Home » date » 2010 » May » 31 »

Paper - Aantal liter rode wijn in Australië - Sander Wetters

*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 17:01:33 +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/t1275325481n0rwu902g2ccbsv.htm/, Retrieved Mon, 31 May 2010 19:04:42 +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/t1275325481n0rwu902g2ccbsv.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 «
464 675 703 887 1139 1077 1318 1260 1120 963 996 960 530 883 894 1045 1199 1287 1565 1577 1076 918 1008 1063 544 635 804 980 1018 1064 1404 1286 1104 999 996 1015 615 722 832 977 1270 1437 1520 1708 1151 934 1159 1209 699 830 996 1124 1458 1270 1753 2258 1208 1241 1265 1828 809 997 1164 1205 1538 1513 1378 2083 1357 1536 1526 1376 779 1005 1193 1522 1539 1546 2116 2326 1596 1356 1553 1613 814 1150 1225 1691 1759 1754 2100 2062 2012 1897 1964 2186 966 1549 1538 1612 2078 2137 2907 2249 1883 1739 1828 1868 1138 1430 1809 1763 2200 2067 2503 2141 2103 1972 2181 2344 970 1199 1718 1683 2025 2051 2439 2353 2230 1852 2147 2286 1007 1665 1642 1518 1831 2207 2822 2393 2306 1785 2047 2171 1212 1335 2011 1860 1954 2152 2835 2224 2182 1992 2389 2724 891 1247 2017 2257 2255 2255 3057 3330 1896 2096 2374 2535 1041 1728 2201 2455 2204 2660 3670 2665 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
alpha0.128930926063041
beta0
gamma0.318961787795898


