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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: Sun, 06 Dec 2009 13:04:01 -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/06/t12601298831b9f307jy0x9bfq.htm/, Retrieved Sun, 06 Dec 2009 21:04:48 +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/06/t12601298831b9f307jy0x9bfq.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 «

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 8

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

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	601	0	61
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	8	8.04604179668616	0.00927598252910209	7.94468222078474	0.0460417966861586
2	8.1	8.3462837166195	-0.0402432527308325	7.89395953611132	0.246283716619509
3	7.7	7.7865253620793	-0.229762213517206	7.8432368514379	0.086525362079299
4	7.5	7.52966050022982	-0.327955571739558	7.79829507150974	0.02966050022982
5	7.6	7.55279582136275	-0.106149112944317	7.75335329158157	-0.0472041786372532
6	7.8	7.65554946596363	0.230889001657578	7.71356153237879	-0.144450534036366
7	7.8	7.57830308442418	0.347927142399811	7.67376977317601	-0.221696915575819
8	7.8	7.69306811491774	0.270021690464528	7.63691019461774	-0.106931885082265
9	7.5	7.2678328709377	0.132116513002829	7.60005061605946	-0.232167129062294
10	7.5	7.49227645585009	-0.0856565668143522	7.59338011096427	-0.00772354414991394
11	7.1	6.89672005383268	-0.283429659701747	7.58670960586907	-0.203279946167322
12	7.5	7.29638137732951	0.0829662151395948	7.62065240753089	-0.203618622670487
13	7.5	7.33612880827818	0.00927598252910209	7.65459520919272	-0.163871191721818
14	7.6	7.54134999789792	-0.0402432527308325	7.69889325483291	-0.058650002102083
15	7.7	7.8865709130441	-0.229762213517206	7.74319130047311	0.186570913044092
16	7.7	7.95319079055902	-0.327955571739558	7.77476478118053	0.253190790559023
17	7.9	8.09981085105636	-0.106149112944317	7.80633826188796	0.199810851056361
18	8.1	8.18560430217692	0.230889001657578	7.7835066961655	0.0856043021769208
19	8.2	8.29139772715714	0.347927142399811	7.76067513044305	0.0913977271571422
20	8.2	8.44246236398471	0.270021690464528	7.68751594555076	0.242462363984712
21	8.2	8.6535267263387	0.132116513002829	7.61435676065847	0.453526726338698
22	7.9	8.3560530131596	-0.0856565668143522	7.52960355365476	0.456053013159597
23	7.3	7.43857931305071	-0.283429659701747	7.44485034665104	0.138579313050708
24	6.9	6.36023752129483	0.0829662151395948	7.35679626356558	-0.539762478705171
25	6.6	5.92198183699078	0.00927598252910209	7.26874218048011	-0.678018163009217
26	6.7	6.26380142878903	-0.0402432527308325	7.1764418239418	-0.436198571210974
27	6.9	6.94562074611371	-0.229762213517206	7.0841414674035	0.0456207461137081
28	7	7.31252496653732	-0.327955571739558	7.01543060520224	0.31252496653732
29	7.1	7.35942936994334	-0.106149112944317	6.94671974300098	0.259429369943338
30	7.2	7.25742731254062	0.230889001657578	6.9116836858018	0.057427312540618
31	7.1	6.97542522899756	0.347927142399811	6.87664762860263	-0.124574771002443
32	6.9	6.69077539404806	0.270021690464528	6.83920291548741	-0.209224605951942
33	7	7.06612528462497	0.132116513002829	6.8017582023722	0.0661252846249747
34	6.8	6.93306391289954	-0.0856565668143522	6.75259265391481	0.133063912899542
35	6.4	6.38000255424432	-0.283429659701747	6.70342710545742	-0.0199974457556777
36	6.7	6.65354049490848	0.0829662151395948	6.66349328995193	-0.0464595050915211
37	6.6	6.56716454302447	0.00927598252910209	6.62355947444643	-0.0328354569755298
38	6.4	6.26209448837782	-0.0402432527308325	6.57814876435302	-0.137905511622183
39	6.3	6.2970241592576	-0.229762213517206	6.5327380542596	-0.00297584074239854
40	6.2	6.2410503096321	-0.327955571739558	6.48690526210745	0.041050309632106
41	6.5	6.66507664298901	-0.106149112944317	6.4410724699553	0.165076642989015
42	6.8	6.92939698715623	0.230889001657578	6.43971401118619	0.129396987156234
43	6.8	6.81371730518311	0.347927142399811	6.43835555241707	0.0137173051831150
44	6.4	6.07172595120633	0.270021690464528	6.45825235832914	-0.328274048793669
45	6.1	5.58973432275596	0.132116513002829	6.47814916424121	-0.510265677244038
46	5.8	5.20077107108401	-0.0856565668143522	6.48488549573034	-0.599228928915987
47	6.1	5.99180783248228	-0.283429659701747	6.49162182721947	-0.108192167517722
48	7.2	7.79131340798095	0.0829662151395948	6.52572037687946	0.591313407980949
49	7.3	8.03090509093145	0.00927598252910209	6.55981892653944	0.730905090931453
50	6.9	7.18945082241255	-0.0402432527308325	6.65079243031828	0.289450822412554
51	6.1	5.68799627942009	-0.229762213517206	6.74176593409711	-0.412003720579905
52	5.8	5.06916045607112	-0.327955571739558	6.85879511566844	-0.73083954392888
53	6.2	5.53032481570455	-0.106149112944317	6.97582429723976	-0.669675184295448
54	7.1	6.881112777519	0.230889001657578	7.08799822082342	-0.218887222481000
55	7.7	7.85190071319311	0.347927142399811	7.20017214440708	0.151900713193110
56	7.9	8.21323193690967	0.270021690464528	7.3167463726258	0.313231936909671
57	7.7	7.83456288615265	0.132116513002829	7.43332060084452	0.134562886152647
58	7.4	7.329024329522	-0.0856565668143522	7.55663223729235	-0.0709756704779974
59	7.5	7.60348578596157	-0.283429659701747	7.67994387374018	0.103485785961571
60	8	8.10923494839076	0.0829662151395948	7.80779883646964	0.109234948390760

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/1hei91260129838.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/1hei91260129838.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/21c341260129838.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/21c341260129838.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/3z2wu1260129838.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/3z2wu1260129838.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/42k0h1260129838.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/06/t12601298831b9f307jy0x9bfq/42k0h1260129838.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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