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Decompositie Loess

*The author of this computation has been verified*

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

Title produced by software: Decomposition by Loess

Date of computation: Fri, 04 Dec 2009 12:24:32 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1.htm/, Retrieved Fri, 04 Dec 2009 20:25:15 +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/2009/Dec/04/t1259954710w2epr5d741btwe1.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 «

7.3 7.6 7.5 7.6 7.9 7.9 8.1 8.2 8 7.5 6.8 6.5 6.6 7.6 8 8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7 7.1 7.2 7.1 6.9 7 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	731	0	74
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	7.3	7.18763782620637	-0.409983371886072	7.8223455456797	-0.112362173793626
2	7.6	7.392994523631	0.0179725289439462	7.78903294742506	-0.207005476369005
3	7.5	7.20802852504988	0.0362511257796950	7.75572034917042	-0.291971474950116
4	7.6	7.47601537864379	0.00546667023471239	7.7185179511215	-0.123984621356211
5	7.9	8.22733551499535	-0.108651068067928	7.68131555307257	0.327335514995354
6	7.9	8.35115213959081	-0.197040223107253	7.64588808351644	0.451152139590811
7	8.1	8.5749689159132	0.0145704701264951	7.61046061396031	0.474968915913196
8	8.2	8.5070876337748	0.309149327901588	7.58376303832361	0.307087633774803
9	8	8.07253961922141	0.370394918091681	7.5570654626869	0.0725396192214127
10	7.5	7.24056712204582	0.220375385620858	7.53905749233332	-0.259432877954179
11	6.8	6.09192775590101	-0.0129772778807477	7.52104952197974	-0.708072244098989
12	6.5	5.73701764597318	-0.245528395303983	7.50851074933081	-0.762982354026824
13	6.6	6.11401139520419	-0.409983371886072	7.49597197668188	-0.485988604795807
14	7.6	7.68483978265982	0.0179725289439462	7.49718768839623	0.0848397826598202
15	8	8.46534547410972	0.0362511257796950	7.49840340011059	0.465345474109716
16	8.1	8.66380655737163	0.00546667023471239	7.53072677239365	0.563806557371635
17	7.7	7.94560092339121	-0.108651068067928	7.56305014467672	0.245600923391212
18	7.5	7.60059888472877	-0.197040223107253	7.59644133837849	0.100598884728766
19	7.6	7.55559699779325	0.0145704701264951	7.62983253208026	-0.0444030022067521
20	7.8	7.66686595053217	0.309149327901588	7.62398472156624	-0.13313404946783
21	7.8	7.61146817085609	0.370394918091681	7.61813691105223	-0.188531829143908
22	7.8	7.78013272949576	0.220375385620858	7.59949188488338	-0.0198672705042355
23	7.5	7.43213041916622	-0.0129772778807477	7.58084685871453	-0.067869580833782
24	7.5	7.65592425991431	-0.245528395303983	7.58960413538968	0.155924259914308
25	7.1	7.01162195982125	-0.409983371886072	7.59836141206482	-0.0883780401787497
26	7.5	7.3552459784757	0.0179725289439462	7.62678149258035	-0.144754021524298
27	7.5	7.30854730112442	0.0362511257796950	7.65520157309588	-0.191452698875578
28	7.6	7.50103060016066	0.00546667023471239	7.69350272960463	-0.0989693998393442
29	7.7	7.77684718195455	-0.108651068067928	7.73180388611338	0.0768471819545473
30	7.7	7.83383444583998	-0.197040223107253	7.76320577726727	0.133834445839981
31	7.9	7.99082186145234	0.0145704701264951	7.79460766842116	0.0908218614523415
32	8.1	8.11331594488118	0.309149327901588	7.77753472721723	0.0133159448811844
33	8.2	8.26914329589503	0.370394918091681	7.76046178601329	0.069143295895028
34	8.2	8.4866699006793	0.220375385620858	7.69295471369984	0.286669900679301
35	8.2	8.78752963649436	-0.0129772778807477	7.62544764138639	0.587529636494356
36	7.9	8.5045535046128	-0.245528395303983	7.54097489069119	0.604553504612792
37	7.3	7.55348123189008	-0.409983371886072	7.456502139996	0.253481231890077
38	6.9	6.41910212980758	0.0179725289439462	7.36292534124848	-0.480897870192424
39	6.6	5.89440033171934	0.0362511257796950	7.26934854250096	-0.705599668280657
40	6.7	6.22348202609747	0.00546667023471239	7.17105130366781	-0.476517973902526
41	6.9	6.83589700323326	-0.108651068067928	7.07275406483467	-0.0641029967667377
42	7	7.19316861063133	-0.197040223107253	7.00387161247592	0.193168610631334
43	7.1	7.25044036975633	0.0145704701264951	6.93498916011717	0.150440369756334
44	7.2	7.18513895109353	0.309149327901588	6.90571172100488	-0.0148610489064662
45	7.1	6.95317080001573	0.370394918091681	6.87643428189259	-0.146829199984267
46	6.9	6.73498293713822	0.220375385620858	6.84464167724092	-0.165017062861778
47	7	7.20012820529149	-0.0129772778807477	6.81284907258925	0.200128205291493
48	6.8	7.08156441494437	-0.245528395303983	6.76396398035962	0.281564414944365
49	6.4	6.49490448375609	-0.409983371886072	6.71507888812998	0.09490448375609
50	6.7	6.71240510892161	0.0179725289439462	6.66962236213445	0.0124051089216088
51	6.6	6.5395830380814	0.0362511257796950	6.62416583613891	-0.0604169619186035
52	6.4	6.22177507952125	0.00546667023471239	6.57275825024403	-0.178224920478746
53	6.3	6.18730040371877	-0.108651068067928	6.52135066434916	-0.112699596281232
54	6.2	6.12169394191127	-0.197040223107253	6.47534628119598	-0.0783060580887316
55	6.5	6.5560876318307	0.0145704701264951	6.42934189804281	0.056087631830696
56	6.8	6.85710862129117	0.309149327901588	6.43374205080725	0.0571086212911665
57	6.8	6.79146287833664	0.370394918091681	6.43814220357168	-0.00853712166336162
58	6.4	6.1159335006161	0.220375385620858	6.46369111376304	-0.284066499383894
59	6.1	5.72373725392635	-0.0129772778807477	6.48924002395439	-0.376262746073645
60	5.8	5.34927158384708	-0.245528395303983	6.4962568114569	-0.450728416152917
61	6.1	6.10670977292666	-0.409983371886072	6.50327359895941	0.00670977292666208
62	7.2	7.8501780280852	0.0179725289439462	6.53184944297085	0.650178028085209
63	7.3	8.00332358723802	0.0362511257796950	6.56042528698228	0.703323587238024
64	6.9	7.13831691582747	0.00546667023471239	6.65621641393782	0.238316915827467
65	6.1	5.55664352717457	-0.108651068067928	6.75200754089336	-0.543356472825432
66	5.8	4.92915458195128	-0.197040223107253	6.86788564115597	-0.870845418048721
67	6.2	5.40166578845492	0.0145704701264951	6.98376374141859	-0.798334211545082
68	7.1	6.79543645127445	0.309149327901588	7.09541422082396	-0.304563548725552
69	7.7	7.82254038167898	0.370394918091681	7.20706470022934	0.122540381678980
70	7.9	8.2546302955515	0.220375385620858	7.32499431882764	0.354630295551503
71	7.7	7.9700533404548	-0.0129772778807477	7.44292393742594	0.270053340454808
72	7.4	7.47499462352625	-0.245528395303983	7.57053377177773	0.0749946235262522
73	7.5	7.71183976575655	-0.409983371886072	7.69814360612952	0.211839765756548

