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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: Tue, 29 Dec 2009 03:58:56 -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/29/t1262084522kubsxw35hl9pp74.htm/, Retrieved Tue, 29 Dec 2009 12:02:08 +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/29/t1262084522kubsxw35hl9pp74.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 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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	8	8.02770098783904	0.0348009045443075	7.93749810761665	0.0277009878390393
2	8.1	8.34918123291692	-0.0371017513872016	7.88792051847028	0.249181232916920
3	7.7	7.7891776745385	-0.227520603862407	7.83834292932391	0.0891776745384965
4	7.5	7.53234823600606	-0.326718670459528	7.79437043445347	0.0323482360060563
5	7.6	7.55551897166034	-0.105916911243376	7.75039793958303	-0.0444810283396588
6	7.8	7.6593005062318	0.229257984599439	7.71144150916877	-0.140699493768207
7	7.8	7.58308201591943	0.344432905326068	7.6724850787545	-0.216917984080571
8	7.8	7.6981393459931	0.265543769202411	7.63631688480449	-0.101860654006905
9	7.5	7.2731964147867	0.126654894358821	7.60014869085448	-0.226803585213306
10	7.5	7.49768819033439	-0.0911246234285577	7.59343643309417	-0.00231180966561340
11	7.1	6.90217997832403	-0.288904153657882	7.58672417533386	-0.197820021675974
12	7.5	7.30295884027578	0.0765965437657685	7.62044461595846	-0.197041159724225
13	7.5	7.31103403887264	0.0348009045443075	7.65416505658306	-0.188965961127363
14	7.6	7.53873043516155	-0.0371017513872016	7.69837131622565	-0.0612695648384447
15	7.7	7.88494302799417	-0.227520603862407	7.74257757586824	0.184943027994171
16	7.7	7.95230335896497	-0.326718670459528	7.77441531149455	0.252303358964975
17	7.9	8.0996638641225	-0.105916911243376	7.80625304712087	0.199663864122505
18	8.1	8.18701481362449	0.229257984599439	7.78372720177607	0.0870148136244913
19	8.2	8.29436573824266	0.344432905326068	7.76120135643127	0.0943657382426641
20	8.2	8.44637690734919	0.265543769202411	7.6880793234484	0.246376907349187
21	8.2	8.65838781517564	0.126654894358821	7.61495729046554	0.458387815175644
22	7.9	8.3612135200285	-0.0911246234285577	7.52991110340005	0.461213520028503
23	7.3	7.44403923732331	-0.288904153657882	7.44486491633457	0.144039237323308
24	6.9	6.36681498419177	0.0765965437657685	7.35658847204247	-0.533185015808234
25	6.6	5.89688706770533	0.0348009045443075	7.26831202775036	-0.703112932294666
26	6.7	6.26118186641252	-0.0371017513872016	7.17591988497468	-0.438818133587477
27	6.9	6.9439928616634	-0.227520603862407	7.083527742199	0.0439928616634067
28	7	7.31163753562518	-0.326718670459528	7.01508113483435	0.311637535625183
29	7.1	7.35928238377368	-0.105916911243376	6.94663452746969	0.259282383773684
30	7.2	7.25883782455108	0.229257984599439	6.91190419084948	0.0588378245510848
31	7.1	6.97839324044467	0.344432905326068	6.87717385422926	-0.121606759555330
32	6.9	6.69468993729474	0.265543769202411	6.83976629350285	-0.205310062705259
33	7	7.07098637286474	0.126654894358821	6.80235873277643	0.0709863728647449
34	6.8	6.93822441909437	-0.0911246234285577	6.75290020433419	0.138224419094368
35	6.4	6.38546247776594	-0.288904153657882	6.70344167589194	-0.014537522234062
36	6.7	6.66011795734216	0.0765965437657685	6.66328549889207	-0.0398820426578359
37	6.6	6.5420697735635	0.0348009045443075	6.62312932189219	-0.0579302264364978
38	6.4	6.25947492614454	-0.0371017513872016	6.57762682524266	-0.140525073855458
39	6.3	6.29539627526928	-0.227520603862407	6.53212432859313	-0.0046037247307229
40	6.2	6.24016287930973	-0.326718670459528	6.4865557911498	0.0401628793097260
41	6.5	6.6649296575369	-0.105916911243376	6.44098725370648	0.164929657536899
42	6.8	6.93080749971032	0.229257984599439	6.43993451569024	0.130807499710319
43	6.8	6.81668531699993	0.344432905326068	6.43888177767401	0.0166853169999257
44	6.4	6.07564049437141	0.265543769202411	6.45881573642618	-0.324359505628594
45	6.1	5.59459541046282	0.126654894358821	6.47874969517836	-0.505404589537182
46	5.8	5.20593157671416	-0.0911246234285577	6.4851930467144	-0.594068423285837
47	6.1	5.99726775540745	-0.288904153657882	6.49163639825043	-0.102732244592545
48	7.2	7.79789087017804	0.0765965437657685	6.5255125860562	0.597890870178035
49	7.3	8.00581032159373	0.0348009045443075	6.55938877386197	0.705810321593726
50	6.9	7.18683126072828	-0.0371017513872016	6.65027049065892	0.286831260728281
51	6.1	5.68636839640653	-0.227520603862407	6.74115220745587	-0.413631603593468
52	5.8	5.07078447632474	-0.326718670459528	6.85593419413478	-0.729215523675256
53	6.2	5.53520073042968	-0.105916911243376	6.9707161808137	-0.664799269570318
54	7.1	6.88054219082248	0.229257984599439	7.09019982457809	-0.219457809177524
55	7.7	7.84588362633146	0.344432905326068	7.20968346834248	0.145883626331456
56	7.9	8.2001774992116	0.265543769202411	7.33427873158598	0.300177499211608
57	7.7	7.81447111081169	0.126654894358821	7.45887399482949	0.114471110811692
58	7.4	7.30046340327366	-0.0911246234285577	7.5906612201549	-0.0995365967263417
59	7.5	7.56645570817757	-0.288904153657882	7.72244844548031	0.0664557081775703
60	8	8.06347913627577	0.0765965437657685	7.85992431995846	0.0634791362757712
61	8.1	8.16779890101908	0.0348009045443075	7.99740019443661	0.067798901019085

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/166ki1262084332.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/166ki1262084332.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/2jl901262084332.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/2jl901262084332.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/3691z1262084332.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/3691z1262084332.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/4gngq1262084332.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/29/t1262084522kubsxw35hl9pp74/4gngq1262084332.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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