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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, 07 Dec 2010 14:26:28 +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/07/t1291731875y643r93jlkfexex.htm/, Retrieved Tue, 07 Dec 2010 15:24:49 +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/07/t1291731875y643r93jlkfexex.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 «
1145.11 1176.86 1206.41 1192.72 1214.82 1199.07 1157.47 1100.1 1095.63 1105.63 1137.79 1124.72 1152.6 1211.85 1239.62 1244.13 1198.42 1227.99 1304.92 1340.26 1307.32 1356.51 1383.29 1437.87 1494.56 1521.42 1498.76 1488.75 1524.62 1439.27 1423.11 1466.85 1425.83 1363.45 1389.18 1395.89 1368.43 1349.03 1299.88 1365.41 1451.04 1433.75 1464.65 1475.57 1471.16 1429.12 1452.46 1538.09 1631.59 1665.5 1690.6 1711.74 1734.1 1748.09 1703.45 1745.74 1751.01 1795.65 1852.13 1877.1 1989.31 2097.76 2154.87 2152.18 2250.27 2346.9 2525.56 2409.36 2394.36 2401.33 2354.32 2450.41 2504.67 2661.39 2880.4 3064.42 3141.12 3327.7 3564.95 3403.13 3149.9 3006.84 3230.66 3361.13 3484.74 3411.13 3288.18 3280.37 3173.95 3165.26 3092.71 3053.05 3181.96 2999.93 3249.57 3210.52 3030.29 2803.47 2767.63 2882.6 2863.36 2897.06 3012.61 3142.95 3032.93 3045.78 3110.52 3013.24 2987.1 2995.55 2833.18 2848.96 2794.83 2845.26 2915.02 2 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.156597557299119
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31206.411208.61-2.19999999999982
41192.721237.81548537394-45.095485373942
51214.821217.06364251916-2.24364251916450
61199.071238.81229358121-39.7422935812108
71157.471216.83874748493-59.3687474849287
81100.11165.94174664888-65.8417466488809
91095.631098.26108995536-2.63108995535822
101105.631093.3790676953212.2509323046850
111137.791105.2975337688732.4924662311341
121124.721142.54577461129-17.8257746112854
131152.61126.6843018501925.9156981498065
141211.851158.6226368761553.2273631238456
151239.621226.2079119228213.4120880771782
161244.131256.07821215399-11.9482121539884
171198.421258.71715131658-60.2971513165824
181227.991203.5647647083124.4252352916897
191304.921236.9596968914467.9603031085551
201340.261324.5321143515515.7278856484475
211307.321362.33506282558-55.0150628255792
221356.511320.7798383724435.730161627564
231383.291375.565094405227.72490559478479
241437.871403.5547957517234.3152042482752
251494.561463.5084729152231.051527084775
261521.421525.06106620711-3.64106620710822
271498.761551.35088413311-52.5908841331109
281488.751520.45528014166-31.7052801416646
291524.621505.4803107180019.1396892820042
301439.271544.34753930702-105.077539307022
311423.111442.54265332454-19.4326533245398
321466.851423.3395472820843.5104527179237
331425.831473.89317789468-48.063177894682
341363.451425.34660164034-61.8966016403417
351389.181353.2737450183535.9062549816524
361395.891384.6265768402311.2634231597663
371368.431393.10040139388-24.6704013938795
381349.031361.77707679801-12.7470767980092
391299.881340.38091570874-40.5009157087366
401365.411284.8885712403780.521428759629
411451.041363.0280302943688.011969705636
421433.751462.44048976335-28.6904897633506
431464.651440.6576291486923.9923708513056
441475.571475.314775817820.255224182176335
451471.161486.27474330132-15.1147433013159
461429.121479.49781142113-50.377811421127
471452.461429.5687692105022.8912307894975
481538.091456.4934800357181.5965199642917
491631.591554.9012957462376.6887042537749
501665.51660.41055950485.08944049519914
511690.61695.11755345437-4.51755345436845
521711.741719.51011561845-7.77011561844597
531734.11739.43333449267-5.3333344926657
541748.091760.95814733886-12.8681473388551
551703.451772.93302689863-69.483026898625
561745.741717.4121546125528.3278453874484
571751.011764.13822600377-13.1282260037731
581795.651767.3523778799128.2976221200886
591852.131816.4237163812935.7062836187092
601877.11878.49523317621-1.39523317621047
611989.311903.2467430689586.0632569310471
622097.762028.9340388775668.8259611224387
632154.872148.16201626816.70798373190019
