Home » date » 2010 » May » 31 »

geboortes new york

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Mon, 31 May 2010 18:02:03 +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/May/31/t12753290381talna6nkphf36q.htm/, Retrieved Mon, 31 May 2010 20:03:59 +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/May/31/t12753290381talna6nkphf36q.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 «
26.663 23.598 26.931 24.740 25.806 24.364 24.477 23.901 23.175 23.227 21.672 21.870 21.439 21.089 23.709 21.669 21.752 20.761 23.479 23.824 23.105 23.110 21.759 22.073 21.937 20.035 23.590 21.672 22.222 22.123 23.950 23.504 22.238 23.142 21.059 21.573 21.548 20.000 22.424 20.615 21.761 22.874 24.104 23.748 23.262 22.907 21.519 22.025 22.604 20.894 24.677 23.673 25.320 23.583 24.671 24.454 24.122 24.252 22.084 22.991 23.287 23.049 25.076 24.037 24.430 24.667 26.451 25.618 25.014 25.110 22.964 23.981 23.798 22.270 24.775 22.646 23.988 24.737 26.276 25.816 25.210 25.199 23.162 24.707 24.364 22.644 25.565 24.062 25.431 24.635 27.009 26.606 26.268 26.462 25.246 25.180 24.657 23.304 26.982 26.199 27.210 26.122 26.706 26.878 26.152 26.379 24.712 25.688 24.990 24.239 26.721 23.475 24.767 26.219 28.361 28.599 27.914 27.784 25.693 26.881 26.217 24.218 27.914 26.975 28.527 27.139 28.982 28.169 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'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.660335318562836
beta0.204922662099265
gammaFALSE


