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Exp smoothing megaliters bier

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 06 Jun 2010 22:35:04 +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/Jun/07/t1275863782120dki9vk140wgp.htm/, Retrieved Mon, 07 Jun 2010 00:36:26 +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/Jun/07/t1275863782120dki9vk140wgp.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 «

93.2 96 95.2 77.1 70.9 64.8 70.1 77.3 79.5 100.6 100.7 107.1 95.9 82.8 83.3 80 80.4 67.5 75.7 71.1 89.3 101.1 105.2 114.1 96.3 84.4 91.2 81.9 80.5 70.4 74.8 75.9 86.3 98.7 100.9 113.8 89.8 84.4 87.2 85.6 72 69.2 77.5 78.1 94.3 97.7 100.2 116.4 97.1 93 96 80.5 76.1 69.9 73.6 92.6 94.2 93.5 108.5 109.4 105.1 92.5 97.1 81.4 79.1 72.1 78.7 87.1 91.4 109.9 116.3 113 100 84.8 94.3 87.1 90.3 72.4 84.9 92.7 92.2 114.9 112.5 118.3 106 91.2 96.6 96.3 88.2 70.2 86.5 88.2 102.8 119.1 119.2 125.1

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	0.0248177025009365
beta	0.0705169005484752
gamma	0.299825872359443

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
13	95.9	95.2328359670504	0.667164032949628
14	82.8	82.3847205438318	0.415279456168221
15	83.3	82.8713514061823	0.428648593817712
16	80	79.3212715048232	0.67872849517677
17	80.4	79.6630333224667	0.736966677533331
18	67.5	66.6294218811812	0.870578118818798
19	75.7	69.9322976840816	5.76770231591844
20	71.1	77.7982686267752	-6.69826862677525
21	89.3	80.9518002633341	8.34819973666589
22	101.1	103.332512310900	-2.23251231089969
23	105.2	102.921554553268	2.27844544673231
24	114.1	109.055953563378	5.04404643662184
25	96.3	97.741984652808	-1.44198465280812
26	84.4	84.4835199637877	-0.0835199637877224
27	91.2	84.9945423494998	6.20545765050016
28	81.9	81.6008674592424	0.299132540757626
29	80.5	81.9883718385475	-1.48837183854752
30	70.4	68.6250953938502	1.77490460614980
31	74.8	73.5272089911712	1.27279100882878
32	75.9	77.751492159424	-1.85149215942394
33	86.3	85.6532403509324	0.646759649067619
34	98.7	105.237888480149	-6.53788848014867
35	100.9	106.071178136997	-5.1711781369971
36	113.8	112.976761834812	0.82323816518823
37	89.8	99.3696110725818	-9.56961107258182
38	84.4	86.0426835940844	-1.64268359408436
39	87.2	88.3698923658617	-1.16989236586168
40	85.6	82.948410455516	2.65158954448397
41	72	82.8390669991697	-10.8390669991697
42	69.2	69.9986789971331	-0.798678997133095
43	77.5	74.6976610443087	2.80233895569133
44	78.1	78.0378598074117	0.0621401925883163
45	94.3	86.7693500645555	7.53064993544446
46	97.7	104.602732780584	-6.90273278058403
47	100.2	105.79895602503	-5.59895602502995
48	116.4	114.502804234035	1.89719576596470
49	97.1	97.6451719437032	-0.545171943703224
50	93	86.6939365495615	6.30606345043854
51	96	89.3882846741228	6.61171532587724
52	80.5	85.2070359491507	-4.70703594915069
53	76.1	80.88964954136	-4.7896495413600
54	69.9	70.9717658399781	-1.07176583997810
55	73.6	76.8181494442719	-3.21814944427189
56	92.6	79.2374283016898	13.3625716983101
57	94.2	90.7061596787905	3.49384032120948
58	93.5	104.472917853241	-10.9729178532409
59	108.5	105.981558475044	2.51844152495588
60	109.4	117.312514017756	-7.91251401775617
61	105.1	99.1917323949438	5.90826760505617
62	92.5	90.2416107285618	2.25838927143825
63	97.1	92.9736903307956	4.12630966920439
64	81.4	85.286514512536	-3.88651451253594
65	79.1	80.8902705288784	-1.79027052887841
66	72.1	71.9777370463087	0.122262953691290
67	78.7	77.333951361812	1.36604863818798
68	87.1	84.8686297746739	2.23137022532609
69	91.4	93.3148786061067	-1.91487860610665
70	109.9	102.845004740847	7.05499525915283
71	116.3	108.878279392439	7.4217206075613
72	113	117.481029004066	-4.48102900406599
73	100	103.203314309358	-3.20331430935849
74	84.8	92.7650016690649	-7.96500166906486
75	94.3	95.839837380656	-1.53983738065592
76	87.1	85.4910672021026	1.60893279789741
77	90.3	81.7750825983484	8.5249174016516
78	72.4	73.517929041401	-1.11792904140100
79	84.9	79.3348229649414	5.5651770350586
80	92.7	87.4162404329703	5.28375956702973
81	92.2	94.9180146596084	-2.71801465960839
82	114.9	107.358314730579	7.5416852694213
83	112.5	113.677822389135	-1.17782238913462
84	118.3	118.709212124037	-0.409212124036799
85	106	104.612183448303	1.3878165516971
86	91.2	92.6327162683265	-1.43271626832654
87	96.6	97.9209706617054	-1.32097066170536
88	96.3	88.2829992059323	8.01700079406768
89	88.2	86.7361763290643	1.46382367093568
90	70.2	75.2051326429617	-5.00513264296166
91	86.5	83.1039399520739	3.39606004792611
92	88.2	91.2696948551364	-3.06969485513638
93	102.8	96.3486909971822	6.45130900281777
94	119.1	112.442143388516	6.65785661148428
95	119.2	116.307306048254	2.89269395174632
96	125.1	121.840064403980	3.25993559602045

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
97	108.011178298607	105.045621419736	110.976735177477
98	94.8383850297408	91.8648531534986	97.811916905983
99	100.381013993757	97.3938105159789	103.368217471535
100	93.3291780990937	90.333647354055	96.3247088441323
101	89.5825356171052	86.5765474219884	92.588523812222
102	75.7651584804458	72.7598751736234	78.7704417872683
103	86.5722027119559	83.5357245078113	89.6086809161005
104	92.9563554345326	89.8885232993188	96.0241875697463
105	101.151416207819	98.0404853469597	104.262347068678
106	117.606294843281	114.412876470844	120.799713215718
107	120.278326729567	117.041626761403	123.51502669773
108	125.99020071115	108.028689666140	143.951711756160

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/1pyue1275863701.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/1pyue1275863701.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/2h8ch1275863701.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/2h8ch1275863701.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/3h8ch1275863701.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jun/07/t1275863782120dki9vk140wgp/3h8ch1275863701.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')

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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