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opgave 10 2 nieuw

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R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Thu, 30 Dec 2010 10:47:18 +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/30/t1293705932d9582nd1fku2rhf.htm/, Retrieved Thu, 30 Dec 2010 11:45:32 +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/30/t1293705932d9582nd1fku2rhf.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:
KDGP2W102
 
Dataseries X:
» Textbox « » Textfile « » CSV «
68897 38683 44720 39525 45315 50380 40600 36279 42438 38064 31879 11379 70249 39253 47060 41697 38708 49267 39018 32228 40870 39383 34571 12066 70938 34077 45409 40809 37013 44953 37848 32745 43412 34931 33008 8620 68906 39556 50669 36432 40891 48428 36222 33425 39401 37967 34801 12657 69116 41519 51321 38529 41547 52073 38401 40898 40439 41888 37898 8771 68184 50530 47221 41756 45633 48138 39486 39341 41117 41629 29722 7054 56676 34870 35117 30169 30936 35699 33228 27733 33666 35429 27438 8170
 
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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.277819840158911
beta0.00090316977252793
gamma0.294847015488245


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137024971014.3015814803-765.301581480278
143925339710.8527884234-457.852788423377
154706047635.4527672573-575.452767257251
164169741988.7273060676-291.727306067616
173870838660.95900439947.040995600968
184926748949.3990594912317.600940508848
193901839929.8661094887-911.866109488743
203222835309.4845196682-3081.48451966818
214087040094.9834112898775.016588710161
223938335911.82691986943471.17308013055
233457130958.29521593913612.70478406090
241206611475.7971259764590.202874023604
257093871750.0461991928-812.046199192831
263407740112.0952689126-6035.09526891258
274540946245.4962690537-836.496269053707
284080940737.497619828371.5023801717034
293701337663.1892276532-650.189227653245
304495347491.0277001042-2538.0277001042
313784837852.9863447481-4.98634474810387
323274533202.8648412825-457.864841282499
334341239397.86755429024014.1324457098
343493136666.7510991591-1735.75109915911
353300830494.57525016492513.42474983514
36862011053.1716924139-2433.17169241385
376890663108.16690708725797.83309291278
383955635157.34860501444398.65139498561
395066945108.63906317705560.36093682295
403643241483.5710994757-5051.57109947571
414089136885.73214922524005.26785077483
424842847768.6412092459659.358790754122
433622239253.8308082136-3031.83080821356
443342533597.9757201134-172.975720113449
453940140929.7030661447-1528.70306614474
463796735533.80313151082433.19686848923
473480131361.56075910853439.43924089148
481265710697.12409712171959.87590287834
496911673361.285399745-4245.28539974494
504151939479.78070197932039.21929802069
515132149649.13077428591671.86922571412
523852942297.7842967754-3768.78429677542
534154739893.07788633871653.92211366131
545207349766.34582290272306.65417709729
553840140458.2728678946-2057.27286789462
564089835452.26699055265445.73300944739
574043944796.7423514500-4357.74235144995
584188839108.37272514342779.62727485658
593789834834.47376562543063.52623437461
60877111982.0036238100-3211.00362381003
616818468898.50359516-714.503595159971
625053038461.203550519912068.7964494801
634722151654.8489989598-4433.84899895985
644175641437.4011455228318.598854477248
654563341317.35354507194315.64645492812
664813852495.176788684-4357.17678868401
673948640319.3352204068-833.335220406778
683934137159.28000716522181.71999283475
694111743429.5369687552-2312.53696875516
704162939809.87752936881819.12247063118
712972235333.79127047-5611.79127047003
72705410448.2665921740-3394.26659217402
735667662778.1260751-6102.12607509996
743487036366.7567259867-1496.75672598666
753511741031.6350956609-5914.63509566088
763016933017.9210381851-2848.92103818506
773093632678.4925929045-1742.49259290455
783569938170.4897376950-2471.48973769496
793322829851.66445881013376.33554118988
802773328996.6041595666-1263.60415956665
813366632138.20919937091527.79080062906
823542930918.99466427904510.00533572104
832743826921.1605618068516.83943819315
8481708015.10017403475154.899825965254


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8556360.218750908653154.188989139259566.248512678
8633974.560400165530585.759337986537363.3614623445
8737866.749012910433878.386693890541855.1113319303
8832173.693286875228079.195050532936268.1915232175
8932870.676028858528336.494078958237404.8579787587
9038878.774389914733456.434536758744301.1142430707
9132143.535820000827073.103461564337213.9681784373
9229305.988525659124211.590005776734400.3870455416
9333527.375875992627587.660360142039467.0913918432
9432464.153310638426381.757398531438546.5492227455
9526484.38738174220971.367479901931997.4072835820
967842.951655195856405.071612593449280.83169779825
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/18ks61293706034.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/18ks61293706034.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/2jb991293706034.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/2jb991293706034.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/3jb991293706034.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/30/t1293705932d9582nd1fku2rhf/3jb991293706034.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=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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