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Opdracht 10 oefening 1 stap 1

*Unverified author*
R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Tue, 28 Dec 2010 17:30:40 +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/28/t1293557336pxukjp4gpamakkn.htm/, Retrieved Tue, 28 Dec 2010 18:29:00 +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/28/t1293557336pxukjp4gpamakkn.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:
KDGP2W101
 
Dataseries X:
» Textbox « » Textfile « » CSV «
41086 39690 43129 37863 35953 29133 24693 22205 21725 27192 21790 13253 37702 30364 32609 30212 29965 28352 25814 22414 20506 28806 22228 13971 36845 35338 35022 34777 26887 23970 22780 17351 21382 24561 17409 11514 31514 27071 29462 26105 22397 23843 21705 18089 20764 25316 17704 15548 28029 29383 36438 32034 22679 24319 18004 17537 20366 22782 19169 13807 29743 25591 29096 26482 22405 27044 17970 18730 19684 19785 18479 10698
 
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'Gwilym Jenkins' @ 72.249.127.135


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225679028753406
beta0.000941496287007171
gamma0.44344288426729


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.2423306442-2020.24233064415
153260934048.8239474297-1439.82394742974
163021230953.0817784330-741.081778432963
172996530167.1615625252-202.161562525176
182835228194.2876712473157.712328752677
192581422076.54434447423737.45565552585
202241420801.92075326841612.07924673158
212050621128.7820231163-622.782023116251
222880626754.52591915812051.47408084193
232222822076.0673309998151.932669000216
241397113470.8643970094500.135602990642
253684537059.4733194593-214.473319459335
263533829795.48397040945542.51602959057
273502233348.72441949391673.27558050609
283477731163.7441308343613.25586916602
292688731542.0186569771-4655.01865697711
302397028668.3449958553-4698.34499585526
312278022752.225994223627.7740057763876
321735120061.3545527709-2710.35455277087
332138218709.04253007292672.95746992712
342456125498.9960342701-937.996034270062
351740920022.1189854637-2613.11898546367
361151411945.6711210862-431.671121086243
373151431811.142739525-297.142739524981
382707127135.2239715724-64.2239715724318
392946227863.02418044181598.97581955821
402610526585.9480635963-480.94806359629
412239723768.4474504734-1371.44745047344
422384321869.56385517731973.4361448227
432170519509.10820626732195.89179373275
441808916761.28097596461327.71902403538
452076418040.74222789162723.25777210841
462531623196.82850721152119.17149278854
471770418102.3007276653-398.30072766529
481554811461.22353787094086.77646212913
492802933585.8002125528-5556.80021255277
502938327714.04861898441668.95138101564
513643829460.21037802746977.78962197263
523203428524.13301245633509.86698754368
532267925984.1070779228-3305.10707792285
542431924768.3603312268-449.36033122677
551800421738.5190502817-3734.51905028165
561753717326.1475284402210.852471559763
572036618790.72385674411575.27614325586
582278223364.3485694369-582.348569436886
591916917096.14672940772072.85327059235
601380712536.44630626181270.55369373823
612974329375.0615334885367.938466511467
622559127375.1673514991-1784.16735149911
632909629845.1799392567-749.179939256675
642648226329.5061513032152.493848696766
652240521403.18892294951001.81107705046
662704422062.65158253674981.34841746334
671797019291.1739870886-1321.17398708861
681873016843.79259252321886.20740747683
691968419125.9670976015558.03290239846
701978522648.0790967243-2863.07909672429
711847916985.57738857441493.42261142559
721069812280.7803828344-1582.78038283441


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326498.981865147523698.880672307929299.0830579871
7423934.863394321220956.288363425226913.4384252173
7526836.693618632623556.492578445430116.8946588198
7624042.233314810720686.841609159527397.6250204618
7719769.007584475916442.310680406523095.7044885453
7821288.456756203617662.497386317524914.4161260896
7916072.176615049512656.443904701019487.909325398
8015124.888989787211597.600805595118652.1771739793
8116273.780768293412429.524494841420118.0370417455
8218070.926523697613805.659849381622336.1931980137
8315008.434190429511001.710892855319015.1574880036
849842.625886160647798.833920998811886.4178513225
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/1kxpd1293557437.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/1kxpd1293557437.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/2kxpd1293557437.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/2kxpd1293557437.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/3d66y1293557437.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/28/t1293557336pxukjp4gpamakkn/3d66y1293557437.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')
 




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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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