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13530488.83695900046341.163040999537
14883814.75523893239868.2447610676024
15894834.61852403814659.3814759618537
161045999.13603200943145.8639679905687
1711991167.5174428106331.482557189365
1812871265.7678925140121.2321074859897
1915651471.5441169062193.4558830937872
2015771416.67395034437160.326049655626
2110761269.32628721627-193.326287216273
229181065.59758763115-147.59758763115
2310081084.10736657534-76.1073665753393
2410631034.9518793466728.0481206533341
25544581.982552876673-37.9825528766735
26635950.01704297119-315.01704297119
27804917.750504008931-113.750504008931
289801063.42543153308-83.425431533082
2910181216.09603740949-198.096037409493
3010641282.55780969-218.557809689996
3114041474.02347356886-70.0234735688623
3212861417.91458147564-131.914581475643
3311041148.84690724577-44.8469072457665
34999983.31927443459815.6807255654018
359961041.62335100716-45.6233510071593
3610151025.66177783381-10.661777833812
37615559.4112478402855.58875215972
38722858.653333515284-136.653333515284
39832906.056318391444-74.0563183914444
409771069.55862086222-92.558620862217
4112701191.2360260260578.7639739739534
4214371290.50915889254146.490841107455
4315201593.93855847725-73.9385584772474
4417081512.02680738276195.973192617235
4511511278.88506606663-127.88506606663
469341101.55325635511-167.553256355113
4711591121.7000205159537.2999794840518
4812091125.0045063484283.9954936515812
49699638.41288507032560.5871149296751
50830909.400985151323-79.4009851513226
51996990.0938507714375.90614922856298
5211241179.04487730169-55.044877301686
5314581375.8299184303282.1700815696847
5412701506.27911116514-236.279111165137
5517531718.3139041886134.6860958113941
5622581723.10131469528534.898685304722
5712081397.79915781359-189.799157813591
5812411178.6847664400162.3152335599891
5912651298.32903611964-33.3290361196446
6018281305.30176605924522.698233940756
61809774.56118204674334.4388179532569
629971040.77010167047-43.7701016704652
6311641168.750736122-4.75073612200322
6412051367.69835490318-162.698354903181
6515381626.18580375516-88.1858037551608
6615131647.32610180476-134.326101804765
6713781994.84739817591-616.847398175911
6820832061.2178209406321.7821790593721
6913571428.82192211009-71.8219221100858
7015361284.72546884146251.274531158537
7115261409.0793621541116.920637845899
7213761598.65940088833-222.659400888332
73779810.737142731786-31.7371427317856
7410051051.93266238054-46.9326623805407
7511931193.37607240146-0.376072401463716
7615221351.58581532865170.414184671352
7715391689.45800268104-150.458002681037
7815461689.68549575823-143.685495758233
7921161905.13461397818210.865386021819
8023262288.7565481025937.2434518974096
8115961559.5920370507736.4079629492337
8213561510.71249582127-154.712495821273
8315531548.271436262074.72856373793252
8416131632.16622149011-19.1662214901114
85814866.034135880248-52.0341358802476
8611501118.2730043574531.7269956425484
8712251295.90142116044-70.9014211604399
8816911506.94089288937184.059107110631
8917591773.46513372944-14.4651337294404
9017541793.43097722-39.4309772200031
9121002150.52505344622-50.5250534462157
9220622474.58202317733-412.582023177332
9320121649.1346153853362.865384614701
9418971579.57425173296317.425748267038
9519641733.10680944282230.893190557183
9621861848.4195148665337.580485133498
97966990.716000674304-24.7160006743045
9815491316.0008105535232.999189446502
9915381516.7255264078221.2744735921835
10016121865.30779150914-253.30779150914
10120782048.0874998808829.912500119121
10221372067.2207979543669.7792020456363
10329072493.16925096452413.830749035475
10422492815.31344148215-566.313441482155
10518832074.76570147992-191.765701479922
10617391898.77284610268-159.772846102682
10718281973.17415285425-145.174152854252
10818682074.50887478497-206.508874784973
10911381014.42752648855123.572473511447
11014301448.76169452103-18.761694521033
11118091560.78133262785248.218667372154
11217631872.46637985904-109.466379859042
11322002167.8289886827532.1710113172498
11420672198.99757413638-131.997574136377
11525032712.5061091222-209.506109122202
11621412677.56580949326-536.565809493257
11721032039.0539358569663.9460641430376
11819721900.5402223616271.4597776383785
11921812012.03876025337168.961239746629
12023442141.73511193064202.26488806936
1219701141.04354334108-171.043543341078
12211991516.72816114098-317.728161140977
12317181667.2649051732250.7350948267826
12416831855.10955042205-172.109550422053
12520252182.6473164392-157.647316439195
12620512143.70912748381-92.7091274838067
12724392637.04671442342-198.046714423421
12823532509.46343944918-156.463439449184
12922302081.6786838611148.321316138897
13018521953.3393933984-101.339393398398
13121472069.793257034177.2067429658987
13222862196.1855440394289.8144559605767
13310071084.64792832793-77.6479283279318
13416651430.19404726692234.805952733082
13516421769.23922025064-127.239220250645
13615181875.82278453686-357.82278453686
13718312191.54539780047-360.545397800471
13822072144.185288992162.8147110079021
13928222637.89742440654184.102575593462
14023932566.47025484257-173.470254842569
14123062207.317854147698.6821458523982
14217851994.72252902757-209.722529027573
14320472151.5657479414-104.565747941396
14421712259.77921774681-88.7792177468114
14512121070.26508143284141.734918567159
14613351544.13335047299-209.133350472994
14720111723.90986670662287.090133293384
14818601818.5252811856541.4747188143513
14919542201.59379662451-247.593796624513
15021522292.73539533376-140.735395333763
15128352817.7963195002117.2036804997865
15222242616.82823281662-392.828232816615
15321822297.14668489139-115.146684891395
15419921965.4977454508326.5022545491749
15523892188.10276913206200.897230867938
15627242345.61843415765378.381565842351
1578911193.66533165031-302.665331650305
15812471519.99089775424-272.990897754237
15920171833.6017823691183.398217630903
16022571846.38991421296410.610085787036
16122552205.6598829930749.3401170069328
16222552371.89557184747-116.895571847472
16330572974.9589710768282.0410289231831
16433302647.35367654447682.646323455534
16518962520.14220101209-624.142201012089
16620962137.97226036437-41.9722603643736
16723742419.71801410653-45.7180141065269
16825352603.13644850773-68.1364485077324
16910411148.50094503261-107.500945032608
17017281528.24102368982199.75897631018
17122012076.81793642793124.182063572066
17224552145.67557931211309.324420687888
17322042408.11543436068-204.115434360685
17426602502.4100837042157.589916295803
17536703252.23288577993417.767114220065
17626653109.72008884198-444.720088841978
17726392442.44363392995196.556366070055
17822262314.42316529854-88.4231652985432
17925862612.65435638818-26.6543563881764
18026842806.99681258428-122.996812584276
18111851211.47427616189-26.4742761618943
18217491730.0709769897818.929023010221
18324592271.62383173616187.37616826384
18426182405.78894534092212.211054659084
18525852517.2877721545867.7122278454153
18633102764.81400431411545.185995685893
18739233717.0807290368205.919270963203


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1883262.851771364683097.721529041743427.98201368762
1892779.903028373292608.905649841752950.90040690483
1902522.426002142672346.03073013672698.82127414863
1912882.932062192462693.719101965713072.14502241921
1923070.847781003572870.962648679823270.73291332731
1931340.563108470271166.828380260631514.2978366799
1941936.536834646321739.119310279852133.95435901279
1952587.659677581382357.764237526132817.55511763663
1962714.660208545362473.435654124752955.88476296597
1972761.519808001632512.879398273643010.16021772961
1983159.455099884382884.328342920713434.58185684806
1993991.417302306393706.135974595574276.69863001721
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/1lq751275325289.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/1lq751275325289.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/2wz6q1275325289.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/2wz6q1275325289.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/3wz6q1275325289.png (open in new window)
http://www.freestatistics.org/blog/date/2010/May/31/t1275325481n0rwu902g2ccbsv/3wz6q1275325289.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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