Home » date » 2010 » Dec » 05 »

*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: Sun, 05 Dec 2010 20:53:51 +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/05/t12915823023y8gnszin1vl90j.htm/, Retrieved Sun, 05 Dec 2010 21:51:43 +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/05/t12915823023y8gnszin1vl90j.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 «
112 118 132 129 121 135 148 148 136 119 104 118 115 126 141 135 125 149 170 170 158 133 114 140 145 150 178 163 172 178 199 199 184 162 146 166 171 180 193 181 183 218 230 242 209 191 172 194 196 196 236 235 229 243 264 272 237 211 180 201 204 188 235 227 234 264 302 293 259 229 203 229 242 233 267 269 270 315 364 347 312 274 237 278 284 277 317 313 318 374 413 405 355 306 271 306 315 301 356 348 355 422 465 467 404 347 305 336 340 318 362 348 363 435 491 505 404 359 310 337 360 342 406 396 420 472 548 559 463 407 362 405 417 391 419 461 472 535 622 606 508 461 390 432
 
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'RServer@AstonUniversity' @ vre.aston.ac.uk


Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.247959489735664
beta0.0345337296488464
gamma1


Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13115110.6431623931624.3568376068376
14126122.0731433875883.92685661241249
15141137.4301320536293.56986794637126
16135132.0625039833172.93749601668324
17125123.063226970461.93677302953955
18149147.499062384581.5009376154205
19170160.1313474162149.86865258378592
20170163.5063250513586.4936749486416
21158153.8500500719094.14994992809099
22133138.731495445679-5.73149544567943
23114123.321997399523-9.32199739952262
24140135.6090430410424.39095695895753
25145136.8604638401148.13953615988575
26150149.1778641595620.822135840438222
27178163.74277873872514.2572212612748
28163160.887368307282.11263169271962
29172151.2616671194820.7383328805198
30178180.52345193849-2.52345193848959
31199198.9079414187770.092058581222858
32199197.6941126433431.30588735665711
33184185.317990243194-1.31799024319412
34162161.6946288593080.305371140692131
35146145.4157878514160.584212148584157
36166170.890657487436-4.89065748743587
37171172.999007307477-1.99900730747703
38180177.5519720772142.44802792278551
39193202.890186966571-9.8901869665709
40181184.973617184963-3.97361718496342
41183187.853581322793-4.85358132279288
42218193.06418760533524.9358123946645
43230220.2479488461149.75205115388616
44242222.44849022136719.5515097786325
45209212.885752351814-3.88575235181398
46191190.0870074036020.912992596398055
47172174.414218571941-2.41421857194123
48194195.248286577793-1.24828657779273
49196200.685635881058-4.68563588105766
50196208.144971709426-12.1449717094265
51236220.68911254080815.310887459192
52235213.78992052088921.2100794791108
53229222.787331740536.21266825947043
54243253.774189579802-10.7741895798021
55264261.0081689744292.99183102557083
56272269.1678075187852.83219248121492
57237237.95618678454-0.956186784540108
58211219.640392882199-8.64039288219888
59180199.162435425533-19.1624354255328
60201216.642919355326-15.6429193553259
61204215.725163322482-11.7251633224818
62188215.568185948207-27.5681859482067
63235244.542771479216-9.54277147921556
64227235.31134790509-8.3113479050898
65234224.8512269469889.14877305301204
66264242.95770303988621.0422969601138
67302267.8723192988734.12768070113
68293283.3377797468779.66222025312288
69259250.734646991188.2653530088202
70229228.7694833009120.230516699088298
71203202.4970072961720.502992703827601
72229227.5877912857491.41220871425051
73242234.0786217080037.92137829199709
74233227.2801229710195.71987702898087
75267278.751213081094-11.7512130810941
76269270.565926630949-1.56592663094943
77270275.634536741208-5.63453674120763
78315299.61859526655415.3814047334461
79364333.52063681328530.4793631867149
80347330.20156310420616.7984368957938
81312298.89764756239913.1023524376009
82274272.7109857773551.28901422264516
83237247.536595543642-10.5365955436417
84278271.109952789846.89004721015976
85284284.437307658674-0.437307658673717
86277274.4220833394962.57791666050417
87317312.4597305930074.54026940699339
88313316.597926811577-3.59792681157705
89318318.709630586872-0.709630586872152
90374360.36858449974713.6314155002531
91413405.8248697102657.17513028973542
92405386.8730198830618.1269801169402
93355353.5646406373531.43535936264743
94306315.946740877587-9.94674087758722
95271279.342602124885-8.34260212488476
96306316.83391044474-10.8339104447398
97315320.372592752745-5.37259275274511
98301311.475546446946-10.4755464469458
99356347.7148140007458.28518599925457
100348346.6559937740841.3440062259159
101355352.2021792990662.79782070093381
102422405.58288763546716.4171123645327
103465446.9653795972118.0346204027904
104467439.1263223763727.8736776236295
105404395.9492591677778.0507408322232
106347351.735857721497-4.73585772149704
107305317.998757011001-12.9987570110005
108336352.790665052808-16.7906650528085
109340359.237140476179-19.2371404761794
110318343.223593245562-25.2235932455621
111362389.947459573451-27.9474595734515
112348374.406789879838-26.4067898798385
113363373.650027638871-10.6500276388712
114435433.3081180437231.69188195627703
115491471.49933393927319.5006660607272
116505470.67927294531334.320727054687
117404413.504477870091-9.50447787009125
118359354.4830410564344.51695894356556
119310316.06644840636-6.0664484063596
120337349.025200176065-12.0252001760649
121360354.1538562087525.84614379124764
122342339.4130666563972.58693334360328
123406390.77767404240915.2223259575908
124396387.2629846674868.73701533251392
125420407.53409746256112.4659025374395
126472482.867470544425-10.8674705444247
127548531.89171001552216.1082899844785
128559541.90102173974217.0989782602576
129463447.87539022493815.1246097750625
130407406.0943450300010.905654969998807
131362359.3809078701012.61909212989883
132405390.64423675049214.3557632495077
133417416.6123145742680.387685425732229
134391398.878286514511-7.87828651451065
135419457.871953443464-38.8719534434641
136461436.32533337469524.6746666253051
137472463.7475613898488.25243861015184
138535520.84739366095514.1526063390452
139622596.93557876272425.0644212372756
140606610.560492406652-4.56049240665152
141508510.143721671589-2.14372167158911
142461453.7040688180887.29593118191156
143390410.234924183382-20.2349241833815
144432444.833325554045-12.8333255540447


Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
145453.497721751321428.415266965019478.580176537622
146429.390569251949403.496001603239455.285136900659
147467.036052088741440.301472551842493.770631625639
148503.25740665386475.65579207998530.85902122774
149512.339520167483.844695250901540.8343450831
150571.887965749639542.4745714567601.301360042577
151652.609534991378622.252994696776682.96607528598
152637.462256917306606.138741269286668.785772565325
153539.754768946301507.441160256023572.068377636578
154490.724986086209457.398842867372524.051129305046
155424.459265263961390.098787394923458.819743132999
156469.531518789793434.115513646614504.947523932972
157491.029240541114446.09196301134535.966518070888
158466.922088041742421.090140639751512.754035443733
159504.567570878534457.816174748357551.318967008711
160540.788925443653493.093767563127588.48408332418
161549.871038956794501.208272912143598.533805001444
162609.419484539432559.765728963449659.073240115416
163690.141053781172639.473388773077740.808718789266
164674.993775707099623.289737529118726.69781388508
165577.286287736094524.52386205752630.048713414667
166528.256504876002474.414118810952582.098890941052
167461.990784053754407.04729721448516.934270893028
168507.063037579586450.997732343634563.128342815539
169528.560759330907464.861422671682592.260095990132
170504.453606831535439.708653578642569.198560084428
171542.099089668327476.286957564125607.911221772529
172578.320444233447511.419913345831645.220975121063
173587.402557746587519.3927486333655.412366859874
174646.951003329225577.811374309983716.090632348467
175727.672572570965657.382916219568797.962228922362
176712.525294496892641.065733457534783.98485553625
177614.817806525887542.168788749912687.466824301861
178565.788023665795491.930317157262639.645730174328
179499.522302843547424.436989994278574.607615692816
180544.59455636938468.263027956773620.926084781987
181566.0922781207483.006199790292649.178356451109
182541.985125621329457.700011407708626.270239834949
183579.63060845812494.127415792212665.133801124028
184615.85196302324529.111919746892702.592006299588
185624.93407653638536.938677829201712.92947524356
186684.482522119018595.213527079886773.751517158151
187765.204091360758674.643519290785855.764663430731
188750.056813286686658.186939716822841.92668685655
189652.34932531568559.152677818696745.545972812664
190603.319542455588508.778896278832697.860188632345
191537.053821633341441.152195185495632.955448081186
192582.126075159173484.846725381216679.40542493713
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/1igff1291582425.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/1igff1291582425.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/2igff1291582425.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/2igff1291582425.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/3t7w01291582425.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/05/t12915823023y8gnszin1vl90j/3t7w01291582425.ps (open in new window)


 
Parameters (Session):
par1 = 3 ; par2 = equal ; par3 = 2 ; par4 = no ;
 
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = no ;
 
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, 48, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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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Software written by Ed van Stee & Patrick Wessa


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