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

Title produced by software: Exponential Smoothing

Date of computation: Tue, 26 Jan 2010 12:49:09 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi.htm/, Retrieved Tue, 26 Jan 2010 20:50:45 +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/Jan/26/t12645354414w4uibgy96cs0xi.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 «

8,82000 8,80000 8,82000 8,58000 8,54000 8,42000 8,43000 8,44000 8,09000 7,69000 7,56000 7,54000 7,40000 7,39000 7,37000 7,31000 7,35000 7,26000 7,37000 7,35000 7,33000 7,32000 7,31000 7,33000 7,32000 7,27000 7,48000 7,70000 7,77000 7,80000 7,84000 7,81000 7,78000 7,82000 7,80000 7,81000 7,80000 7,66000 7,41000 7,35000 7,39000 7,32000 7,32000 7,30000 7,29000 7,26000 7,22000 7,21000 7,21000 7,21000 7,20000 7,19000 7,18000 7,12000 7,12000 7,07000 7,08000 7,05000 7,06000 7,07000 7,08000 7,08000 7,09000 7,07000 7,06000 6,99000 6,99000 6,99000 6,98000 6,96000 6,95000 6,91000 6,91000 6,87000 6,91000 6,89000 6,88000 6,90000 6,91000 6,85000 6,86000 6,82000 6,80000 6,83000 6,84000 6,89000 7,14000 7,21000 7,25000 7,31000 7,30000 7,48000 7,49000 7,40000 7,44000 7,42000 7,14000 7,24000 7,33000 7,61000 7,66000 7,69000 7,70000 7,68000 7,71000 7,71000 7,72000 7,68000 7,72000 7,74000 7,76000 7,90000 7,97000 7,96000 etc...