642152.182206.32247013492-54.1424701349174
652250.272195.1538915656555.1161084343512
662346.92301.874939514345.0250604856983
672525.562405.55575400361120.004245996393
682409.362603.00812579216-193.648125792165
692394.362456.48330231756-62.1233023175591
702401.332431.75494492327-30.4249449232748
712354.322433.96047286733-79.6404728673292
722450.412374.4789693541675.9310306458406
732504.672482.459583276522.2104167234979
742661.392540.197680282121.192319718002
752880.42715.89610151325164.503898486750
763064.422960.66701018246103.752989817542
773141.123160.93447495037-19.8144749503658
783327.73234.5315765739793.1684234260265
793564.953435.7015240999129.248475900101
803403.133693.19151971049-290.061519710489
813149.93485.94859425736-336.048594257356
823006.843180.09420526285-173.254205262851
833230.663009.90301992689220.756980073111
843361.133268.2930237630792.836976236932
853484.743413.3010674688171.4389325311913
863411.133548.09822979925-136.968229799249
873288.183453.0393395851-164.859339585103
883280.373304.27276970813-23.9027697081292
893173.953292.71965435915-118.769654359153
903165.263167.70061660525-2.44061660524858
913092.713158.62842200656-65.9184220065636
923053.053075.75575813932-22.7057581393228
933181.963032.54009187808149.419908121919
942999.933184.84888450183-184.918884501832
953249.572973.86103889037275.708961109633
963210.523266.67638872561-56.1563887256139
973030.293218.83243542444-188.542435424442
982803.473009.07715058975-205.607150589748
992767.632750.0595730441617.5704269558391
1002882.62716.97105898615165.628941013852
1012863.362857.878146566965.48185343304294
1022897.062839.4965914240457.5634085759561
1033012.612882.21088059685130.399119403151
1043142.953018.18106416934124.768935830661
1053032.933168.05957474723-135.129574747231
1063045.783036.878613422958.90138657705438
1073110.523051.1225488174959.3974511825118
1083013.243125.16404458246-111.924044582463
1092987.13010.35701259781-23.2570125978114
1102995.552980.5750212349214.9749787650808
1112833.182991.37006633014-158.190066330138
1122848.962804.2278883538544.732111646148
1132794.832827.01282777047-32.1828277704703
1142845.262767.8430755546477.4169244453637
1152915.022830.3963768163984.6236231836087
1162892.632913.40822949675-20.7782294967451
1172604.422887.76440951255-283.344409512554
1182641.652555.1833671085386.4666328914732
1192659.812605.9538306072153.8561693927886
1202638.532632.547575179615.98242482039086
1212720.252612.20440829321108.045591706792
1222745.882710.8440840314335.0359159685700
1232735.72741.96062288985-6.26062288984531
1242811.72730.8002246381280.8997753618755
1252799.432819.46893184584-20.0389318458415
1262555.282804.0608840679-248.780884067899
1272304.982520.95240532015-215.972405320151
1282214.952236.831654203-21.8816542029999
1292065.812143.37504060515-77.5650406051459
1301940.491982.08854471457-41.5985447145731
13120421850.25431422507191.745685774927
1321995.371981.7912202400713.5787797599289
1331946.811937.287623981589.52237601842148
1341765.91890.21880480575-124.318804805747
1351635.251689.84078364682-54.5907836468211
1361833.421550.64200027668282.777999723316
1371910.431793.09434429129117.335655708713
1381959.671888.4788213593671.1911786406386
1391969.61948.8671860357320.7328139642691
1402061.411962.0438940584799.3661059415276
1412093.482069.4143835272424.0656164727588
1422120.882105.2530002817715.6269997182276
1432174.562135.1001502655639.4598497344386
1442196.722194.959466345361.76053365463531
1452350.442217.39516161522133.044838384777
1462440.252391.9496583175448.3003416824645
1472408.642489.32337384172-80.6833738417222
1482472.812445.0785545834627.731445416543
1492407.62513.59123119606-105.991231196062
1502454.622431.7832632956322.8367367043679
1512448.052482.37944048022-34.3294404802186
1522497.842470.4335339575727.4064660424287
1532645.642524.51531959402121.124680405983
1542756.762691.2831486742365.47685132577
1552849.272812.6566636514836.6133363485164
1562921.442910.9002226882310.5397773117679
