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ES 2

*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 17:33:07 +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/t1293643855hjrhux1bszaf4hk.htm/, Retrieved Wed, 29 Dec 2010 18:30:58 +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/t1293643855hjrhux1bszaf4hk.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 «
34420 34070 33978 34484 34645 34410 34534 35019 35508 35488 35709 36534 36066 35724 35727 36281 36017 35780 36003 36285 36419 36413 36663 37451 37063 36613 36564 37064 36817 36621 36798 36967 36926 36975 37324 38159 37776 37465 37451 37944 37737 37603 37813 37960 37934 37975 38241 39176 39137 38797 38730 39031 38851 38727 39291 39407 39326 39326 39617 40458 40425 40092 39939 40174 40065 39922 40107 40163 40116 40118 40416 41215 40852 40497 40430 40766 40626 40442 40590 40673 40660 40736 41082 41873 41507 41104 40963 41227 41063 40873 41016 41433 41345 41375 41597 42225 41937 41642 41551 41866 41744 41615 41764 41828 41786 41852 42183 42937 42635 42292 42202 42577 42600 42433 42584 42660 42659 42712 43039 43664 43397 43110 43005 43159 43066 42977 43139 43226 43242 43348 43605 44225 43983 43754 43632 43868 43864 43808 43954 44032 44090 44210 44435 44919 44785 44616 44 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.602510164692305
beta0.0371124448631074
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133606635295.1672008547770.832799145297
143572435433.4680543628290.531945637187
153572735657.129237486369.8707625137322
163628136314.6105020958-33.610502095813
173601736089.2000344138-72.2000344138287
183578035866.2578766791-86.2578766790903
193600335930.916946029272.083053970804
203628536457.0481910739-172.048191073925
213641936831.9491076652-412.949107665161
223641336537.5126397425-124.512639742468
233666336670.7862284662-7.78622846624057
243745137496.0062282017-45.0062282016879
253706337307.1509680786-244.150968078568
263661336625.8700334212-12.8700334211535
273656436555.10456062048.89543937959388
283706437109.4380738528-45.438073852798
293681736836.0212066517-19.0212066516833
303662136615.17987515675.82012484326697
313679836775.962599875922.037400124078
323696737151.488902342-184.48890234196
333692637399.4480771431-473.448077143097
343697537158.1677133686-183.167713368573
353732437276.143805975547.856194024549
363815938094.983778602364.01622139768
373777637869.9848721452-93.9848721451708
383746537351.7973945642113.20260543577
393745137349.1476226548101.852377345167
403794437923.47429221120.5257077889837
413773737687.359377093549.6406229065105
423760337506.354660989196.6453390109018
433781337718.930599504594.069400495464
443796038047.9993859604-87.9993859604074
453793438233.6282838202-299.628283820173
463797538210.7384690545-235.738469054479
473824138385.9731496463-144.97314964627
483917639087.846492334888.1535076651999
493913738807.9180054195329.08199458052
503879738629.7788592647167.221140735324
513873038659.163419423870.8365805761932
523903139185.7819148269-154.781914826948
533885138855.000953049-4.00095304895513
543872738658.546774964368.453225035737
553929138850.6686114931440.331388506878
563940739321.291750611385.7082493886992
573932639536.6436172188-210.643617218811
583932639603.9359618375-277.935961837466
593961739800.0533949491-183.0533949491
604045840581.0258602769-123.025860276895
614042540274.2815603651150.718439634897
624009239925.0054727709166.994527229101
633993939916.603503389222.396496610796
644017440323.934037023-149.934037023035
654006540055.69501192129.30498807878757
663992239896.042268451925.9577315481365
674010740209.412372869-102.412372868952
684016340198.966140622-35.9661406220039
694011640207.3887352263-91.388735226341
704011840306.6295885941-188.629588594107
714041640583.1110747281-167.111074728113
724121541386.7469646424-171.746964642378
734085241147.5665261802-295.56652618017
744049740513.9978242041-16.9978242040597
754043040311.2771959534118.7228040466
764076640684.314440447381.6855595526868
774062640600.272396425325.727603574669
784044240438.84888787193.15111212810734
794059040668.6571362223-78.6571362222749
804067340680.6717349964-7.67173499637283
814066040666.4811167579-6.48111675789551
824073640762.4950481267-26.4950481266642
834108241133.1106887791-51.1106887791248
844187341995.2821676848-122.282167684782
854150741728.2807153165-221.280715316527
864110441243.452234384-139.452234383964
874096341011.4150297169-48.4150297168817
884122741255.806676038-28.8066760380098
894106341067.2571165608-4.25711656078784
904087340862.431004696310.5689953037145
914101641047.9939456257-31.9939456257416
924143341101.1862743413331.813725658692
934134541284.45017057760.5498294229983
944137541406.8322629706-31.8322629706017
954159741758.265035904-161.265035903947
964222542517.1316668999-292.131666899943
974193742095.999512736-158.999512736038
984164241670.1709898121-28.1709898121262
994155141532.805458813518.1945411864654
1004186641818.050830782747.9491692173106
1014174441680.148618156163.8513818439023
1024161541518.417715787296.5822842128036
1034176441736.975430265527.0245697344581
1044182841969.7457857018-141.74578570178
1054178641748.6804545137.319545489976
1064185241808.645511534143.3544884658622
1074218342143.912467155139.0875328449256
1084293742965.9370227472-28.9370227472318
1094263542756.6478128254-121.64781282538
1104229242406.5091019762-114.509101976219
1114220242234.8052590862-32.8052590861553
1124257742499.26095877477.7390412260283
1134260042384.4055984648215.594401535214
