Home » date » 2010 » Jun » 04 »

Opgave 10: Goudkoers 2009 exponential smoothing

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Fri, 04 Jun 2010 15:22:07 +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/Jun/04/t1275664964mm1eiybwp9tma08.htm/, Retrieved Fri, 04 Jun 2010 17:22:49 +0200
 
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/Jun/04/t1275664964mm1eiybwp9tma08.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:
KDGP2W62
 
Dataseries X:
» Textbox « » Textfile « » CSV «
23100 22650 22440 22910 22980 22535 22300 22780 22780 23300 23800 24510 24660 24730 25070 24690 24880 23920 23880 23990 24590 23610 23580 23360 23910 23940 23060 22800 23020 22890 22780 22530 22290 22820 22480 22110 22000 22230 22260 22590 22820 22420 22230 21600 21000 21360 21640 21450 21710 21620 21800 21490 21670 22130 22050 22050 22140 22390 22220 21790 21510 21670 21745 21850 22105 22050 21670 21680 21800 21920 21980 22270 21740 21950 22010 21890 21920 22110 22340 22210 22240 21960 22220 22060 22090 21960 21940 21790 21710 21690 21710 21670 21640 21500 21290 21250 21580 21670 21620 21510 21360 21420 21470 21370 21370 21340 21130 21130 20990 21240 21320 21430 21390 21530 21510 21630 21560 21610 21560 21310 21340 21410 21550 21380 21600 21530 21560 21670 21540 21540 21550 21590 21420 21420 21370 21380 21210 21505 21365 21385 21350 21360 21530 21380 21630 22145 22 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
beta0.109263095532174
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32244022200240
42291022016.2231429277893.776857072276
52298022583.8799690465396.120030953542
62253522697.1612698307-162.16126983074
72230022234.443027513665.5569724863926
82278022006.6059852612773.394014738813
92278022571.1094093776208.890590622395
102330022593.9334419366706.066558063445
112380023191.0804597223608.919540277686
122451023757.6128936231752.387106376918
132466024549.8210379043110.178962095681
142473024711.859532365418.1404676345846
152507024783.8416160136286.158383986429
162469025155.1081668604-465.108166860413
172488024724.2890087919155.710991208052
182392024931.3024736997-1011.30247369972
192388023860.804434903919.1955650960517
202399023822.9018017668167.098198233169
212459023951.1594681636638.840531836366
222361024620.9611622235-1010.96116222350
232358023530.500416176249.4995838238465
242336023505.9088939323-145.908893932301
252391023269.9664365156640.033563484416
262394023889.898484906450.1015150936219
272306023925.3727315364-865.372731536361
282280022950.8194280996-150.819428099563
292302022674.340430519345.659569480988
302289022932.1082650808-42.1082650808239
312278022797.5073856906-17.5073856906056
322253022685.5944745354-155.594474535374
332229022418.5937405999-128.593740599936
342282022164.5431904359655.456809564075
352248022766.1604304365-286.160430436539
362211022394.8936559882-284.893655988224
372200021993.76529323756.23470676252691
382223021884.4465165981345.55348340192
392226022152.2027598665107.797240133499
402259022193.9810200133396.018979986689
412282022567.2512796562252.748720343847
422242022824.8673872327-404.867387232716
432223022380.6303232236-150.630323223646
442160022174.1719878272-574.17198782722
452100021481.4361790694-481.436179069355
462136020828.8329718431531.167028156946
472164021246.8699255841393.130074415891
482145021569.8245344616-119.824534461583
492171021366.7321349056343.267865094393
502162021664.2386444425-44.2386444425429
512180021569.4049932086230.595006791398
522149021774.6005174649-284.600517464893
532167021433.5041839366236.495816063380
542213021639.3444488801490.655551119886
552205022152.9549932355-102.954993235518
562205022061.7058119741-11.7058119741123
572214022060.426798722179.5732012778972
582239022159.1212130151230.878786984871
592222022434.3477439738-214.347743973809
602179022240.9274459469-450.927445946894
612151021761.6577173423-251.657717342317
622167021454.1608161309215.839183869062
632174521637.7440734976107.255926502392
