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*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: Tue, 30 Nov 2010 16:31:19 +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/Nov/30/t1291134613x2wt2x3059l3819.htm/, Retrieved Tue, 30 Nov 2010 17:30:17 +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/Nov/30/t1291134613x2wt2x3059l3819.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 «
15086 20559 39383 68032 42346 40184 29183 18049 24377 48033 61410 40637 37914 22481 17061 21921 34043 36152 38929 36713 27928 14178 19331 35030 37834 45257 39650 33001 22268 34283 63733 54548 31666 32654 28409 16234 19544 33375 30839 27581 28596 28542 14285 20799 28729 30278 31266 38341 24938 15700 17382 34229 29584 33909 29397 24644 14124 18770 32681 30518 34310 24217 15806 12362 13751 25312 23549 30305 30411 15593 17382 15806 29183 33348 33589 30198 23469 15593 16474 27341 26673 33268 26406 23656 15086 18316 27528 30305 34550 34710 23843 12362 21200 27261 31586 33322 32814 21974 17115 14445 26673 31746 28249 29103 21974 17622 21066 28382 32147 35885 40824 28622 24297 30465 47927 51665 57058 48407 30011 21413 30518 41171 37487 44456 41465 28409 34870 29557 44936 44028 45310 39302 28516 19865 30091 38101 44402 52359 71182 60796 43735 63947 89071 86321 90967 54441 36 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time42 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.747438902191031
beta0
gamma0.304106950569212


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
81804915199.30458736212849.69541263792
92437723548.7822910227828.21770897734
104803348019.54343715413.4565628460186
116141063009.7128158693-1599.71281586933
124063767950.8866488059-27313.8866488059
133791429232.19857741448681.80142258559
142248133388.0343270543-10907.0343270543
151706111383.05355511485677.94644488521
162192121024.8712603180896.128739681957
173404342991.5008921374-8948.50089213743
183615247524.3729927215-11372.3729927215
193892941077.9998066308-2148.99980663083
203671325866.031912342810846.9680876572
212792830136.7267853712-2208.72678537123
221417813662.3086384283515.691361571684
231933118444.2485605412886.751439458785
243503037027.2522843021-1997.25228430207
253783446354.5224143309-8520.52241433095
264525742875.14101655732381.85898344269
273965030108.64206201539541.35793798469
283300132052.8184460428948.181553957198
292226815852.78205432406415.21794567596
303428327134.17111925247148.82888074758
316373362455.34784161391277.65215838614
325454881735.1331269196-27187.1331269196
333166667235.5713924955-35569.5713924955
343265427831.41362552694822.58637447306
352840926591.48229770961817.51770229035
361623413815.53113311642418.46886688363
371954420389.2514112876-845.251411287634
383337537413.5324119917-4038.53241199168
393083942751.2620067868-11912.2620067868
402758135772.2224334590-8191.22243345904
412859622015.62640825636580.37359174369
422854222628.28090390415913.71909609592
431428513461.3689335963823.631066403652
442079918094.84084606572704.15915393431
452872937873.7980354618-9144.79803546183
463027837876.3639429212-7598.36394292122
473126634230.6164222483-2964.61642224826
483834124744.520610462613596.4793895374
492493829273.8514507247-4335.8514507247
501570012798.96042579942901.03957420058
511738219351.5065254783-1969.50652547832
523422932562.78027588041666.21972411955
532958441448.4875420218-11864.4875420218
543390935027.4992493504-1118.49924935037
552939727413.84925462791983.15074537214
562464423225.26645074521418.73354925483
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581877017250.03150370251519.96849629746
593268133899.7769577748-1218.77695777478
603051839163.9540352302-8645.95403523017
613431036079.2000740112-1769.20007401123
622421728084.9225080144-3867.92250801443
631580620231.8840770009-4425.88407700095
64123628601.613432764093760.38656723591
651375114355.5063744984-604.506374498353
662531225396.9878401194-84.9878401193782
672354929544.2196985469-5995.21969854694
683030528109.81083253032195.18916746966
693041123846.96257281656564.03742718349
701559322898.5372141922-7305.53721419221
71173829273.960528390228108.03947160978
721580618752.8414729070-2946.84147290695
732918330328.0746716335-1145.07467163348
743334833751.2414396095-403.241439609548
753358938442.6640156577-4853.66401565773
763019828238.51516755521959.48483244482
772346922499.6022905918969.397709408182
781559313282.95499703592310.04500296408
791647417397.6852592617-923.685259261729
802734130948.0873458454-3607.08734584538
812667332419.9417903130-5746.94179031297
823326832002.46108172671265.53891827325
832640627149.9579151696-743.957915169583
842365620105.63764373713550.36235626295
851508613128.68457269931957.3154273007
861831616644.35429473131671.64570526869
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903471028609.48202853516100.51797146494