1572981.852984.72072606973-2.87072606973197
1583080.583044.6811773795435.8988226204633
1593106.223149.03284531182-42.8128453118161
1603119.313167.96845831496-48.6584583149602
1613061.263173.43866260090-112.178662600896
1623097.313097.82175805651-0.511758056514282
1633161.693133.7916179949427.8983820050644
1643257.163202.5404364695354.619563530473
1653277.013306.56372669914-29.5537266991423
1663295.323321.78568528897-26.4656852889711
1673363.993335.9512236204728.0387763795284
1683494.173409.0120275111685.1579724888388
1693667.033552.52755798746114.502442012541
1703813.063743.3183607114169.7416392885925
1713917.963900.2697310660417.6902689339631
1723895.514007.93998396906-112.429983969060
1733801.063967.88372311233-166.823723112327
1743570.123847.30953557339-277.189535573391
1753701.613572.96233139372128.647668606279
1763862.273724.59824204969137.671757950309
1773970.13906.8173030537863.2826969462153
1784138.524024.55721881486113.962781185138
1794199.754210.82351197147-11.07351197147
1804290.894270.3194270460120.5705729539859
1814443.914364.6807285228579.2292714771474
1824502.644530.10783890276-27.4678389027613
1834356.984584.53644242630-227.556442426305
1844591.274403.24165939467188.028340605334
1854696.964666.9764382364729.9835617635308
1864621.44777.36179076777-155.961790767766
1874562.844677.37855530154-114.538555301537
1884202.524600.88209732475-398.362097324746
1894296.494178.17956596314118.310434036863
1904435.234290.67669093631144.553309063692
1914105.184452.05338603519-346.873386035186
1924116.684067.6838610948.9961389099976
1933844.494086.8565367604-242.366536760397
1943720.983776.71252913267-55.7325291326706
1953674.43644.4749512083929.9250487916074
1963857.623602.58114075122255.038859248784
1973801.063825.73960312593-24.6796031259287
1983504.373765.3148375613-260.944837561297
1993032.63427.76151340938-395.161513409382
2003047.032894.11018567085152.919814329151
2012962.342932.4870550574329.8529449425705
2022197.822852.47195331362-654.651953313621
2032014.451985.4350565436129.0149434563889
2041862.831806.6087258140556.2212741859464
2051905.411663.79284001982241.617159980183
2061810.991744.2094970742666.7805029257358
2071670.071660.247160707649.82283929235905
2081864.441520.86539334657343.574606653434
2092052.021769.0383374985282.9816625015
2102029.62000.9325746066828.6674253933215
2112070.831983.0018233973387.8281766026726
2122293.412037.98550131534255.424498684658
2132443.272300.56435388371142.705646116289
2142513.172472.7717094783140.3982905216853
2152466.922548.99798309307-82.0779830930705
2162502.662489.8947714326612.7652285673425


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
2172527.633775044672284.634523923792770.63302616555
2182552.607550089342181.071476446912924.14362373176
2192577.581325134002087.818801960943067.34384830707
2202602.555100178671996.395437635193208.71476272216
2212627.528875223341903.911744846063351.14600560063
2222652.502650268011809.092875049233495.91242548679
2232677.476425312681711.308476993073643.64437363229
2242702.450200357351610.232642890003794.66775782469
2252727.423975402011505.698887846773949.14906295725
2262752.397750446681397.630032454474107.16546843889
2272777.371525491351286.001213166594268.74183781611
2282802.345300536021170.819088347184433.87151272486
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/1m3bf1291731983.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/1m3bf1291731983.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/2xcai1291731983.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/2xcai1291731983.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/3xcai1291731983.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/07/t1291731875y643r93jlkfexex/3xcai1291731983.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Double ; 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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We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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