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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 10:24:30 -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/t12599475028e5tknb53cixtp3.htm/, Retrieved Fri, 04 Dec 2009 18:25:07 +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/t12599475028e5tknb53cixtp3.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 «

3.2 1.9 0 0.6 0.2 0.9 2.4 4.7 9.4 12.5 15.8 18.2 16.8 17.3 19.3 17.9 20.2 18.7 20.1 18.2 18.4 18.2 18.9 19.9 21.3 20 19.5 19.6 20.9 21 19.9 19.6 20.9 21.7 22.9 21.5 21.3 23.5 21.6 24.5 22.2 23.5 20.9 20.7 18.1 17.1 14.8 13.8 15.2 16 17.6 15 15 16.3 19.4 21.3 20.5 21.1 21.6 22.6

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	3.2	7.6084016560807	0.956435326458233	-2.16483698253893	4.40840165608070
2	1.9	3.97796962104776	0.611960317885162	-0.789929938932922	2.07796962104776
3	0	-0.532462231003066	-0.0525148736700193	0.584977104673086	-0.532462231003066
4	0.6	-0.25950548872391	-0.549246048825175	2.00875153754909	-0.85950548872391
5	0.2	-2.2465484458311	-0.785977524593984	3.43252597042509	-2.4465484458311
6	0.9	-2.38689985563016	-0.677484899815958	4.86438475544612	-3.28689985563016
7	2.4	-1.00725014139458	-0.488993399072576	6.29624354046716	-3.40725014139458
8	4.7	2.05827709532959	-0.375288900076775	7.71701180474719	-2.64172290467041
9	9.4	9.72380387459762	-0.0615839436248335	9.13778006902722	0.323803874597619
10	12.5	14.0145521326778	0.252702143824412	10.7327457234978	1.51455213267781
11	15.8	18.6853003646176	0.58698825741407	12.3277113779683	2.88530036461760
12	18.2	21.9927171345137	0.583003848711857	13.8242790167744	3.7927171345137
13	16.8	17.3227180179612	0.956435326458233	15.3208466555805	0.522718017961219
14	17.3	17.6177052402835	0.611960317885162	16.3703344418313	0.31770524028353
15	19.3	21.2326926455880	-0.0525148736700193	17.4198222280821	1.93269264558795
16	17.9	18.4116668251766	-0.549246048825175	17.9375792236486	0.51166682517659
17	20.2	22.7306413053789	-0.785977524593984	18.4553362192151	2.53064130537889
18	18.7	19.3854733698770	-0.677484899815958	18.6920115299389	0.685473369877034
19	20.1	21.7603065584098	-0.488993399072576	18.9286868406628	1.66030655840982
20	18.2	17.7126145814614	-0.375288900076775	19.0626743186153	-0.487385418538562
21	18.4	17.6649221470569	-0.0615839436248335	19.1966617965679	-0.735077852943082
22	18.2	16.8660491809767	0.252702143824412	19.2812486751989	-1.33395081902333
23	18.9	17.847176188756	0.58698825741407	19.3658355538299	-1.05282381124399
24	19.9	19.7337400447457	0.583003848711857	19.4832561065424	-0.166259955254286
25	21.3	22.0428880142868	0.956435326458233	19.6006766592549	0.74288801428683
26	20	19.6042523823945	0.611960317885162	19.7837872997203	-0.39574761760548
27	19.5	19.0856169334843	-0.0525148736700193	19.9668979401857	-0.414383066515679
28	19.6	19.5582304872347	-0.549246048825175	20.1910155615905	-0.0417695127653062
29	20.9	22.1708443415987	-0.785977524593984	20.4151331829953	1.27084434159872
30	21	22.0773335307296	-0.677484899815958	20.6001513690864	1.07733353072960
31	19.9	19.5038238438951	-0.488993399072576	20.7851695551774	-0.396176156104865
32	19.6	18.6189112959071	-0.375288900076775	20.9563776041697	-0.98108870409289
33	20.9	20.7339982904629	-0.0615839436248335	21.1275856531619	-0.166001709537067
34	21.7	21.8077938346725	0.252702143824412	21.3395040215031	0.107793834672481
35	22.9	23.6615893527416	0.58698825741407	21.5514223898443	0.761589352741613
36	21.5	20.6737650468102	0.583003848711857	21.7432311044779	-0.826234953189765
37	21.3	19.7085248544303	0.956435326458233	21.9350398191115	-1.59147514556973
38	23.5	24.4290164933415	0.611960317885162	21.9590231887733	0.929016493341521
39	21.6	21.2695083152349	-0.0525148736700193	21.9830065584351	-0.330491684765104
40	24.5	27.8798187467971	-0.549246048825175	21.6694273020281	3.37981874679709
41	22.2	23.8301294789729	-0.785977524593984	21.3558480456210	1.63012947897294
42	23.5	26.9210871757855	-0.677484899815958	20.7563977240305	3.4210871757855
43	20.9	22.1320459966327	-0.488993399072576	20.1569474024399	1.23204599663270
44	20.7	22.3170465835931	-0.375288900076775	19.4582423164837	1.61704658359312
45	18.1	17.5020467130974	-0.0615839436248335	18.7595372305274	-0.597953286902609
46	17.1	15.8712912893264	0.252702143824412	18.0760065668492	-1.22870871067365
47	14.8	11.6205358394149	0.58698825741407	17.3924759031710	-3.1794641605851
48	13.8	10.0518336219026	0.583003848711857	16.9651625293855	-3.7481663780974
49	15.2	12.9057155179417	0.956435326458233	16.5378491556001	-2.29428448205830
50	16	14.8084432711164	0.611960317885162	16.5795964109984	-1.19155672888355
51	17.6	18.6311712072733	-0.0525148736700193	16.6213436663967	1.0311712072733
52	15	13.358999009526	-0.549246048825175	17.1902470392992	-1.64100099047401
53	15	13.0268271123923	-0.785977524593984	17.7591504122016	-1.97317288760765
54	16.3	14.9430435719134	-0.677484899815958	18.3344413279025	-1.35695642808658
55	19.4	20.3792611554691	-0.488993399072576	18.9097322436034	0.979261155469128
56	21.3	23.4554012939674	-0.375288900076775	19.5198876061094	2.15540129396743
57	20.5	20.9315409750096	-0.0615839436248335	20.1300429686153	0.431540975009579
58	21.1	21.1789636933023	0.252702143824412	20.7683341628733	0.0789636933023097
59	21.6	21.2063863854546	0.58698825741407	21.4066253571313	-0.393613614545377
60	22.6	22.5602945883497	0.583003848711857	22.0567015629385	-0.039705411650349

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/1d6di1259947468.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/1d6di1259947468.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/2ql201259947468.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/2ql201259947468.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/3lpj91259947468.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/3lpj91259947468.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/4n7kn1259947468.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t12599475028e5tknb53cixtp3/4n7kn1259947468.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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