Home » date » 2009 » Jun » 02 »

extraponential smoothing - werkloosheid in australie - Magali van de Wildebergh

*Unverified author*
R Software Module: rwasp_exponentialsmoothing.wasp (opens new window with default values)
Title produced by software: Exponential Smoothing
Date of computation: Tue, 02 Jun 2009 05:41:08 -0600
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g.htm/, Retrieved Tue, 02 Jun 2009 13:44:38 +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/2009/Jun/02/t1243943074uuj09g1du3akh6g.htm/},
    year = {2009},
}
@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 = {2009},
    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 «
428800 424800 403400 398400 393500 380500 398300 387300 370400 372800 444600 449900 458100 424800 420600 400100 393000 387100 377500 400400 391400 363600 431000 441700 448500 415600 408000 416600 409300 387600 394500 407600 378500 359600 435700 433800 427700 413300 379500 379300 353700 378200 380600 394000 374000 375000 437600 443900 488800 463900 440000 453800 451600 453400 461400 509100 540600 555100 677400 694600 750100 733900 709300 720500 693200 687200 686800 720900 653100 624700 690000 717800 736500 699900 675600 635600 632500 594900 604000 620800 578400 571200 627400 657700 674100 672800 615300 609100 607600 566900 572700 589200 534800 543100 591100 624800 665300 642600 608700 594500 563800 596100 597600 633100 591000 584200 655800 670700 699700 712900 652000 635100 603100 610100 602000 597600 585400 567100 620600 646200 644800 645200 644800 593000 569100 518800 538700 554600 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'George Udny Yule' @ 72.249.76.132


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.72210178265567
beta0.166056440303876
gamma0.526285174526362


