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Aantal openstaande VDAB-vacatures: Triple Exponential Smoothing

*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, 27 Dec 2010 18:28:16 +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/27/t1293474378giqx8j1yw3e8udc.htm/, Retrieved Mon, 27 Dec 2010 19:26:22 +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/27/t1293474378giqx8j1yw3e8udc.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 «
27.951 29.781 32.914 33.488 35.652 36.488 35.387 35.676 34.844 32.447 31.068 29.010 29.812 30.951 32.974 32.936 34.012 32.946 31.948 30.599 27.691 25.073 23.406 22.248 22.896 25.317 26.558 26.471 27.543 26.198 24.725 25.005 23.462 20.780 19.815 19.761 21.454 23.899 24.939 23.580 24.562 24.696 23.785 23.812 21.917 19.713 19.282 18.788 21.453 24.482 27.474 27.264 27.349 30.632 29.429 30.084 26.290 24.379 23.335 21.346 21.106 24.514 28.353 30.805 31.348 34.556 33.855 34.787 32.529 29.998 29.257 28.155 30.466 35.704 39.327 39.351 42.234 43.630 43.722 43.121 37.985 37.135 34.646 33.026 35.087 38.846 42.013 43.908 42.868 44.423 44.167 43.636 44.382 42.142 43.452 36.912 42.413 45.344 44.873 47.510 49.554 47.369 45.998 48.140 48.441 44.928 40.454 38.661 37.246 36.843 36.424 37.594 38.144 38.737 34.560 36.080 33.508 35.462 33.374 32.110 35.533 35.532 37.903 36.763 40.399 44.164 44.496 43.110 etc...
 
Output produced by software:


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.94592858766538
beta0.0390410580898643
gamma0.774358779506533