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/1f50l1259954670.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/1f50l1259954670.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/2t81b1259954670.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/2t81b1259954670.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/3axw31259954670.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/3axw31259954670.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/4o4mh1259954670.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259954710w2epr5d741btwe1/4o4mh1259954670.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) #seasonal period

if (par2 != 'periodic') par2 <- as.numeric(par2) #s.window

par3 <- as.numeric(par3) #s.degree

if (par4 == '') par4 <- NULL else par4 <- as.numeric(par4)#t.window

par5 <- as.numeric(par5)#t.degree

if (par6 != '') par6 <- as.numeric(par6)#l.window

par7 <- as.numeric(par7)#l.degree

if (par8 == 'FALSE') par8 <- FALSE else par9 <- TRUE #robust

nx <- length(x)

x <- ts(x,frequency=par1)

if (par6 != '') {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.window=par6, l.degree=par7, robust=par8)

} else {

m <- stl(x,s.window=par2, s.degree=par3, t.window=par4, t.degre=par5, l.degree=par7, robust=par8)

}

m$time.series

m$win

m$deg

m$jump

m$inner

m$outer

bitmap(file='test1.png')

plot(m,main=main)

dev.off()

mylagmax <- nx/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(as.numeric(m$time.series[,'trend']),na.action=na.pass,lag.max = mylagmax,main='Trend')

acf(as.numeric(m$time.series[,'seasonal']),na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(as.numeric(m$time.series[,'remainder']),na.action=na.pass,lag.max = mylagmax,main='Remainder')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

spectrum(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'trend']),'trend']),main='Trend')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'seasonal']),'seasonal']),main='Seasonal')

cpgram(as.numeric(m$time.series[!is.na(m$time.series[,'remainder']),'remainder']),main='Remainder')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Seasonal Decomposition by Loess - Parameters',4,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Component',header=TRUE)

a<-table.element(a,'Window',header=TRUE)

a<-table.element(a,'Degree',header=TRUE)

a<-table.element(a,'Jump',header=TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,m$win['s'])

a<-table.element(a,m$deg['s'])

a<-table.element(a,m$jump['s'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,m$win['t'])

a<-table.element(a,m$deg['t'])

a<-table.element(a,m$jump['t'])

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'Low-pass',header=TRUE)

a<-table.element(a,m$win['l'])

a<-table.element(a,m$deg['l'])

a<-table.element(a,m$jump['l'])

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,'Seasonal Decomposition by Loess - Time Series Components',6,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,'Seasonal',header=TRUE)

a<-table.element(a,'Trend',header=TRUE)

a<-table.element(a,'Remainder',header=TRUE)

a<-table.row.end(a)

for (i in 1:nx) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,x[i]+m$time.series[i,'remainder'])

a<-table.element(a,m$time.series[i,'seasonal'])

a<-table.element(a,m$time.series[i,'trend'])

a<-table.element(a,m$time.series[i,'remainder'])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable1.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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