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13458100456110.2029914531989.79700854671
14424800425004.865593658-204.865593658236
15420600419648.526389863951.473610136658
16400100399870.439322215229.560677785252
17393000394440.250846746-1440.25084674591
18387100388789.921848848-1689.92184884817
19377500401119.167035188-23619.1670351877
20400400369189.43242406931210.5675759307
21391400375198.96186801616201.0381319843
22363600391541.910847728-27941.9108477278
23431000442796.152883703-11796.1528837035
24441700437590.636279074109.3637209296
25448500448400.12247222599.877527774719
26415600413943.5017339761656.49826602405
27408000408657.979521394-657.979521393776
28416600385976.73599748330623.2640025173
29409300404258.7920813315041.20791866921
30387600406038.523504067-18438.5235040669
31394500403844.323886398-9344.32388639846
32407600392731.2064470414868.7935529604
33378500385275.251196561-6775.25119656051
34359600376345.970560008-16745.9705600080
35435700437163.75937287-1463.75937287020
36433800442102.0383933-8302.03839330014
37427700442231.09486336-14531.0948633598
38413300394550.95774593718749.0422540632
39379500400432.925349469-20932.9253494691
40379300364418.37788525214881.6221147476
41353700362436.593457869-8736.59345786914
42378200344025.95852612434174.0414738762
43380600380654.807107233-54.8071072332677
44394000380406.18810249113593.8118975091
45374000369326.4253446174673.57465538307
46375000369041.3131696055958.68683039455
47437600453046.968847030-15446.9688470304
48443900449768.815091445-5868.81509144505
49488800453916.64217551534883.3578244845
50463900455884.1411801628015.8588198385
51440000456023.038716392-16023.0387163921
52453800437191.69831987816608.3016801223
53451600441609.30480959990.69519050024
54453400453849.904905493-449.904905493138
55461400467171.285456483-5771.28545648284
56509100470806.12903795838293.8709620417
57540600485234.6612335355365.3387664703
58555100536797.50256474318302.4974352574
59677400643121.51916659734278.4808334028
60694600699649.133031355-5049.13303135522
61750100732945.38955960617154.6104403938
62733900738651.98810968-4751.98810967989
63709300744994.965640613-35694.9656406129
64720500733311.635511074-12811.6355110742
65693200728570.158091934-35370.1580919340
66687200714142.379235556-26942.3792355565
67686800711992.272405551-25192.2724055512
68720900710156.16281727710743.8371827226
69653100705992.300529198-52892.3005291984
70624700659785.162104691-35085.1621046915
71690000709316.33848042-19316.3384804192
72717800694386.62919098323413.3708090172
73736500727891.4202163168608.57978368353
74699900699606.571721198293.42827880173
75675600681055.900500962-5455.90050096181
76635600674169.553348291-38569.5533482911
77632500624054.8750915118445.12490848894
78594900624278.564665846-29378.5646658456
79604000602112.9019960551887.09800394485
80620800609821.37972191310978.6202780871
81578400581282.922391457-2882.92239145702
82571200564551.5012804886648.49871951155
83627400642288.642367468-14888.6423674682
84657700633100.24726810524599.7527318948
85674100661733.41814321612366.5818567839
86672800631833.67558004140966.3244199587
87615300643576.755006667-28276.7550066673
88609100614396.633292866-5296.63329286571
89607600598202.4051773939397.59482260747
90566900596714.17436561-29814.1743656107
91572700581886.596951374-9186.59695137397
92589200584680.4863628944519.51363710559
93534800550428.162993806-15628.1629938064
94543100525336.6777282217763.3222717802
95591100608732.031598043-17632.0315980432
96624800603791.06146265721008.9385373431
97665300628064.68594100337235.3140589965
98642600623310.05233556319289.9476644371
99608700609678.851893173-978.851893173298
100594500607250.132641147-12750.1326411475
101563800590607.668115761-26807.6681157607
102596100555684.18849262740415.8115073731
103597600601451.424859782-3851.4248597821
104633100617606.9157481115493.0842518904
105591000597152.286469738-6152.28646973835
106584200593743.557929223-9543.55792922259
107655800658926.085284109-3126.08528410888
108670700678532.895361163-7832.89536116295
109699700689316.15877201710383.8412279827
110712900664290.91252842748609.0874715734
111652000674125.83608096-22125.8360809603
112635100657428.628884928-22328.6288849284
113603100633388.374795499-30288.3747954987
114610100606940.6101557973159.38984420313
115602000616020.721919631-14020.7219196314
116597600623132.806191955-25532.8061919553
117585400560438.84690755824961.1530924417
118567100573283.258627779-6183.25862777897
119620600636515.831738768-15915.8317387683
120646200639350.1290610886849.87093891227
121644800658312.089330393-13512.089330393
122645200613668.76026902131531.2397309791
123644800590825.3227159953974.6772840095
124593000628174.787039401-35174.7870394011
125569100591277.792871466-22177.7928714656
126518800574134.72669012-55334.7266901197
127538700530005.6414447028694.35855529818
128554600546102.5620805148497.43791948631
129507900513713.307731813-5813.30773181305
130488400494436.761768649-6036.76176864904
131563300551025.58312157712274.4168784230
132592400575599.848173616800.1518264000
133598100598016.2168856783.7831143303774
134546300570655.82709393-24355.8270939301
135516100504914.85777009111185.1422299088
136518500487372.78701211731127.2129878835
137477400497248.998142214-19848.9981422142
138483400474213.0333526359186.9666473646
139469400491051.242243692-21651.2422436916
140501300486579.59263075414720.4073692461
141457400458709.992601083-1309.99260108336
142446700445311.6451438831388.35485611670
143501900513489.60504465-11589.6050446497
144550400522181.36705760628218.6329423937
145593700552455.24065663841244.7593433616
146548900558235.510075241-9335.51007524051
147534200517332.44671968816867.5532803118
148550500516285.34249763934214.6575023613
149541800530780.84263637811019.1573636224
150569300547828.13527559521471.8647244048
151587400584046.8559838073353.14401619346
152627700620968.4418001536731.55819984747
153607000602045.6687020954954.3312979046
154629500611376.69158264118123.3084173588
155704600709558.846477612-4958.84647761239
156767700749473.81559026918226.1844097311
157812200793852.07455729818347.9254427025
158824600792370.22680679732229.7731932029
159856300806967.18206141949332.817938581
160812200857446.63846711-45246.6384671098
161764100827188.647590749-63088.6475907486
162801700799383.1487927312316.85120726866
163806000823955.038318916-17955.0383189163
164867200848263.96496347118936.0350365289
165801600841637.486542566-40037.4865425657
166817500818754.242367754-1254.24236775434
167920900895592.82013200925307.1798679914
168959700960407.863986725-707.863986724522
169997700988515.2691239669184.7308760339
170949100978731.829726943-29631.8297269433
171910900940026.88748547-29126.8874854703
172920400899476.87071081720923.1292891834
173914200901784.1373582312415.8626417693
174926300934513.506813203-8213.50681320345
175906400943701.005234177-37301.005234177
176926100952300.30122322-26200.3012232207
177902500891908.085273110591.9147268991
178895300904779.957068015-9479.95706801547
179979900972100.4372345327799.56276546803
18010097001010906.06963403-1206.06963402720
18110438001030478.4754291813321.5245708239
1829798001008879.12468186-29079.1246818635
183921600961587.384701492-39987.3847014921
184923500910152.94910505413347.0508949463
185914500894474.81664208320025.1833579167
186891700919323.719219721-27623.7192197209
187916000897555.393166218444.6068337996
188931700942031.130206948-10331.1302069485
189902400894380.8518895778019.14811042347
190893700898052.621826747-4352.62182674708
191941500967810.854062996-26310.8540629956
192980100972786.1185389227313.8814610776
1931006900993775.06719242613124.9328075737
194949200958948.488004216-9748.48800421564
195883200919453.974778265-36253.9747782646
196849900874397.38526633-24497.3852663293
197839200823712.09144462715487.9085553734
198803900829115.399688619-25215.3996886188
199797900806912.178655593-9012.17865559319
200830800815148.81952631415651.1804736863
201753300779855.79613657-26555.7961365693
202764100743517.23615605620582.7638439441
203807600817825.591507595-10225.5915075951
204853700831018.28299756222681.7170024378
205886200857481.50059417528718.4994058247
206815700825966.799760484-10266.7997604843
207743000777556.395096687-34556.395096687
208753600730983.54017106522616.4598289349
209724800721355.1046867663444.89531323384
210709600711852.917331436-2252.91733143583
211721900711097.94586592710802.0541340732


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
212742122.7240281699575.884474405784669.563581794
213692351.437380277636730.768240965747972.10651959
214688263.759814781619208.319910993757319.199718569
215746916.061654926663926.456031525829905.667278328
216777244.267408808679768.231018893874720.303798722
217790430.902167649677898.155299443902963.649035854
218731252.175360743603090.34315282859414.007568667
219686709.48836395542351.799711872831067.177016029
220677601.742217359516490.797576544838712.686858174
221650276.208513364471865.743247826828686.673778902
222638478.253877957442233.836317312834722.671438603
223642554.726615533427953.876998094857155.576232973
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/1r1j81243942865.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/1r1j81243942865.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/2t9wl1243942865.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/2t9wl1243942865.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/30wsm1243942865.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/02/t1243943074uuj09g1du3akh6g/30wsm1243942865.ps (open in new window)


 
Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
 
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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