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1329.81230.4108518601392-0.598851860139202
1430.95131.0277203611790-0.0767203611790386
1532.97433.1828321772309-0.208832177230875
1632.93633.249221569499-0.313221569499035
1734.01234.3593559417831-0.347355941783128
1832.94633.2493306419754-0.303330641975421
1931.94831.65535680191760.292643198082377
2030.59931.7001352790484-1.10113527904840
2127.69129.4968068936204-1.80580689362036
2225.07325.4577397593152-0.384739759315206
2323.40623.6621771137398-0.256177113739838
2422.24821.59782796163870.650172038361298
2522.89622.60714867557630.288851324423700
2625.31723.62048087685031.69651912314973
2726.55826.9221072279287-0.36410722792866
2826.47126.6602191539865-0.189219153986528
2927.54327.47894514098190.0640548590181105
3026.19826.7928178426481-0.594817842648137
3124.72525.0794719940671-0.354471994067122
3225.00524.35803847689440.646961523105634
3323.46223.9090564767751-0.447056476775064
3420.7821.5302491452802-0.750249145280151
3519.81519.58431792413240.230682075867612
3619.76118.26562268815291.49537731184706
3721.45420.03942024646131.41457975353869
3823.89922.20994593374191.68905406625807
3924.93925.4276607847813-0.488660784781327
4023.5825.1501356347057-1.57013563470565
4124.56224.5980484598158-0.0360484598158379
4224.69623.90002450067620.795975499323752
4323.78523.67485719581570.110142804184282
4423.81223.56870955402760.24329044597237
4521.91722.8451750415451-0.928175041545053
4619.71320.1933602161703-0.480360216170343
4719.28218.68472408594580.597275914054247
4818.78817.90122600287840.886773997121558
4921.45319.14614626960942.30685373039060
5024.48222.28977160733212.19222839266788
5127.47426.08548054118821.3885194588118
5227.26427.8050665240494-0.54106652404943
5327.34928.7855240097176-1.43652400971756
5430.63226.99310881340423.63889118659579
5529.42929.5911524772775-0.162152477277477
5630.08429.57360491931550.510395080684464
5726.2929.1809859682926-2.89098596829262
5824.37924.6190217369547-0.240021736954745
5923.33523.444077155783-0.109077155783009
6021.34621.9685466339507-0.622546633950737
6121.10622.0727240154377-0.96672401543771
6224.51422.11286160553652.40113839446347
6328.35326.09356926175282.25943073824721
6430.80528.62805531986372.17694468013628
6531.34832.5008305921727-1.15283059217267
6634.55631.33555556805003.22044443194997
6733.85533.41169220475950.443307795240472
6834.78734.20056288908660.586437110913359
6932.52933.7395689877443-1.21056898774427
7029.99830.7127497827325-0.714749782732468
7129.25729.09508643245810.161913567541873
7228.15527.719528695220.435471304779995
7330.46629.3037962070331.16220379296698
7435.70432.37768414883723.32631585116278
7539.32738.4205232333710.906476766628963
7639.35140.1684440499140-0.817444049913959
7742.23441.76848900501560.465510994984413
7843.6342.6391538634730.990846136527011
7943.72242.38900930035291.33299069964707
8043.12144.3427201392084-1.22172013920841
8137.98541.9708497812421-3.9858497812421
8237.13536.07136923631261.06363076368743
8334.64636.0739805912821-1.42798059128206
8433.02632.97923187492460.04676812507536
8535.08734.47566887717950.611331122820509
8638.84637.43757045688021.40842954311976
8742.01341.75500787987060.257992120129366
8843.90842.79929969734381.10870030265615
8942.86846.5348530217785-3.66685302177846
9044.42343.39112112163811.03187887836193
9144.16743.04349329919011.12350670080986
9243.63644.5618201396121-0.925820139612135
9344.38242.20103833733692.18096166266308
9442.14242.09908649920320.0429135007968355
9543.45240.91017559490562.54182440509438
9636.91241.3642332326973-4.45223323269729
9742.41338.82291769154383.59008230845622
9845.34445.23102721237830.112972787621679
9944.87348.8288267624973-3.95582676249727
10047.5145.91717102565381.59282897434619
10149.55450.0413328798024-0.487332879802373
10247.36950.2350603672695-2.86606036726945
10345.99846.0411439298867-0.0431439298867033
10448.1446.27854693588061.86145306411944
10548.44146.52518810006331.91581189993671
10644.92845.8500197481911-0.922019748191069
10740.45443.7143775324225-3.2603775324225
10838.66138.30326069482230.357739305177731
10937.24640.6562035443757-3.41020354437566
11036.84339.6721259494619-2.82912594946193
11136.42439.2988683660116-2.87486836601157
11237.59437.05426299091560.539737009084412
11338.14439.1388326121083-0.994832612108254
11438.73738.17569277228650.561307227713549
11534.5637.2507179739447-2.69071797394471
11636.0834.54685675245391.5331432475461
11733.50834.4595659913753-0.951565991375311
11835.46231.30865905961574.15334094038426
11933.37433.8781803729084-0.50418037290838
12032.1131.40388702837880.706112971621174
12135.53333.40556207888842.12743792111159
12235.53237.5401587191845-2.00815871918453
12337.90337.85930909424760.0436909057523636
12436.76338.6635397739057-1.90053977390566
12540.39938.36870623368442.03029376631564
12644.16440.48262847077933.68137152922071
12744.49642.4127960557422.08320394425800
12843.1144.8981254831121-1.78812548311215
12943.8841.56417136882542.31582863117459
13043.9341.52121164369012.40878835630993
13144.32742.19744920510252.12955079489754


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13242.037050955412338.716787532670145.3573143781545
13344.240579393891439.451622149387349.0295366383954
13446.963449281118740.849536740638353.0773618215991
13550.428521084825942.970717629457157.8863245401946
13651.757330496274343.268769916446260.2458910761025
13754.652162163796844.909523862553664.39480046504
13855.440767307905644.801315406395266.080219209416
13953.665133545620442.61981950065364.7104475905877
14054.263277114000342.369619827568166.1569344004326
14152.64805518003740.389930264528864.9061800955453
14250.1009197997237.722945181607662.4788944178323
14348.297233328126833.421932868157263.1725337880964
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/1pn9r1293474493.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/1pn9r1293474493.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/2hwqu1293474493.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/2hwqu1293474493.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/3hwqu1293474493.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/27/t1293474378giqx8j1yw3e8udc/3hwqu1293474493.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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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