642185021724.4631880414125.536811958569
652210521843.1797287193261.820271280736
662205022126.7870220325-76.787022032473
672167022063.3970343085-393.397034308506
682168021640.413256566839.5867434332176
692180021654.7386266963145.261373303667
702192021790.6103340047129.389665995252
712198021924.747849441355.2521505587392
722227021990.7848704461279.215129553879
732174022311.2927798206-571.292779820593
742195021718.8715622422231.128437757787
752201021954.125370817155.8746291828538
762189022020.2304057634-130.230405763377
772192021886.001028497333.9989715027405
782211021919.7158613686190.284138631439
792234022130.5068953861209.493104613895
802221022383.3967604889-173.396760488864
812224022234.45089368265.54910631740131
822196022265.0572062163-305.057206216276
832222021951.7257115507268.274288449313
842206022241.0381907584-181.038190758351
852209022061.257397626528.7426023734515
862196022094.3979033355-134.397903335524
872194021949.7131723841-9.71317238405027
882179021928.6518811019-138.651881101930
892171021763.5023473714-53.5023473713736
902169021677.656515279312.3434847206590
912171021659.005202629650.9947973704257
922167021684.5770520463-14.5770520463047
932164021642.984318216-2.98431821598933
942150021612.6582423697-112.65824236966
952129021460.3488540711-170.348854071137
962125021231.736010955018.2639890450373
972158021193.7315909348386.268409065211
982167021565.9364730155104.063526984457
992162021667.3067761059-47.3067761058628
1002151021612.1378913089-102.137891308888
1012136021490.9779891333-130.977989133349
1022142021326.666928594193.3330714059412
1032147021396.864788891473.1352111086017
1042137021454.8557684495-84.8557684495245
1052137021345.584164515024.4158354850333
1062134021348.2519142801-8.25191428006656
1072113021317.3502845818-187.350284581760
1082113021086.879812539543.1201874604776
1092099021091.5912577014-101.591257701384
1102124020940.4910824059299.508917594078
1112132021223.216353881796.783646118256
1122143021313.7912346535116.208765346488
1132139021436.4885640832-46.4885640832435
1142153021391.4090796647138.590920335337
1152151021546.5519526332-36.5519526331555
1162163021522.5581731407107.441826859289
1172156021654.297599733-94.2975997329886
1182161021573.994352084936.0056479150917
1192156021627.9284406328-67.9284406327533
1202131021570.5063689345-260.506368934544
1212134021292.042636658947.957363341091
1222141021327.282606631182.7173933688828
1232155021406.3205650850143.679434915044
1242138021562.0194249081-182.019424908085
1252160021372.1314190956227.868580904356
1262153021617.0290456198-87.0290456197763
1272156021537.519982694122.4800173058502
1282167021569.9762189726100.023781027397
1292154021690.9051269145-150.905126914487
1302154021544.4167656161-4.41676561613713
1312155021543.93417613276.06582386732407
1322159021554.596946825435.4030531746248
1332142021598.4651940065-178.465194006523
1342142021408.965534464611.0344655353801
1352137021410.1711943266-40.1711943265582
1362138021355.781965283224.2180347167850
1372121021368.4281027241-158.428102724076
1382150521181.1177578012323.882242198844
1392136521511.5061341717-146.506134171701
1402138521355.498420437629.5015795623513
1412135021378.7218543437-28.7218543437193
1422136021340.583615628719.4163843712995
1432153021352.7051098892177.294890110847
1442138021542.0768984047-162.076898404699
1452163021374.3678747707255.632125229251
1462214521652.2990320908492.700967909233
1472231522221.133065016293.8669349837728
1482234022401.3892569007-61.3892569006712
1492244022419.681676659320.3183233407144
1502213522521.9017195635-386.901719563513
1512195522174.6276400173-219.627640017283
1522206021970.630444204689.3695557954306
1532205022085.3952385171-35.3952385171142
1542203522071.5278451896-36.5278451896338
1552228022052.5366997511227.463300248906
1562231522322.3900440563-7.39004405625383
1572220522356.5825849665-151.582584966549
1582197022230.0202025043-260.020202504336
1592207521966.6095902778108.390409722193
