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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: Wed, 02 Dec 2009 14:17:02 -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/02/t1259788667lwh0pzdv1bxpzmf.htm/, Retrieved Wed, 02 Dec 2009 22:17:52 +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/02/t1259788667lwh0pzdv1bxpzmf.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 «

0.0314796223103059 -3.00870920563557 -2.07677512619799 -1.25010391965540 0.817975239137125 0.0252076485413113 0.554937772830776 0.230027371950115 2.35672227418686 1.41350455171120 2.73311719024401 1.31551925971717 -2.70076272244080 -0.721411049152714 -0.149388576811997 -0.118199629770334 -0.676562489695275 1.79699928690761 1.79845572032988 0.245100010770855 1.80710848932636 -1.75934771184948 -0.0186697168761931 0.189651523600062 -1.84149562719087 -1.07019530156943 -0.507291477584104 0.866365633831705 -1.76077926699189 -0.580719393339347 -0.435702079860853 -0.994868534845203 1.63136048315789 -1.1949403709466 -1.00525975426991 1.32302234837564 -0.628357549594746 0.632048410440518 -2.16903155809288 2.53779364144266 -0.632933703679292 -1.41749196342200 -0.455343045381255 0.812255211942954 0.627897309219833 0.650904313655623 -1.29800419154382 0.74391671726854 -1.50461634127457 -1.42734677658523 0.263353807408564 - etc...

