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Decomposition by 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: Thu, 03 Dec 2009 06:27:56 -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/03/t12598469191hohhih9qclgnki.htm/, Retrieved Thu, 03 Dec 2009 14:28:45 +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/2009/Dec/03/t12598469191hohhih9qclgnki.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:

JSSHWWS9P8

Dataseries X:

» Textbox « » Textfile « » CSV «

11.1 10.9 10 9.2 9.2 9.5 9.6 9.5 9.1 8.9 9 10.1 10.3 10.2 9.6 9.2 9.3 9.4 9.4 9.2 9 9 9 9.8 10 9.8 9.3 9 9 9.1 9.1 9.1 9.2 8.8 8.3 8.4 8.1 7.7 7.9 7.9 8 7.9 7.6 7.1 6.8 6.5 6.9 8.2 8.7 8.3 7.9 7.5 7.8 8.3 8.4 8.2 7.7 7.2 7.3 8.1

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	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	11.1	11.4912445929011	0.724583428074431	9.98417197902451	0.391244592901057
2	10.9	11.3769942866534	0.498763968064267	9.92424174528233	0.476994286653403
3	10	10.0427438627743	0.0929446256855824	9.86431151154015	0.0427438627742696
4	9.2	8.84154750338496	-0.252669942000527	9.81112243861556	-0.358452496615037
5	9.2	8.7603513792587	-0.118284744949682	9.75793336569098	-0.439648620741297
6	9.5	9.20397898475474	0.088838570339697	9.70718244490556	-0.296021015245259
7	9.6	9.44760649875959	0.0959619771202658	9.65643152412015	-0.152393501240415
8	9.5	9.46811270729899	-0.0756727163547582	9.60756000905577	-0.0318872927010148
9	9.1	8.94861870671568	-0.307307200707074	9.5586884939914	-0.151381293284324
10	8.9	8.81753033943586	-0.56062594984511	9.54309561040925	-0.0824696605641417
11	9	8.9864421420683	-0.513944868895403	9.5275027268271	-0.0135578579317031
12	10.1	10.3506652693741	0.327412855148319	9.52192187547763	0.250665269374053
13	10.3	10.3590755477974	0.724583428074431	9.51634102412815	0.0590755477974216
14	10.2	10.3996844196747	0.498763968064267	9.50155161226102	0.199684419674716
15	9.6	9.62029317392053	0.0929446256855824	9.48676220039389	0.0202931739205319
16	9.2	9.1798535332355	-0.252669942000527	9.47281640876502	-0.0201464667644942
17	9.3	9.25941412781353	-0.118284744949682	9.45887061713615	-0.0405858721864707
18	9.4	9.2698739707096	0.088838570339697	9.4412874589507	-0.1301260292904
19	9.4	9.28033372211448	0.0959619771202658	9.42370430076526	-0.119666277885521
20	9.2	9.07200354455857	-0.0756727163547582	9.40366917179618	-0.127996455441425
21	9	8.92367315787997	-0.307307200707074	9.3836340428271	-0.0763268421200323
22	9	9.19598933027585	-0.56062594984511	9.36463661956926	0.19598933027585
23	9	9.16830567258399	-0.513944868895403	9.34563919631142	0.168305672583987
24	9.8	9.94805819533463	0.327412855148319	9.32452894951705	0.148058195334629
25	10	9.97199786920288	0.724583428074431	9.30341870272269	-0.0280021307971214
26	9.8	9.8167862663082	0.498763968064267	9.28444976562754	0.0167862663081966
27	9.3	9.24157454578203	0.0929446256855824	9.26548082853238	-0.0584254542179661
28	9	9.01890920521249	-0.252669942000527	9.23376073678804	0.0189092052124877
29	9	8.91624409990599	-0.118284744949682	9.2020406450437	-0.0837559000940118
30	9.1	8.99488210138615	0.088838570339697	9.11627932827416	-0.105117898613853
31	9.1	9.07352001137511	0.0959619771202658	9.03051801150462	-0.0264799886248888
32	9.1	9.37641259527792	-0.0756727163547582	8.89926012107684	0.276412595277916
33	9.2	9.93930497005801	-0.307307200707074	8.76800223064906	0.739304970058013
34	8.8	9.52136262258848	-0.56062594984511	8.63926332725664	0.721362622588476
35	8.3	8.6034204450312	-0.513944868895403	8.51052442386421	0.303420445031195
36	8.4	8.0920105885215	0.327412855148319	8.38057655633018	-0.307989411478502
37	8.1	7.22478788312941	0.724583428074431	8.25062868879616	-0.87521211687059
38	7.7	6.80584672265855	0.498763968064267	8.09538930927718	-0.894153277341448
39	7.9	7.76690544455621	0.0929446256855824	7.9401499297582	-0.133094555443786
40	7.9	8.2447042142546	-0.252669942000527	7.80796572774592	0.344704214254609
41	8	8.44250321921605	-0.118284744949682	7.67578152573363	0.442503219216049
42	7.9	8.0798658269718	0.088838570339697	7.6312956026885	0.179865826971799
43	7.6	7.51722834323636	0.0959619771202658	7.58680967964338	-0.0827716567636418
44	7.1	6.68591094964692	-0.0756727163547582	7.58976176670784	-0.414089050353083
45	6.8	6.31459334693477	-0.307307200707074	7.59271385377231	-0.485406653065234
46	6.5	5.96354072518522	-0.56062594984511	7.59708522465989	-0.536459274814781
47	6.9	6.71248827334793	-0.513944868895403	7.60145659554747	-0.187511726652071
48	8.2	8.43037291019948	0.327412855148319	7.6422142346522	0.230372910199481
49	8.7	8.99244469816864	0.724583428074431	7.68297187375692	0.292444698168644
50	8.3	8.34334464693413	0.498763968064267	7.7578913850016	0.0433446469341323
51	7.9	7.87424447806814	0.0929446256855824	7.83281089624628	-0.0257555219318615
52	7.5	7.39000338229118	-0.252669942000527	7.86266655970934	-0.109996617708816
53	7.8	7.82576252177727	-0.118284744949682	7.8925222231724	0.0257625217772732
54	8.3	8.59709282864308	0.088838570339697	7.91406860101722	0.297092828643083
55	8.4	8.7684230440177	0.0959619771202658	7.93561497886203	0.3684230440177
56	8.2	8.520766857479	-0.0756727163547582	7.95490585887576	0.320766857478998
57	7.7	7.73311046181759	-0.307307200707074	7.97419673888948	0.0331104618175910
58	7.2	6.97215588303982	-0.56062594984511	7.9884700668053	-0.227844116960184
59	7.3	7.1112014741743	-0.513944868895403	8.0027433947211	-0.188798525825701
60	8.1	7.8605721287678	0.327412855148319	8.01201501608388	-0.239427871232195

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/12p391259846874.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/12p391259846874.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/2xat61259846874.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/2xat61259846874.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/3lifn1259846874.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/3lifn1259846874.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/4jh7m1259846874.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t12598469191hohhih9qclgnki/4jh7m1259846874.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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