1602211522083.452661970131.5473380299445
1612210522126.899621779-21.8996217790082
1622188522114.5068013124-229.506801312447
1632180521869.4301777554-64.4301777553628
1642191021782.3903370881127.609662911877
1652199521901.333363877793.666636122307
1662224521996.5676704885248.432329511499
1672210022273.7121558412-173.712155841196
1682213022109.731827962420.2681720375804
1692230022141.9463911800158.053608819973
1702291522329.2158177397585.784182260271
1712304023008.220410807331.7795891927308
1722288023136.6927470972-256.692747097208
1732300022948.645702948751.3542970512899
1742316023074.256832413485.7431675865882
1752302023243.6253963247-223.625396324656
1762277023079.1913932826-309.191393282614
1772266022795.4081845407-135.408184540651
1782274022670.613067137369.3869328626533
1792290522758.1944982114146.805501788596
1802272022939.2349217780-219.234921777981
1812270522730.2806355758-25.2806355757639
1822273522712.518395075722.4816049242654
1832260022744.9748048223-144.97480482229
1842251022594.1344088732-84.1344088732367
1852256022494.941622919065.0583770810226
1862257522552.050102589122.9498974108537
1872268522569.5576794224115.442320577597
1882298022692.1712647241287.828735275871
1892327523018.6203233235256.379676676519
1902384523341.6331604287503.366839571303
1912364023966.6325795085-326.632579508503
1922364023725.9436927697-85.9436927697461
1932383523716.5532188563118.446781143743
1942362523924.4950808198-299.495080819845
1952405523681.7713211928373.228678807191
1962400524152.5514419807-147.551441980668
1972432524086.4295146796238.570485320375
1982444524432.496464408312.5035355916589
1992467024553.8626394122116.137360587818
2002461524791.5521669369-176.552166936945
2012470024717.2615306545-17.2615306545013
2022506524800.3754823816264.624517618435
2032518525194.2891763303-9.28917633026504
2042522025313.2742121695-93.2742121694755
2052523525338.0827830145-103.082783014514
2062497525341.8196390463-366.819639046276
2072505525041.739789782113.2602102179153
2082552025123.1886413979396.811358602099
2092588025631.5454787811248.454521218904
2102596026018.6923888684-58.692388868436
2112574026092.2794767765-352.279476776494
2122496525833.7883306514-868.788330651438
2132523524963.8618282822271.138171717768
2142489525263.4872242410-368.487224241049
2152463524883.2251694564-248.225169456415
2162483524596.1033190526238.896680947393
2172463524822.2059099253-187.205909925284
2182469524601.751212704993.2487872950733
2192509024671.9398638594418.06013614059
2202522025112.6184084527107.381591547266
2212474025254.3512535484-514.351253548357
2222500524718.1516433948286.848356605191
2232465025014.4935827858-364.49358278581
2242446024619.667885629-159.66788562902
2252468024412.2220781881267.777921811885
2262484024661.4803228405178.519677159544
2272463024840.9859353803-210.985935380311
2282449024607.9329589669-117.932958966907
2292469524455.0472388049239.952761195087


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
23024686.265220274624140.815003532725231.7154370165
23124677.530440549223862.914718723725492.1461623746
23224668.795660823723617.438324432825720.1529972146
23324660.060881098323383.393302816625936.7284593801
23424651.326101372923153.231949764926149.4202529809
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/1jike1275664923.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/1jike1275664923.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/2jike1275664923.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/2jike1275664923.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/3u92h1275664923.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Jun/04/t1275664964mm1eiybwp9tma08/3u92h1275664923.ps (open in new window)


 
Parameters (Session):
par1 = 5 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 5 ; par2 = Double ; par3 = multiplicative ;
 
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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