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	0.0314796223103059	1.87321254936343	-1.19588792169410	-0.61436538304872	1.84173292705313
2	-3.00870920563557	-4.55079684931365	-0.988963661933574	-0.477657900023914	-1.54208764367808
3	-2.07677512619799	-3.01222666298964	-0.800373172407236	-0.340950416999108	-0.935451536791646
4	-1.2501039196554	-2.72409111758413	0.445741960882114	-0.22185868260878	-1.47398719792873
5	0.817975239137125	1.991244563012	-0.252527136519296	-0.102766948218452	1.17326932387487
6	0.0252076485413113	-0.375634086288501	0.427857223294647	-0.00180783992352354	-0.400841734829812
7	0.554937772830776	1.22002149116338	-0.209297213873228	0.0991512683714053	0.665083718332599
8	0.230027371950115	0.353947551489241	-0.095865316424969	0.201972508835958	0.123920179539126
9	2.35672227418686	3.14559081676575	1.26305998230745	0.304793749300511	0.788868542578895
10	1.4135045517112	2.28956251643775	0.149716530307800	0.387730056676852	0.876057964726548
11	2.73311719024401	4.70327970816012	0.292288308274703	0.470666364053192	1.97016251791611
12	1.31551925971717	1.18184876440666	0.964249587262434	0.484940167765245	-0.133670495310508
13	-2.7007627224408	-4.7048514946648	-1.19588792169410	0.499213971477297	-2.004088772224
14	-0.721411049152714	-0.92733387350979	-0.988963661933574	0.473475437137936	-0.205922824357076
15	-0.149388576811997	0.0538591159846669	-0.800373172407236	0.447736902798575	0.203247692796664
16	-0.118199629770334	-1.03585801822908	0.445741960882114	0.353716797806298	-0.917658388458746
17	-0.676562489695275	-1.36029453568527	-0.252527136519296	0.25969669281402	-0.683732045989999
18	1.79699928690761	2.99062802053107	0.427857223294647	0.175513329989506	1.19362873362346
19	1.79845572032988	3.71487868736800	-0.209297213873228	0.0913299671649926	1.91642296703812
20	0.245100010770855	0.524671650072147	-0.095865316424969	0.0613936878945323	0.279571639301292
21	1.80710848932636	2.31969958772119	1.26305998230745	0.0314574086240719	0.512591098394835
22	-1.75934771184948	-3.63704116011412	0.149716530307800	-0.0313707938926448	-1.87769344826464
23	-0.0186697168761931	-0.235428745617727	0.292288308274703	-0.0941989964093614	-0.216759028741534
24	0.189651523600062	-0.381010042930919	0.964249587262434	-0.203936497131391	-0.570661566530981
25	-1.84149562719087	-2.17342933483422	-1.19588792169410	-0.313673997853420	-0.331933707643352
26	-1.07019530156943	-0.761158836295816	-0.988963661933574	-0.390268104909470	0.309036465273614
27	-0.507291477584104	0.252652429204548	-0.800373172407236	-0.466862211965520	0.759943906788652
28	0.866365633831705	1.76438870777614	0.445741960882114	-0.477399400994847	0.898023073944438
29	-1.76077926699189	-2.78109480744031	-0.252527136519296	-0.487936590024174	-1.02031554044842
30	-0.580719393339347	-1.12426954196994	0.427857223294647	-0.465026468003397	-0.543550148630596
31	-0.435702079860853	-0.219990599865857	-0.209297213873228	-0.44211634598262	0.215711479994996
32	-0.994868534845203	-1.50108925075388	-0.095865316424969	-0.392782502511560	-0.506220715908674
33	1.63136048315789	2.34310964304883	1.26305998230745	-0.343448659040499	0.711749159890936
34	-1.1949403709466	-2.26262676230438	0.149716530307800	-0.276970509896624	-1.06768639135778
35	-1.00525975426991	-2.09231545606177	0.292288308274703	-0.210492360752749	-1.08705570179186
36	1.32302234837564	1.84364189260388	0.964249587262434	-0.161846783115037	0.520619544228244
37	-0.628357549594746	0.0523740279819322	-1.19588792169410	-0.113201205477326	0.680731577576678
38	0.632048410440518	2.33065109086444	-0.988963661933574	-0.0775906080498263	1.69860268042392
39	-2.16903155809288	-3.49570993315620	-0.800373172407236	-0.0419800106223271	-1.32667837506332
40	2.53779364144266	4.66224988384955	0.445741960882114	-0.0324045618463407	2.12445624240689
41	-0.632933703679292	-0.990511157768934	-0.252527136519296	-0.0228291130703542	-0.357577454089642
42	-1.417491963422	-3.19268886749136	0.427857223294647	-0.0701522826472916	-1.77519690406936
43	-0.455343045381255	-0.583913424665053	-0.209297213873228	-0.117475452224229	-0.128570379283798
44	0.812255211942954	1.89430600393893	-0.095865316424969	-0.173930263628049	1.08205079199597
45	0.627897309219833	0.223119711164081	1.26305998230745	-0.230385075031869	-0.404777598055752
46	0.650904313655623	1.37564487943307	0.149716530307800	-0.223552782429629	0.724740565777451
47	-1.29800419154382	-2.67157620153495	0.292288308274703	-0.216720489827389	-1.37357200999113
48	0.74391671726854	0.73692155827649	0.964249587262434	-0.213337711001844	-0.00699515899204942
49	-1.50461634127457	-1.60338982867874	-1.19588792169410	-0.2099549321763	-0.098773487404171
50	-1.42734677658523	-1.59783698839723	-0.988963661933574	-0.26789290283966	-0.170490211811996
51	0.263353807408564	1.65291166072738	-0.800373172407236	-0.32583087350302	1.38955785331882
52	-0.430830854870631	-0.97516364190150	0.445741960882114	-0.332240028721877	-0.544332787030868
53	0.379576092518008	1.35032850549605	-0.252527136519296	-0.338649183940734	0.970752412978038
54	1.70309353400146	3.30300584493743	0.427857223294647	-0.32467600022916	1.59991231093597
55	-3.12314448117342	-5.72628893195603	-0.209297213873228	-0.310702816517586	-2.60314445078261
56	-1.32526207118689	-2.24798052385366	-0.095865316424969	-0.306678302095155	-0.922718452666766
57	-0.60032490743804	-2.16105600951081	1.26305998230745	-0.302653787672723	-1.56073110207277
58	1.23607137604666	2.62358008383809	0.149716530307800	-0.30115386205257	1.38750870779143
59	0.738007075905376	1.48337977996847	0.292288308274703	-0.299653936432416	0.74537270406309
60	0.899100896289585	1.12679082957359	0.964249587262434	-0.292838624256857	0.227689933284008

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/1z44h1259788618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/1z44h1259788618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/2pu491259788618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/2pu491259788618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/31or51259788618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/31or51259788618.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/453r81259788618.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259788667lwh0pzdv1bxpzmf/453r81259788618.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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