912384325435.3131147822-1592.31311478216
921236213963.0083738782-1601.00837387816
932120014515.98032055926684.01967944081
942726135172.6950769153-7911.69507691526
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963332237362.4761666487-4040.47616664871
973281428639.64371023064174.3562897694
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1001444518907.273307063-4462.27330706301
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1032824936630.0023914926-8381.00239149257
1042910325810.16114296383292.83885703619
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1143046525079.18324408385385.81675591618
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1193001135657.0594290539-5646.05942905392
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1254146540235.74718689561229.25281310438
1262840929527.1689135996-1118.16891359964
1273487018006.685601638816863.3143983612
1282955734211.9327759668-4654.93277596679
1294493649982.3874223517-5046.38742235167
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1314531054250.3267750006-8940.32677500056
1323930242790.2040186548-3488.20401865479
1332851628677.6716574933-161.671657493334
1341986518736.61259199291128.38740800710
1353009120747.12927854959343.87072145046
1363810145247.5613082379-7146.56130823795
1374440246063.0797161589-1661.07971615894
1385235952394.9000292909-35.9000292909113
1397118247481.664410238623700.3355897614
1406079646829.512510209113966.4874897909
1414373537766.56419894835968.43580105168
1426394745711.40481245618235.595187544
1438907193100.2776145957-4029.2776145957
14486321105161.407035098-18840.4070350984
14590967106788.544555097-15821.5445550972
1465444188526.3905021094-34085.3905021094
1473633944881.9798481776-8542.97984817755
1482929025187.8095537324102.190446268
1496584230967.250474385234874.7495256148
1509940487115.753750302712288.2462496973
15183865111009.146038893-27144.1460388933
15284452106702.241074093-22250.2410740928
1537630981522.5811267203-5213.5811267203
1546955456673.023117272712880.9768827273
1554461644630.8370034924-14.8370034924301
1566733750642.613073508716694.3869264913
1579414492991.24574861921152.7542513808
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1824814051426.545604921-3286.545604921
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187103516105473.461590915-1957.46159091471
188100285102521.521318632-2236.52131863171
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1905198551582.8721578507402.127842149304
1917222460250.636591021811973.3634089782
1929935194850.8927622594500.10723774097
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19597669105676.231492165-8007.23149216542
1967171678132.8446678729-6416.84466787288
1975158451405.7009683349178.299031665061
1986341360609.82582757062803.17417242944
1998813785118.02795413423018.97204586575
2008653588212.825036116-1677.82503611594
2019195598097.212897743-6142.21289774297
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2044093140827.2584117504103.741588249562
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2067657676242.1760664469333.823933553067
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2086031589420.509213793-29105.5092137929
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2103748743234.5029012015-5747.50290120148
2111997227995.4589820590-8023.45898205897
2122533826317.7684456719-979.768445671856
2132354934208.1688275159-10659.1688275159
2141978526453.9243485104-6668.92434851037
2152963723243.23718791926393.76281208082
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2172691425665.02423195191248.97576804812
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2192400328824.1616225140-4821.16162251396
2201935832764.5758092076-13406.5758092076
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3584736645678.38069073981687.61930926020
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11353089236933.6889709422-6041.68897094224
11364010346780.3263524315-6677.3263524315
11375943457573.27218088811860.72781911191
11386760457323.433749604810280.5662503952
11397019467377.68250225742816.31749774255
11406376060980.53375631892779.46624368114
11415310647982.82649913875123.17350086134
11423431038108.5123785395-3798.51237853949
11434488351001.7448538832-6118.7448538832
11446805864918.07436598573139.92563401429
11457433366029.87766326328303.1223367368
11467115674203.0784326455-3047.07843264546
11476733763142.08142957474194.9185704253
11485227950644.74280211941634.25719788056
11493772737547.580298164179.419701836021
11504325454389.3700964597-11135.3700964597
11517449365303.90457708819189.09542291187
11527799171218.24391329986772.75608670023
11536869977420.0537895047-8721.05378950472
11546648362749.75027459773733.24972540225
11556231849959.427455948412358.5725440516
