Copyright

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Software written by Ed van Stee & Patrick Wessa


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