Home » date » 2009 » Jun » 06 »

Vincent Van Roy, exonential smoothing, eigen gegevens

*Unverified author*

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

Title produced by software: Exponential Smoothing

Date of computation: Sat, 06 Jun 2009 10:50:56 -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/06/t12443071771tw8n2yh49m7qwo.htm/, Retrieved Sat, 06 Jun 2009 18:52:57 +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/06/t12443071771tw8n2yh49m7qwo.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 «

4.73 4.73 4.73 4.73 4.74 4.74 4.74 4.74 4.74 4.76 4.76 4.76 4.76 4.76 4.76 4.77 4.77 4.78 4.78 4.79 4.83 4.84 4.85 4.85 4.86 4.87 4.87 4.9 4.9 4.92 4.92 4.95 4.96 4.95 4.95 4.95 4.96 4.96 4.96 4.96 4.97 4.97 4.97 5.03 5.08 5.1 5.11 5.13 5.13 5.13 5.15 5.15 5.15 5.17 5.17 5.18 5.2 5.22 5.23 5.23 5.26 5.27 5.28 5.31 5.31 5.32 5.33 5.34 5.38 5.39 5.41 5.44 5.44 5.44 5.46 5.47 5.47 5.49 5.49 5.5 5.52 5.59 5.6 5.6

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.0719407104710672
gamma	0

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	4.73	4.73	0
4	4.73	4.73	0
5	4.74	4.73	0.00999999999999979
6	4.74	4.74071940710471	-0.000719407104710967
7	4.74	4.74066765244648	-0.000667652446479927
8	4.74	4.74061962105513	-0.000619621055132136
9	4.74	4.7405750450762	-0.000575045076203651
10	4.76	4.74053367592487	0.0194663240751316
11	4.76	4.76193409710909	-0.00193409710909354
12	4.76	4.76179495678895	-0.00179495678894526
13	4.76	4.76166582632228	-0.00166582632228351
14	4.76	4.76154598559314	-0.00154598559313701
15	4.76	4.76143476629119	-0.00143476629118844
16	4.77	4.76133154818484	0.00866845181515874
17	4.77	4.77195516276711	-0.00195516276710705
18	4.78	4.77181450696856	0.00818549303144511
19	4.78	4.78240337715279	-0.00240337715279360
20	4.79	4.78223047649289	0.00776952350710847
21	4.83	4.79278942153401	0.0372105784659853
22	4.84	4.8354663769859	0.00453362301410287
23	4.85	4.84579252904654	0.0042074709534603
24	4.85	4.85609521749622	-0.00609521749621766
25	4.86	4.85565672321906	0.00434327678093638
26	4.87	4.86596918163646	0.00403081836354247
27	4.87	4.87625916157331	-0.0062591615733103
28	4.9	4.87580887304277	0.0241911269572270
29	4.9	4.90754919990317	-0.00754919990317227
30	4.92	4.90700610509865	0.0129938949013502
31	4.92	4.92794089512964	-0.00794089512963936
32	4.95	4.92736962149224	0.0226303785077633
33	4.96	4.95899766700031	0.00100233299968533
34	4.95	4.96906977554844	-0.0190697755484397
35	4.95	4.95769788234696	-0.007697882346962
36	4.95	4.9571440912218	-0.00714409122179838
37	4.96	4.95663014022363	0.00336985977636761
38	4.96	4.96687257033013	-0.006872570330132
39	4.96	4.96637815273782	-0.0063781527378195
40	4.96	4.96591930389837	-0.00591930389836826
41	4.97	4.96549346497043	0.00450653502957454
42	4.97	4.97581766830222	-0.00581766830221575
43	4.97	4.97539914111127	-0.00539914111126905
44	5.03	4.97501072306379	0.054989276936209
45	5.08	5.03896669071487	0.0410333092851278
46	5.1	5.09191865613782	0.00808134386217585
47	5.11	5.11250003375683	-0.00250003375682883
48	5.13	5.12232017955216	0.0076798204478381
49	5.13	5.14287267129147	-0.0128726712914693
50	5.13	5.1419466021731	-0.0119466021731007
51	5.15	5.14108715512505	0.00891284487494826
52	5.15	5.16172835151767	-0.0117283515176743
53	5.15	5.16088460557684	-0.0108846055768383
54	5.17	5.16010155931844	0.00989844068155588
55	5.17	5.18081366017363	-0.0108136601736302
56	5.18	5.18003571777795	-3.57177779468643e-05
57	5.2	5.19003314821562	0.00996685178437584
58	5.22	5.21075017061415	0.00924982938584673
59	5.23	5.23141560991191	-0.00141560991190559
60	5.23	5.24131376992909	-0.0113137699290942
61	5.26	5.24049984928229	0.0195001507177102
62	5.27	5.27190270397921	-0.00190270397921388
63	5.28	5.28176582210313	-0.00176582210313203
64	5.31	5.29163878760647	0.0183612123935308
65	5.31	5.32295970627117	-0.0129597062711690
66	5.32	5.32202737579452	-0.00202737579452439
67	5.33	5.33188152493948	-0.00188152493947502
68	5.34	5.34174616669856	-0.00174616669856054
69	5.38	5.35162054622566	0.0283794537743356
70	5.39	5.39366218429297	-0.00366218429297138
71	5.41	5.40339872415306	0.00660127584694159
72	5.44	5.4238736246275	0.0161263753724974
73	5.44	5.45503376752912	-0.0150337675291237
74	5.44	5.45395222761202	-0.0139522276120214
75	5.46	5.45294849444496	0.00705150555504108
76	5.47	5.47345578476448	-0.00345578476447983
77	5.47	5.48320717315329	-0.0132071731532877
78	5.49	5.48225703973333	0.00774296026667454
79	5.49	5.50281407379606	-0.0128140737960596
80	5.5	5.50189222022314	-0.00189222022314262
81	5.52	5.51175609255592	0.00824390744407832
82	5.59	5.53234916511451	0.0576508348854938
83	5.6	5.60649660713542	-0.00649660713541955
84	5.6	5.61602923660245	-0.0160292366024457

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	5.61487608193296	5.58697821091768	5.64277395294823
86	5.62975216386591	5.58885482802714	5.67064949970468
87	5.64462824579887	5.59275379492313	5.69650269667461
88	5.65950432773183	5.5975249200941	5.72148373536955
89	5.67438040966478	5.60274164173718	5.74601917759238
90	5.68925649159774	5.60819470658204	5.77031827661344
91	5.7041325735307	5.61376552882163	5.79449961823976
92	5.71900865546365	5.61938065514332	5.81863665578398
93	5.73388473739661	5.6249917804887	5.84277769430452
94	5.74876081932957	5.63056576166005	5.86695587699908
95	5.76363690126252	5.6360791446698	5.89119465785525
96	5.77851298319548	5.64151495061237	5.91551101577859

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/1mo291244307051.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/1mo291244307051.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/2yytp1244307051.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/2yytp1244307051.ps (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/35wpl1244307051.png (open in new window)

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2009/Jun/06/t12443071771tw8n2yh49m7qwo/35wpl1244307051.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = multiplicative ;

Parameters (R input):

par1 = 12 ; par2 = Double ; 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=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')

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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