11563588542767.6144729432-6882.61447294316
11574990253277.3465303246-3375.34653032458
11587823174029.83341406994201.16658593008
11596704475927.7131843379-8883.71318433789
11607147669185.03113195612290.96886804387
11616811263621.72478289964490.27521710036
11625249251648.3304442729843.669555727094
11634149236650.33190724744841.6680927526
11644680557542.3228559835-10737.3228559835
11656984772898.6379519421-3051.63795194209
11667347868508.83679702444969.16320297563
11677863273014.84802066895617.1519793311
11687481369475.13426366915337.86573633089
11696018256431.24894096363750.75105903638
11704130541859.3637917857-554.363791785654
11713911657703.5388173488-18587.5388173488
11727201065370.78192914486639.21807085523
11737924668821.784689711910424.2153102881
11747169077477.5082768622-5787.50827686215
11756942065819.24657725293600.75342274709
11765793952587.31230146085351.68769853915
11774629839753.75798490216544.24201509791
11786042260196.2515091506225.748490849401
11798103593788.339066486-12753.3390664859
11808263782710.4638504968-73.4638504968461
11817972682221.9175733562-2495.91757335622
11828634873038.998989819213309.0010101808
11836629663905.9541894752390.04581052499
11843369546334.4582745423-12639.4582745423
11855219949194.44876901793004.55123098214
11867251778967.6764803978-6450.6764803978
11877227773635.4050767586-1358.40507675859
11887307872069.69105588551008.30894411450
11897676367166.12389539929596.8761046008
11906565556706.88768479278948.11231520725
11913465743415.7241497251-8758.7241497251
11925641750726.13017680295690.86982319706
11936869983464.0123476958-14765.0123476958
11947716372308.67656611514854.32343388486
11957970075550.91725065454149.08274934547
11967815173184.7353369834966.26466301696
11975978158711.84001554861069.15998445145
11984482939582.42707380775246.5729261923
11994699261453.8978499777-14461.8978499777
12007703075080.71862045711949.28137954288
12019259678009.31197212214586.6880278779
12028493388387.108367891-3454.10836789098
12038391879914.34331991464003.65668008545
12046330663075.9777877716230.022212228352
12054728642399.60648267394886.39351732607
12067740363042.977322806214360.0226771938
1207102768112052.890744839-9284.89074483946
1208118361108278.42303391710082.5769660829
1209107708113351.364327949-5643.36432794936
121094705102338.297198986-7633.29719898617
12117612273269.49231467242852.50768532764
12124541750946.2955869702-5529.29558697024
12137980664517.927657436715288.0723425633
1214106346112876.824523258-6530.82452325831
121595826112757.086613556-16931.0866135560
12169379796933.5470601537-3136.54706015369
12179935188511.149521858910839.8504781411
12188383873916.00589748429921.99410251578
12195417454297.6492084312-123.649208431176
12208455976556.5508447568002.44915524407
1221116492120248.255698814-3756.25569881430
1222114543121592.170661768-7049.17066176792
1223123407113836.0887227649570.91127723639
1224114677114486.868331064190.131668935937
122511037887766.794509788522611.2054902115
12269604069217.696800575126822.3031994249
1227141857127042.39951004414814.600489956
1228233465199250.94513729934214.0548627005
1229146022232273.681309306-86251.6813093062
1230142124165995.4306771-23871.4306771000
1231118067139364.636333654-21297.6363336538
12328301096074.539569994-13064.5395699941
12337569557440.196514229118254.8034857709
123410415799697.1269648614459.87303513907
1235150161149140.5678220651020.43217793459
1236174832147032.49493276727799.5050672329
1237139935170685.070006768-30750.0700067684
1238108749138816.684613071-30067.6846130713
123910997790695.035822895819281.9641771042
12407887272170.82620297536701.17379702469
1241126451106505.36330798619945.6366920136
1242161295175262.524754302-13967.5247543018


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1243163639.163111119144493.081258922182785.244963315
1244161722.127739993136011.27630324187432.979176746
1245151399.692382014121584.510688206181214.874075821
1246122114.25262445892070.7661305483152157.739118368
124783236.183687341355745.2351918822110727.132182800
1248115542.92229992374341.011270294156744.833329552
1249163636.979373179106397.184989356220876.773757001
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/1l9o31291134636.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/1l9o31291134636.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/2v0no1291134636.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/2v0no1291134636.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/3v0no1291134636.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/30/t1291134613x2wt2x3059l3819/3v0no1291134636.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
 
R code (references can be found in the software module):
par1 <- 7
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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