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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: Mon, 29 Nov 2010 19:15:15 +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/29/t1291058039h9bgcv47gl9u7jj.htm/, Retrieved Mon, 29 Nov 2010 20:13:59 +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/29/t1291058039h9bgcv47gl9u7jj.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 time21 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
220559150865473
33938320558.638196600518824.3618033995
46803239381.755578641828650.2444213582
54234668030.1060193993-25684.1060193993
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104803324376.581723808823656.4182761912
116141048031.436146071313378.5638539287
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142248137914.1801000326-15433.1801000326
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173404321920.678743858412122.3212561416
183615234042.19863017722109.80136982277
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11344955566802.7370281443-17247.7370281443
11353089249556.1401954851-18664.1401954851
11364010330893.23382959469209.76617040543
11375943440102.391170343719331.6088296563
11386760459432.72204608228171.27795391777
11397019467603.45982164412590.54017835589
11406376070193.8287472605-6433.82874726054
11415310663760.4253208683-10654.4253208683
11423431053106.7043316829-18796.7043316829
11434488334311.242593006810571.7574069932
11446805844882.301133241723175.6988667583
11457433368056.46792497076276.53207502929
11467115674332.5850775367-3176.58507753669
11476733771156.209994387-3819.20999438695
11485227967337.2524763675-15058.2524763675
11493772752279.9954553145-14552.9954553145
11504325437727.96205430815526.03794569188
11517449343253.634690423131239.3653095769
11527799174490.93486048483500.06513951518
11536869977990.7686213291-9291.76862132909
11546648368699.6142505891-2216.61425058915
11556231866483.1465336326-4165.14653363259
11563588562318.2753451809-26433.2753451809
11574990235886.747423511614015.2525764884
11587823149901.073494239628329.9265057604
11596704478229.1271946434-11185.1271946434
11607147667044.73941477124431.26058522883
11616811271475.7070628278-3363.70706282776
11625249268112.2223644528-15620.2223644528
11634149252493.0326054362-11001.0326054362
11644680541492.72724483735312.27275516272
11656984746804.648821790323042.3511782097
11667347869845.47674018123632.5232598188
11677863273477.75986492525154.24013507475
11687481378631.6592688466-3818.65926884659
11696018274813.2524399607-14631.2524399607
11704130560182.9672276396-18877.9672276396
11713911641306.2479650499-2190.24796504992
11727201039116.144790637632893.8552093624
11737924672007.8254871857238.17451281504
11747169079245.5215062772-7555.52150627722
11756942071690.4994725682-2270.49947256820
11765793969420.1500958209-11481.1500958209
11774629857939.7589839457-11641.7589839457
11786042246298.769601311214123.2303986888
11798103560421.066356153920613.9336438461
11808263781033.63727548531603.36272451471
11817972682636.8940065623-2910.89400656233
11828634879726.19243035766621.8075696424
11836629686347.5622524229-20051.5622524229
11843369566297.3255478509-32602.3255478509
11855219933697.15524067518501.8447593250
11867251752197.776899263620319.2231007364
11877227772515.6567579038-238.65675790378
11887307872277.015776873800.984223126929
11897676373077.94704936693685.05295063308
11906565576762.756392347-11107.7563923470
11913465765655.7343000225-30998.7343000225
11925641734659.049232130321757.9507678697
11936869956415.561647989512283.4383520105
11947716368698.18797921568464.8120207844
11957970077162.44041699892537.55958300112
11967815179699.8322496467-1548.83224964672
11975978178151.1023885937-18370.1023885937
11984482959782.2143916486-14953.2143916486
11994699244829.98851156592162.01148843412
12007703046991.857075990130038.1429240099
12019259677028.014269646615567.9857303534
12028493392594.970847769-7661.970847769
12038391884933.5065096107-1015.50650961071
12046330683918.0671320496-20612.0671320496
12054728663307.3626011253-16021.3626011253
12067740347287.059123598330115.9408764017
120710276877401.009126660425366.9908733396
1208118361102766.32306531515594.6769346853
1209107708118359.969083295-10651.9690832946
121094705107708.704169309-13003.7041693085
12117612294705.859635369-18583.8596353689
12124541776123.2285224907-30706.2285224907
12137980645419.029895462234386.9701045378
121410634679803.726781896326542.2732181037
121595826106344.245370970-10518.2453709702
12169379795826.6953292402-2029.69532924023
12179935193797.13417699075553.86582300931
12188383899350.6328508067-15512.6328508067
12195417483839.0254930203-29665.0254930203
12208455954175.961064693830383.0389353062
122111649284556.991469619331935.0085303807
1222114543116489.888873625-1946.88887362531
1223123407114543.1287029088863.87129709247
1224114677123406.414036403-8729.41403640274
1225110378114677.577075036-4299.57707503633
122696040110378.284231976-14338.2842319755
122714185796040.947860401645816.0521395984
1228233465141853.97124001291611.028759988
1229146022233458.943873262-87436.9438732624
1230142124146027.780190669-3903.78019066935
1231118067142124.258067046-24057.2580670462
123283010118068.590352229-35058.5903522293
12337569583012.3176168775-7317.31761687747
123410415775695.483725632928461.5162743671
1235150161104155.11849564446005.8815043564
1236174832150157.95869096924674.0413090306
1237139935174830.368874105-34895.3688741048
1238108749139937.306826802-31188.3068268015
1239109977108751.0617641941225.93823580597
124078872109976.918956948-31104.9189569484
124112645178874.056251675347576.9437483247
1242161295126447.85483281834847.1451671816


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1243161292.696361121122659.710650799199925.682071443
1244161292.696361121106659.209871352215926.182850891
1245161292.69636112194381.3512307044228204.041491538
1246161292.69636112184030.5557727602238554.836949482
1247161292.69636112174911.2826806912247674.110041551
1248161292.69636112166666.8072473935255918.585474849
1249161292.69636112159085.2154622291263500.177260013
1250161292.69636112152028.4322450283270556.960477214
1251161292.69636112145400.5496299245277184.843092318
1252161292.69636112139131.7372330138283453.655489229
1253161292.69636112133169.2785319318289416.114190311
1254161292.69636112127472.2178932613295113.174828981
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/1a9u31291058090.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/1a9u31291058090.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/2l0bo1291058090.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/2l0bo1291058090.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/3l0bo1291058090.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/29/t1291058039h9bgcv47gl9u7jj/3l0bo1291058090.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Single ; 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

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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