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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 09:23:59 -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/t1259943863bsq8c88jqs0bfdf.htm/, Retrieved Fri, 04 Dec 2009 17:24:28 +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/t1259943863bsq8c88jqs0bfdf.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 «

12,6 15,7 13,2 20,3 12,8 8 0,9 3,6 14,1 21,7 24,5 18,9 13,9 11 5,8 15,5 22,4 31,7 30,3 31,4 20,2 19,7 10,8 13,2 15,1 15,6 15,5 12,7 10,9 10 9,1 10,3 16,9 22 27,6 28,9 31 32,9 38,1 28,8 29 21,8 28,8 25,6 28,2 20,2 17,9 16,3 13,2 8,1 4,5 -0,1 0 2,3 2,8 2,9 0,1 3,5 8,6 13,8

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	12.6	11.2415363654928	0.401852082078905	13.5566115524283	-1.35846363450716
2	15.7	17.8929639591765	0.0151888826402476	13.4918471581833	2.19296395917649
3	13.2	14.0843905072467	-1.11147327118500	13.4270827639383	0.884390507246726
4	20.3	28.2379608497765	-1.06414577840815	13.4261849286316	7.93796084977653
5	12.8	13.6315274673084	-1.45681456063336	13.4252870933250	0.831527467308387
6	8	4.138463782767	-1.59318245966145	13.4547186768945	-3.861536217233
7	0.9	-9.83460143098397	-1.84954882947996	13.4841502604639	-10.7346014309840
8	3.6	-4.96471194576904	-1.26297234214039	13.4276842879094	-8.56471194576904
9	14.1	14.7451782583041	0.083603426340928	13.3712183153549	0.645178258304128
10	21.7	27.9502637209878	1.91243489674281	13.5373013822694	6.25026372098778
11	24.5	32.6153485955136	2.68126695530253	13.7033844491839	8.11534859551358
12	18.9	19.5394308194771	3.24379148490463	15.0167776956182	0.639430819477145
13	13.9	11.0679769758685	0.401852082078905	16.3301709420526	-2.83202302413147
14	11	4.19227626609496	0.0151888826402476	17.7925348512648	-6.80772373390504
15	5.8	-6.54342548929202	-1.11147327118500	19.2548987604770	-12.3434254892920
16	15.5	12.3349236161878	-1.06414577840815	19.7292221622204	-3.16507638381225
17	22.4	26.0532689966696	-1.45681456063336	20.2035455639638	3.65326899666957
18	31.7	44.816974690969	-1.59318245966145	20.1762077686924	13.1169746909690
19	30.3	42.3006788560589	-1.84954882947996	20.1488699734211	12.0006788560589
20	31.4	44.0008302123807	-1.26297234214039	20.0621421297597	12.6008302123807
21	20.2	20.3409822875607	0.083603426340928	19.9754142860984	0.140982287560696
22	19.7	18.207316290798	1.91243489674281	19.2802488124592	-1.49268370920200
23	10.8	0.333649705877455	2.68126695530253	18.58508333882	-10.4663502941225
24	13.2	5.9516508985873	3.24379148490463	17.2045576165081	-7.2483491014127
25	15.1	13.9741160237250	0.401852082078905	15.8240318941961	-1.12588397627504
26	15.6	16.329321084309	0.0151888826402476	14.8554900330508	0.729321084308992
27	15.5	18.2245250992796	-1.11147327118500	13.8869481719054	2.72452509927961
28	12.7	12.3758452953743	-1.06414577840815	14.0883004830339	-0.324154704625734
29	10.9	8.96716176647097	-1.45681456063336	14.2896527941624	-1.93283823352903
30	10	6.24682117529538	-1.59318245966145	15.3463612843661	-3.75317882470462
31	9.1	3.64647905491021	-1.84954882947996	16.4030697745697	-5.45352094508979
32	10.3	3.92398103521132	-1.26297234214039	17.9389913069291	-6.37601896478868
33	16.9	14.2414837343707	0.083603426340928	19.4749128392884	-2.65851626562933
34	22	20.8582213925898	1.91243489674281	21.2293437106674	-1.14177860741024
35	27.6	29.534958462651	2.68126695530253	22.9837745820465	1.93495846265101
36	28.9	29.9780192071162	3.24379148490463	24.5781893079791	1.07801920711624
37	31	35.4255438840093	0.401852082078905	26.1726040339118	4.42554388400929
38	32.9	38.572894932946	0.0151888826402476	27.2119161844138	5.67289493294599
39	38.1	49.0602449362693	-1.11147327118500	28.2512283349157	10.9602449362693
40	28.8	30.4392238024025	-1.06414577840815	28.2249219760056	1.63922380240252
41	29	31.2581989435378	-1.45681456063336	28.1986156170955	2.25819894353782
42	21.8	18.1918441393956	-1.59318245966145	27.0013383202659	-3.60815586060442
43	28.8	33.6454878060437	-1.84954882947996	25.8040610234362	4.84548780604374
44	25.6	28.7152896275461	-1.26297234214039	23.7476827145943	3.11528962754606
45	28.2	34.6250921679066	0.083603426340928	21.6913044057524	6.42509216790662
46	20.2	19.1976949317568	1.91243489674281	19.2898701715004	-1.00230506824323
47	17.9	16.2302971074491	2.68126695530253	16.8884359372484	-1.66970289255094
48	16.3	14.7509939860352	3.24379148490463	14.6052145290602	-1.54900601396478
49	13.2	13.6761547970492	0.401852082078905	12.3219931208719	0.476154797049196
50	8.1	5.87631456424334	0.0151888826402476	10.3084965531164	-2.22368543575666
51	4.5	1.81647328582408	-1.11147327118500	8.29499998536092	-2.68352671417592
52	-0.1	-6.53298960627676	-1.06414577840815	7.39713538468491	-6.43298960627676
53	0	-5.04245622337555	-1.45681456063336	6.4992707840089	-5.04245622337555
54	2.3	0.381727004391410	-1.59318245966145	5.81145545527004	-1.91827299560859
55	2.8	2.32590870294878	-1.84954882947996	5.12364012653118	-0.474091297051217
56	2.9	2.52529647743295	-1.26297234214039	4.53767586470745	-0.374703522567055
57	0.1	-3.83531502922465	0.083603426340928	3.95171160288372	-3.93531502922465
58	3.5	1.61087268258275	1.91243489674281	3.47669242067444	-1.88912731741725
59	8.6	11.5170598062323	2.68126695530253	3.00167323846516	2.91705980623231
60	13.8	21.7329682878351	3.24379148490463	2.62324022726031	7.93296828783506

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/1qrrg1259943837.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/1qrrg1259943837.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/2bz4d1259943837.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/2bz4d1259943837.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/3gp3s1259943837.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/3gp3s1259943837.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/4p8c11259943837.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259943863bsq8c88jqs0bfdf/4p8c11259943837.ps (open in new window)

Parameters (Session):

par1 = 0.01 ; par2 = 0.99 ; par3 = 0.005 ;

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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