1144243342329.2818614225103.718138577467
1154258442526.820330931857.1796690681731
1164266042713.6790410377-53.6790410376925
1174265942621.82479674937.1752032510485
1184271242689.071816080622.9281839194082
1194303943014.849000640724.1509993592845
1204366443805.0144398978-141.014439897801
1214339743493.0190954196-96.0190954196078
1224311043163.4058316499-53.4058316499068
1234300543064.6064039468-59.606403946811
1244315943359.8677134641-200.867713464097
1254306643128.7285710375-62.7285710374854
1264297742852.0027759918124.99722400817
1274313943034.89939522104.100604779953
1284322643198.048270099627.9517299003855
1294324243185.401383224156.5986167758747
1304334843253.03283051394.967169486983
1314360543618.6557988437-13.6557988436762
1324422544315.5007969972-90.5007969971775
1334398344048.0652668853-65.0652668852563
1344375443750.97212459863.02787540143618
1354363243681.903593497-49.9035934970161
1364386843925.2716501225-57.2716501224713
1374386443837.181038045326.8189619546974
1384380843692.6515136386115.348486361363
1394395443864.836601248389.1633987517489
1404403243991.79137328840.2086267119812
1414409044001.264428910988.7355710890988
1424421044107.5766211621102.423378837906
1434443544438.7490247558-3.74902475576528
1444491945115.4728901307-196.472890130666
1454478544796.3838999384-11.3838999383515
1464461644561.986446266154.0135537339302
1474449644507.0234428669-11.0234428668991
1484460044776.1837014241-176.183701424074
1494446344652.5088290468-189.508829046819
1504423244410.6282688313-178.628268831308
1514424844386.5066341314-138.506634131394
1524428244342.9635956367-60.9635956366619
1534431144294.640774636116.3592253638635
1544436244345.040315605216.9596843948311
1554461744562.860569973554.1394300264947
1564502245179.4945089174-157.4945089174
1574488244939.970431466-57.9704314660339
1584459444684.9662877542-90.9662877542287
1594450244495.02541686246.97458313759853
1604475244688.008097920663.9919020793532
1614469044687.74329471152.25670528854971
1624453344554.0147570414-21.014757041441
1634460444632.6155707137-28.6155707136786
1644464644680.3735808835-34.3735808834826
1654465244673.6691151378-21.6691151378036
1664471844695.407098999822.5929010002219
1674492844925.53818507652.46181492349569
1684528545419.8961427873-134.896142787285
1694518345227.0355800765-44.0355800765465
1704496444961.11136076512.88863923487952
1714487544862.547745159812.4522548402383
1724507145077.5152751062-6.51527510621236
1734498545004.6741744789-19.6741744789106
1744485444842.435607640211.5643923597891
1754492544932.326652501-7.32665250098216
1764497044985.7809439897-15.7809439896664
1774501144990.902612158720.097387841306
1784510745051.90695043755.0930495630382
1794530645290.852438253415.1475617466494
1804577345735.773590579837.2264094201673
1814562545684.1018283413-59.1018283412559
1824539145428.7821138675-37.7821138675208
1834532545309.636144989715.3638550103205
1844543045519.0043973653-89.00439736533
1854532145389.5735790903-68.5735790902909
1864523845207.537561185930.4624388140874
1874524645298.9763694249-52.9763694248904
1884528145318.2154879136-37.2154879136069
1894529745320.8543482926-23.8543482925816
1904534945364.4754008961-15.4754008961099
1914553645538.634462242-2.63446224204381
1924590345974.8299723284-71.8299723283635
1934571645809.9346577496-93.9346577495526
1944541945532.096816993-113.096816993013
1954523745377.0085101999-140.008510199863
1964534945436.1143443928-87.1143443927504
1974526045300.8219382199-40.8219382199168
1984513945160.3715138983-21.3715138982807
1994515445171.7538584391-17.7538584391077
2004518645203.6073832205-17.6073832204784
2014526245208.937387857653.0626121423556
2024522745289.5182933928-62.5182933928081
2034531345426.6718239449-113.671823944853
2044556445752.2129657218-188.212965721832
2054539245489.5582130413-97.5582130413313
2064511445182.9882410881-68.9882410881255
2074499645025.8328316848-29.8328316847546
2084515945156.86327895872.13672104132274
2094510745080.259771072326.7402289276506
2104496344976.271780715-13.2717807150329
2114500544982.177588750222.8224112497919
2124502445027.6495722837-3.64957228366984
2134502545058.9046314937-33.9046314936859
2144505345028.624738480224.3752615198391
2154514345187.2225897415-44.222589741461


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
21645515.954262251345265.185373644545766.723150858
21745397.918644218545102.217195439645693.6200929973
21845158.850790322444821.534287604145496.1672930406
21945057.734024464844680.935472436845434.5325764928
22045219.022358899144804.18936967145633.8553481271
22145150.439051326344698.583888514845602.2942141377
22245013.365458034344525.205575248245501.5253408205
22345040.841512512444516.885175888845564.7978491361
22445060.756882763444501.358556463545620.1552090632
22545080.982840439944486.380712771645675.5849681083
22645093.852698938344464.195065220645723.5103326559
22745209.50841400944544.872793078645874.1440349394
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/1lnms1293643985.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/1lnms1293643985.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/210b11293643985.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/210b11293643985.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/310b11293643985.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293643855hjrhux1bszaf4hk/310b11293643985.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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