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326.93120.5336.398
424.7422.55858782951392.18141217048609
525.80622.09499740655993.71100259344012
624.36423.14361379216591.22038620783408
724.47722.71272803316661.76427196683342
823.90122.87972642429211.02127357570793
923.17522.69429309820630.480706901793653
1023.22722.21695264385351.01004735614654
1121.67222.225831643249-0.553831643248994
1221.8721.12708289709610.742917102903913
1321.43920.98515295970710.453847040292946
1421.08920.7137533750820.375246624917981
1523.70920.44122865960013.26777134039994
1621.66922.5209273818803-0.85192738188029
1721.75221.7649627065185-0.0129627065184863
1820.76121.5612419540641-0.800241954064106
1923.47920.72936603113682.7496339688632
2023.82422.61367262238781.21032737761217
2123.10523.6452993876586-0.540299387658632
2223.1123.4478134152256-0.337813415225558
2321.75923.3383239572017-1.57932395720174
2422.07322.1953107997344-0.122310799734429
2521.93721.9978640771515-0.0608640771515283
2620.03521.8327568105106-1.79775681051055
2723.5920.27744966221113.31255033778892
2821.67222.5449054106038-0.872905410603835
2922.22221.93043737657220.291562623427755
3022.12322.1243622880064-0.00136228800644034
3123.9522.1246741930931.82532580690701
3223.50423.5782116009096-0.0742116009095852
3322.23823.7673752283907-1.52937522839075
3423.14222.78869142381950.353308576180453
3521.05923.1010191228925-2.04201912289253
3621.57321.55530607015730.0176939298426753
3721.54821.37208859363150.175911406368467
382021.3171516267447-1.31715162674471
3922.42420.09805851529612.32594148470388
4020.61521.5993694395753-0.98436943957526
4121.76120.78156256480910.97943743519087
4222.87421.39306192125851.48093807874148
4324.10422.53611695716711.56788304283285
4423.74823.9487471059544-0.20074710595442
4523.26224.1663236711128-0.904323671112795
4622.90723.796932807655-0.889932807655011
4721.51923.316621104406-1.797621104406
4822.02521.99368085873380.0313191412661631
4922.60421.88269248608510.721307513914937
5020.89422.32493345841-1.43093345841001
5124.67721.15234311919043.52465688080961
5223.67323.7290524667336-0.056052466733604
5325.3223.93370807731371.38629192268633
5423.58325.2783844245591-1.69538442455908
5524.67124.35870556695060.312294433049431
5624.45424.8070269228112-0.353026922811182
5724.12224.7682423080814-0.646242308081412
5824.25224.4483892142491-0.196389214249063
5922.08424.399015075287-2.31501507528695
6022.99122.63737500431430.35362499568572
6123.28722.68578393568710.601216064312904
6223.04922.9790411520410.069958847958965
6325.07622.93095713359182.14504286640821
6424.03724.5433865871555-0.506386587155465
6524.4324.33646047407240.0935395259275573
6624.66724.53834431281470.128655687185283
6726.45124.78082598108471.6701740189153
6825.61826.2672307070104-0.649230707010435
6925.01426.134198186919-1.12019818691905
7025.1125.5385865958361-0.428586595836066
7122.96425.3416752249488-2.3776752249488
7223.98123.53597031856330.445029681436662
7323.79823.6544175359220.143582464077962
7422.2723.5932377536632-1.32323775366318
7524.77522.3844073241692.39059267583096
7622.64623.9514397284824-1.30543972848235
7723.98822.90120233351831.08679766648166
7824.73723.57770671030151.15929328969851
7926.27624.4589553759191.81704462408102
8025.81626.0204187257454-0.204418725745406
8125.2126.2193769645512-1.00937696455125
8225.19925.7502063079399-0.55120630793991
8323.16225.5089939637899-2.34699396378987
8424.70723.76436984797150.942630152028546
8524.36424.31955523774840.0444447622516186
8622.64424.2876512537704-1.64365125377043
8725.56522.91862278910292.64637721089707
8824.06224.7405532390089-0.67855323900891
8925.43124.27509443688181.1559055631182
9024.63525.1774080213587-0.542408021358675
9127.00924.88486777363422.12413222636577
9226.60626.64057085638-0.0345708563799612
9326.26826.966128003516-0.698128003516029
9426.46226.7590458747677-0.297045874767711
9525.24626.7766168852162-1.53061688521619
9625.1825.7724978768615-0.592497876861504
9724.65725.3076765497571-0.650676549757069
9823.30424.7163897546322-1.41238975463215
9926.98223.43099553506573.55100446493428
10026.19925.90361947380660.295380526193387
10127.2126.26641014680730.943589853192744
10226.12227.1849207138986-1.06292071389856
10326.70626.63462953062690.0713704693730755
10426.87826.84300856292330.0349914370767195
10526.15227.0321001951219-0.880100195121909
10626.37926.4978313938928-0.118831393892794
10724.71226.4501752815295-1.73817528152945
10825.68825.09800337575210.589996624247934
10924.9925.3630425763476-0.373042576347583
11024.23924.9416737268806-0.70267372688059
11126.72124.20755361417222.51344638582782
11223.47525.937264912639-2.46226491263898
11324.76724.0481503515110.718849648488966
11426.21924.35691114798051.86208885201953
11528.36125.67256669542392.68843330457612
11628.59927.89767920456560.70132079543442
11727.91428.9055322388762-0.991532238876164
11827.78428.661362791854-0.877362791854043
11925.69328.3738607730715-2.68086077307152
12026.88126.53267750328710.348322496712896
12126.21726.7389051220778-0.521905122077811
12224.21826.2998677232028-2.08186772320277
12327.91424.54901843078853.36498156921155
12426.97526.85025757115280.124742428847195
12528.52727.0287322215361.49826777846395
12627.13928.3169362780652-1.17793627806516
12728.98227.6785526822311.30344731776899
12828.16928.855093769407-0.686093769407005
12928.05628.6250299977794-0.56902999777936
13029.13628.39526775484920.740732245150763
13126.29129.1306219423596-2.83962194235958
13226.98727.1174907781151-0.130490778115142
13326.58926.8756368960123-0.286636896012318
13424.84826.4918871801118-1.64388718011182
13527.54324.98945018030292.55354981969712
13626.89626.60426949420840.29173050579158
13728.87826.76500592364242.1129940763576
13827.3928.4143124511391-1.02431245113907
13928.06527.85333709774080.211662902259246
14028.14128.13716165411110.0038383458888589
14129.04828.28427171187310.763728288126945
14228.48429.0365098702151-0.552509870215065
14326.63428.8448251359239-2.2108251359239
14427.73527.25893255320020.476067446799821
14527.13227.5117103783438-0.379710378343777
14624.92427.1480063565142-2.2240063565142
14728.96325.26550120116633.69749879883373
14826.58927.7935119662539-1.20451196625391
14927.93126.92156013678251.00943986321746
15028.00927.64815394557450.360846054425483
15129.22927.99528720282361.23371279717644
15228.75929.0857483415485-0.326748341548516
15328.40529.1015670524301-0.696567052430147
15427.94528.7789235755717-0.833923575571667
15525.91228.2527341389109-2.3407341389109
15626.61926.41480177594790.204198224052067
15726.07626.2850097637772-0.209009763777161
15825.28625.854079208805-0.568079208805045
15927.6625.10917126178182.55082873821817
16025.95126.7689605924133-0.817960592413257
16126.39826.09353482460310.304465175396924
16225.56526.2004859522873-0.6354859522873
16328.86525.60076167339443.26423832660561
1643028.01787219762551.98212780237454
16529.26129.856576778957-0.595576778957042
16629.01229.9125399215708-0.90053992157075
16726.99229.6452661651048-2.65326616510479
16827.89727.86157156730620.0354284326937844


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
16927.858111066275124.870079915581730.8461422169685
17027.83125591985524.012809677390831.6497021623193
17127.804400773434923.080125977566832.528675569303
17227.777545627014822.079298255849533.4757929981801
17327.750690480594621.015614014839934.4857669463494
17427.723835334174519.893162370679635.5545082976695
17527.696980187754418.715246150690336.6787142248185
17627.670125041334317.484618290159937.8556317925087
17727.643269894914216.203627659126239.0829121307021
17827.61641474849414.874314550685640.3585149463025
17927.589559602073913.498476332596741.6806428715512
18027.562704455653812.077714424126543.0476944871811
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/1l8ap1275328918.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/1l8ap1275328918.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/2ehsa1275328918.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/2ehsa1275328918.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/3ehsa1275328918.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t12753290381talna6nkphf36q/3ehsa1275328918.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; 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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