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.178814212435339
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	8.82	8.78	0.0399999999999991
4	8.58	8.80715256849741	-0.227152568497415
5	8.54	8.52653446085889	0.0134655391411140
6	8.42	8.48894229063542	-0.0689422906354196
7	8.43	8.35661442923196	0.0733855707680409
8	8.44	8.37973681227296	0.0602631877270348
9	8.09	8.40051272672522	-0.310512726725216
10	7.69	7.9949886380447	-0.304988638044698
11	7.56	7.54045233493101	0.0195476650689903
12	7.54	7.41394773526527	0.126052264734731
13	7.4	7.4164876717095	-0.0164876717095011
14	7.39	7.27353944167788	0.116460558322125
15	7.37	7.28436424469403	0.085635755305975
16	7.31	7.27967713483537	0.0303228651646306
17	7.35	7.22509929408856	0.124900705911435
18	7.26	7.28743331544874	-0.0274333154487358
19	7.37	7.19252784875228	0.17747215124772
20	7.35	7.33426239170685	0.0157376082931533
21	7.33	7.3170764997394	0.0129235002605981
22	7.32	7.29938740526041	0.0206125947395908
23	7.31	7.29307323015502	0.0169267698449813
24	7.33	7.28609997717392	0.0439000228260777
25	7.32	7.31394992518146	0.00605007481853903
26	7.27	7.30503176454531	-0.0350317645453142
27	7.48	7.24876758715792	0.231232412842078
28	7.7	7.5001152289498	0.199884771050198
29	7.77	7.75585746686296	0.0141425331370382
30	7.8	7.8283863527877	-0.0283863527877006
31	7.84	7.85331046947006	-0.0133104694700563
32	7.81	7.89093036835462	-0.0809303683546245
33	7.78	7.84645886827519	-0.0664588682751894
34	7.82	7.80457507808522	0.0154249219147822
35	7.8	7.84733327334929	-0.0473332733492873
36	7.81	7.81886941135335	-0.00886941135334762
37	7.8	7.82728343454743	-0.0272834345474333
38	7.66	7.8124047686863	-0.152404768686303
39	7.41	7.64515263000227	-0.235152630002272
40	7.35	7.35310399766632	-0.00310399766631697
41	7.39	7.29254895876821	0.0974510412317864
42	7.32	7.34997458995708	-0.029974589957078
43	7.32	7.27461470726083	0.0453852927391685
44	7.3	7.28273024263813	0.0172697573618663
45	7.29	7.26581832069974	0.0241816793002556
46	7.26	7.26014234863918	-0.000142348639184497
47	7.22	7.23011689467938	-0.0101168946793768
48	7.21	7.18830785012499	0.0216921498750073
49	7.21	7.18218671482092	0.0278132851790787
50	7.21	7.18716012550546	0.0228398744945419
51	7.2	7.19124421967532	0.0087557803246785
52	7.19	7.18280987763834	0.00719012236166439
53	7.18	7.17409557370575	0.00590442629424892
54	7.12	7.16515136904344	-0.0451513690434391
55	7.12	7.09707766254756	0.0229223374524405
56	7.07	7.1011765022663	-0.0311765022662946
57	7.08	7.04560170056706	0.0343982994329410
58	7.05	7.06175260538927	-0.0117526053892751
59	7.06	7.02965107251253	0.0303489274874718
60	7.07	7.04507789207946	0.0249221079205428
61	7.08	7.0595343191795	0.0204656808205019
62	7.08	7.07319387377737	0.00680612622263066
63	7.09	7.0744109058776	0.0155890941223955
64	7.07	7.08719845746568	-0.0171984574656801
65	7.06	7.06412312883885	-0.00412312883885324
66	6.99	7.05338585480276	-0.063385854802763
67	6.99	6.97205156309667	0.0179484369033336
68	6.99	6.97526099870598	0.0147390012940187
69	6.98	6.97789654161445	0.00210345838554549
70	6.96	6.96827266986906	-0.00827266986905695
71	6.95	6.94679339892168	0.00320660107831650
72	6.91	6.9373667847681	-0.0273667847680974
73	6.91	6.8924732147029	0.0175267852970977
74	6.87	6.89560725301233	-0.0256072530123266
75	6.91	6.8510283122323	0.0589716877677056
76	6.89	6.90157328813646	-0.0115732881364599
77	6.88	6.87950381973305	0.000496180266948976
78	6.9	6.86959254381671	0.0304074561832888
79	6.91	6.89502982914629	0.0149701708537116
80	6.85	6.90770670845752	-0.057706708457518
81	6.86	6.83738792883245	0.0226120711675497
82	6.82	6.8514312885298	-0.0314312885298076
83	6.8	6.80581092742552	-0.00581092742552247
84	6.83	6.78477185101441	0.0452281489855917
85	6.84	6.82285928685518	0.0171407131448245
86	6.89	6.83592428997675	0.0540757100232527
87	7.14	6.89559379547644	0.244406204523563
88	7.21	7.18929709845263	0.0207029015473719
89	7.25	7.26299907148795	-0.0129990714879478
90	7.31	7.30067465275744	0.00932534724255962
91	7.3	7.3623421573803	-0.0623421573803036
92	7.48	7.34119449360683	0.138805506393175
93	7.49	7.54601489091421	-0.0560148909142093
94	7.4	7.54599863231073	-0.145998632310733
95	7.44	7.42989200185745	0.0101079981425469
96	7.42	7.47169945558461	-0.0516994555846111
97	7.14	7.44245485815091	-0.302454858150913
98	7.24	7.10837163089341	0.131628369106585
99	7.33	7.23190865404936	0.0980913459506425
100	7.61	7.33944878082224	0.270551219177756
101	7.66	7.66782718400294	-0.00782718400293536
102	7.69	7.71642757225986	-0.0264275722598635
103	7.7	7.74170194673964	-0.0417019467396385
104	7.68	7.74424504597637	-0.06424504597637
105	7.71	7.71275711867723	-0.00275711867723238
106	7.71	7.74226410667237	-0.0322641066723728
107	7.72	7.73649482584782	-0.0164948258478228
108	7.68	7.74354531655459	-0.0635453165545856
109	7.72	7.69218251082092	0.0278174891790766
110	7.74	7.7371566732404	0.0028433267595922
111	7.76	7.75766510047562	0.00233489952437793
112	7.9	7.77808261369519	0.121917386304812
113	7.97	7.93988317510946	0.0301168248905412
114	7.96	8.01526849143331	-0.0552684914333126
115	7.95	7.99538569966518	-0.045385699665176
116	7.97	7.97727009152372	-0.00727009152372116
117	7.93	7.99597009583357	-0.065970095833574
118	7.99	7.94417370510281	0.045826294897191
119	7.96	8.01236809793368	-0.0523680979336811
120	7.92	7.97300393774493	-0.0530039377449327
121	7.97	7.9235260803611	0.046473919638899
122	7.98	7.98183627770011	-0.00183627770011263
123	8	7.99150792514936	0.0084920748506443
124	8.04	8.01302642882571	0.0269735711742847
125	8.17	8.05784968671181	0.112150313288188
126	8.29	8.20790375665682	0.082096243343182
127	8.26	8.34258373175413	-0.0825837317541271
128	8.3	8.29781658680054	0.00218341319945914
129	8.32	8.33820701211222	-0.0182070121122244
130	8.28	8.35495133958058	-0.0749513395805774
131	8.27	8.3015489748225	-0.0315489748225009
132	8.32	8.28590756973647	0.0340924302635273

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
133	8.34200378080405	8.17261936140155	8.51138820020656
134	8.3640075616081	8.10216735651265	8.62584776670356
135	8.38601134241216	8.03752547229325	8.73449721253107
136	8.40801512321621	7.97307584606497	8.84295440036746
137	8.43001890402027	7.90696596245355	8.95307184558698
138	8.45202268482432	7.83841549487378	9.06562987477485
139	8.47402646562837	7.76706454748196	9.18098838377478
140	8.49603024643243	7.69274744604355	9.2993130468213
141	8.51803402723648	7.61539741048462	9.42067064398834
142	8.54003780804053	7.53500112488941	9.54507449119165
143	8.56204158884458	7.45157518124672	9.67250799644244
144	8.58404536964864	7.36515310495042	9.80293763434685

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/1kyih1264535347.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/1kyih1264535347.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/2eni61264535347.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/2eni61264535347.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/3xawb1264535347.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Jan/26/t12645354414w4uibgy96cs0xi/3xawb1264535347.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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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