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*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 05:23:04 -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/t1259929445yy6i6rekldfmtdb.htm/, Retrieved Fri, 04 Dec 2009 13:24:10 +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/t1259929445yy6i6rekldfmtdb.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 «

1,4816 1,4562 1,4268 1,4088 1,4016 1,3650 1,3190 1,3050 1,2785 1,3239 1,3449 1,2732 1,3322 1,4369 1,4975 1,5770 1,5553 1,5557 1,5750 1,5527 1,4748 1,4718 1,4570 1,4684 1,4227 1,3896 1,3622 1,3716 1,3419 1,3511 1,3516 1,3242 1,3074 1,2999 1,3213 1,2881 1,2611 1,2727 1,2811 1,2684 1,2650 1,2770 1,2271 1,2020 1,1938 1,2103 1,1856 1,1786 1,2015 1,2256 1,2292 1,2037 1,2165 1,2694 1,2938 1,3201 1,3014 1,3119 1,3408 1,2991

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

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	1.4816	1.54981263254267	-0.00877603705127088	1.42216340450861	0.0682126325426657
2	1.4562	1.49054999569459	0.0097111728540948	1.41213883145132	0.0343499956945852
3	1.4268	1.43650735713431	0.0149783844716564	1.40211425839403	0.00970735713430892
4	1.4088	1.4017762316438	0.0219420616289651	1.39388170672724	-0.00702376835620178
5	1.4016	1.40502514122055	0.0125257037190104	1.38564915506044	0.00342514122055104
6	1.365	1.33018477254508	0.0207472856917986	1.37906794176312	-0.0348152274549154
7	1.319	1.25446440185681	0.0110488696773944	1.37248672846580	-0.0645355981431894
8	1.305	1.24250844738303	0.00032603431149997	1.36716551830547	-0.06249155261697
9	1.2785	1.22267248016583	-0.0275167883109758	1.36184430814515	-0.0558275198341696
10	1.3239	1.29463909677622	-0.0136787624126713	1.36683966563645	-0.0292609032237827
11	1.3449	1.32382571119081	-0.0058607343185717	1.37183502312776	-0.0210742888091910
12	1.2732	1.19144662426480	-0.0354471332996005	1.39040050903480	-0.0817533757352034
13	1.3322	1.26421004210943	-0.00877603705127088	1.40896599494185	-0.0679899578905743
14	1.4369	1.43450296847996	0.0097111728540948	1.42958585866595	-0.002397031520045
15	1.4975	1.52981589313829	0.0149783844716564	1.45020572239006	0.0323158931382883
16	1.577	1.66522845221953	0.0219420616289651	1.46682948615151	0.0882284522195294
17	1.5553	1.61462104636803	0.0125257037190104	1.48345324991296	0.0593210463680338
18	1.5557	1.59813108378950	0.0207472856917986	1.49252163051870	0.0424310837894981
19	1.575	1.63736111919815	0.0110488696773944	1.50159001112445	0.0623611191981548
20	1.5527	1.60702013577433	0.00032603431149997	1.49805382991417	0.0543201357743293
21	1.4748	1.48259913960709	-0.0275167883109758	1.49451764870389	0.00779913960708511
22	1.4718	1.47785951150484	-0.0136787624126713	1.47941925090783	0.00605951150483675
23	1.457	1.45553988120679	-0.0058607343185717	1.46432085311178	-0.00146011879320684
24	1.4684	1.52691783140285	-0.0354471332996005	1.44532930189675	0.0585178314028547
25	1.4227	1.42783828636956	-0.00877603705127088	1.42633775068171	0.00513828636955815
26	1.3896	1.36098638337685	0.0097111728540948	1.40850244376905	-0.0286136166231452
27	1.3622	1.31875447867196	0.0149783844716564	1.39066713685639	-0.0434455213280445
28	1.3716	1.3452766036985	0.0219420616289651	1.37598133467253	-0.0263233963014997
29	1.3419	1.30997876379231	0.0125257037190104	1.36129553248868	-0.0319212362076911
30	1.3511	1.33198566765245	0.0207472856917986	1.34946704665575	-0.0191143323475509
31	1.3516	1.35451256949978	0.0110488696773944	1.33763856082282	0.00291256949978203
32	1.3242	1.31949686999388	0.00032603431149997	1.32857709569462	-0.00470313000611622
33	1.3074	1.32280115774457	-0.0275167883109758	1.31951563056641	0.0154011577445667
34	1.2999	1.30168061507310	-0.0136787624126713	1.31179814733957	0.00178061507310412
35	1.3213	1.34438007020585	-0.0058607343185717	1.30408066411273	0.0230800702058462
36	1.2881	1.31599698136205	-0.0354471332996005	1.29565015193755	0.0278969813620469
37	1.2611	1.24375639728889	-0.00877603705127088	1.28721963976238	-0.0173436027111109
38	1.2727	1.25808078780430	0.0097111728540948	1.27760803934160	-0.0146192121956967
39	1.2811	1.27922517660752	0.0149783844716564	1.26799643892082	-0.00187482339247835
40	1.2684	1.25641180614889	0.0219420616289651	1.25844613222214	-0.0119881938511075
41	1.265	1.26857847075753	0.0125257037190104	1.24889582552346	0.00357847075752704
42	1.277	1.29210226523642	0.0207472856917986	1.24115044907178	0.015102265236423
43	1.2271	1.20974605770251	0.0110488696773944	1.23340507262009	-0.0173539422974884
44	1.202	1.17561328670043	0.00032603431149997	1.22806067898807	-0.0263867132995688
45	1.1938	1.19240050295493	-0.0275167883109758	1.22271628535604	-0.0013994970450677
46	1.2103	1.21534046648201	-0.0136787624126713	1.21893829593066	0.00504046648201184
47	1.1856	1.16190042781330	-0.0058607343185717	1.21516030650528	-0.0236995721867037
48	1.1786	1.17719954879610	-0.0354471332996005	1.21544758450350	-0.00140045120389720
49	1.2015	1.19604117454955	-0.00877603705127088	1.21573486250172	-0.00545882545044951
50	1.2256	1.21944545296292	0.0097111728540948	1.22204337418299	-0.00615454703708052
51	1.2292	1.21506972966409	0.0149783844716564	1.22835188586425	-0.0141302703359072
52	1.2037	1.144422530745	0.0219420616289651	1.24103540762604	-0.0592774692550002
53	1.2165	1.16675536689317	0.0125257037190104	1.25371892938782	-0.0497446331068296
54	1.2694	1.25197981326245	0.0207472856917986	1.26607290104575	-0.0174201867375514
55	1.2938	1.29812425761892	0.0110488696773944	1.27842687270369	0.0043242576189193
56	1.3201	1.34841720971517	0.00032603431149997	1.29145675597333	0.0283172097151698
57	1.3014	1.325830149068	-0.0275167883109758	1.30448663924297	0.0244301490680012
58	1.3119	1.31918003540027	-0.0136787624126713	1.31829872701240	0.00728003540026934
59	1.3408	1.35534991953674	-0.0058607343185717	1.33211081478183	0.014549919536742
60	1.2991	1.28729027040019	-0.0354471332996005	1.34635686289941	-0.0118097295998076

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/13bgj1259929381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/13bgj1259929381.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/2h87u1259929381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/2h87u1259929381.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/3ov841259929381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/3ov841259929381.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/49mfm1259929381.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929445yy6i6rekldfmtdb/49mfm1259929381.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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