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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: Wed, 09 Dec 2009 09:12:31 -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/09/t1260375197zjjo36di74mxc9k.htm/, Retrieved Wed, 09 Dec 2009 17:13:22 +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/09/t1260375197zjjo36di74mxc9k.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 «

153.4 145 137.7 148.3 152.2 169.4 168.6 161.1 174.1 179 190.6 190 181.6 174.8 180.5 196.8 193.8 197 216.3 221.4 217.9 229.7 227.4 204.2 196.6 198.8 207.5 190.7 201.6 210.5 223.5 223.8 231.2 244 234.7 250.2 265.7 287.6 283.3 295.4 312.3 333.8 347.7 383.2 407.1 413.6 362.7 321.9 239.4 191 159.7 163.4 157.6 166.2 176.7 198.3 226.2 216.2 235.9 226.9

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	153.4	155.548329402848	-13.0543605572819	164.306031154434	2.14832940284754
2	145	146.936965508469	-21.5224563469274	164.585490838458	1.93696550846897
3	137.7	138.325606463122	-27.790556985604	164.864950522482	0.625606463121585
4	148.3	155.479078402935	-24.3585721701985	165.479493767264	7.17907840293464
5	152.2	159.832540762309	-21.5265777743547	166.094037012045	7.63254076230919
6	169.4	181.774763528673	-10.1322363399386	167.157472811266	12.3747635286729
7	168.6	168.416979903724	0.562111485790318	168.220908610486	-0.183020096276124
8	161.1	140.204912668219	12.3832245286684	169.611862803112	-20.8950873317806
9	174.1	150.252853222534	26.9443297817278	171.002816995739	-23.8471467774663
10	179	151.209387763944	33.2346056599951	173.556006576061	-27.7906122360559
11	190.6	177.005946942622	28.0848569009950	176.109196156383	-13.5940530573782
12	190	182.245890432563	17.1756873877285	180.578422179708	-7.75410956743684
13	181.6	191.206712354248	-13.0543605572819	185.047648203033	9.6067123542484
14	174.8	181.255086310147	-21.5224563469274	189.86737003678	6.45508631014746
15	180.5	194.103465115078	-27.790556985604	194.687091870526	13.6034651150777
16	196.8	219.716908453086	-24.3585721701985	198.241663717113	22.9169084530860
17	193.8	207.330342210656	-21.5265777743547	201.796235563699	13.5303422106559
18	197	200.816244624436	-10.1322363399386	203.315991715503	3.81624462443602
19	216.3	227.202140646903	0.562111485790318	204.835747867306	10.9021406469035
20	221.4	224.846631281548	12.3832245286684	205.570144189784	3.44663128154772
21	217.9	202.551129706011	26.9443297817278	206.304540512261	-15.3488702939893
22	229.7	219.10310329638	33.2346056599951	207.062291043625	-10.5968967036199
23	227.4	218.895101524017	28.0848569009950	207.820041574988	-8.50489847598314
24	204.2	182.271459490732	17.1756873877285	208.952853121539	-21.9285405092678
25	196.6	196.168695889191	-13.0543605572819	210.085664668090	-0.431304110808554
26	198.8	207.727670463196	-21.5224563469274	211.394785883731	8.9276704631959
27	207.5	230.086649886232	-27.790556985604	212.703907099372	22.5866498862315
28	190.7	191.680642836993	-24.3585721701985	214.077929333205	0.980642836993127
29	201.6	209.274626207316	-21.5265777743547	215.451951567038	7.6746262073163
30	210.5	213.106068086547	-10.1322363399386	218.026168253391	2.60606808654737
31	223.5	225.837503574466	0.562111485790318	220.600384939744	2.33750357446567
32	223.8	209.246441727325	12.3832245286684	225.970333744007	-14.5535582726755
33	231.2	204.115387670002	26.9443297817278	231.340282548270	-27.0846123299979
34	244	214.953632461127	33.2346056599951	239.811761878878	-29.0463675388733
35	234.7	193.031901889519	28.0848569009950	248.283241209486	-41.6680981104814
36	250.2	223.702280508298	17.1756873877285	259.522032103973	-26.4977194917015
37	265.7	273.693537558822	-13.0543605572819	270.760822998460	7.99353755882225
38	287.6	312.393633807136	-21.5224563469274	284.328822539792	24.7936338071357
39	283.3	296.493734904480	-27.790556985604	297.896822081124	13.1937349044803
40	295.4	304.664209817754	-24.3585721701985	310.494362352444	9.2642098177543
41	312.3	323.03467515059	-21.5265777743547	323.091902623765	10.7346751505899
42	333.8	349.319430071098	-10.1322363399386	328.41280626884	15.5194300710984
43	347.7	361.104178600294	0.562111485790318	333.733709913916	13.4041786002942
44	383.2	425.151254606670	12.3832245286684	328.865520864662	41.9512546066696
45	407.1	463.258338402864	26.9443297817278	323.997331815408	56.158338402864
46	413.6	482.023386874357	33.2346056599951	311.942007465648	68.4233868743565
47	362.7	397.428459983117	28.0848569009950	299.886683115889	34.7284599831165
48	321.9	342.699624429809	17.1756873877285	283.924688182463	20.7996244298089
49	239.4	223.891667308245	-13.0543605572819	267.962693249037	-15.5083326917546
50	191	152.316490143536	-21.5224563469274	251.205966203391	-38.6835098564640
51	159.7	112.741317827858	-27.790556985604	234.449239157746	-46.9586821721421
52	163.4	125.589786639445	-24.3585721701985	225.568785530754	-37.8102133605554
53	157.6	120.038245870593	-21.5265777743547	216.688331903762	-37.5617541294072
54	166.2	133.590879041810	-10.1322363399386	208.941357298128	-32.6091209581895
55	176.7	151.643505821715	0.562111485790318	201.194382692494	-25.0564941782847
56	198.3	189.796352068802	12.3832245286684	194.420423402529	-8.50364793119789
57	226.2	237.809206105708	26.9443297817278	187.646464112565	11.6092061057076
58	216.2	217.079168602519	33.2346056599951	182.086225737486	0.879168602519144
59	235.9	267.189155736598	28.0848569009950	176.525987362407	31.2891557365981
60	226.9	264.733379046165	17.1756873877285	171.890933566107	37.833379046165

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/1jcv51260375149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/1jcv51260375149.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/251gg1260375149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/251gg1260375149.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/3kg9j1260375149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/3kg9j1260375149.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/40c5k1260375149.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/09/t1260375197zjjo36di74mxc9k/40c5k1260375149.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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