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Paper

*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, 28 Dec 2010 17:08:24 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd.htm/, Retrieved Tue, 28 Dec 2010 18:06:21 +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/2010/Dec/28/t1293555980vitmktculffpcbd.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

9.3 14.2 17.3 23 16.3 18.4 14.2 9.1 5.9 7.2 6.8 8 14.3 14.6 17.5 17.2 17.2 14.1 10.4 6.8 4.1 6.5 6.1 6.3 9.3 16.4 16.1 18 17.6 14 10.5 6.9 2.8 0.7 3.6 6.7 12.5 14.4 16.5 18.7 19.4 15.8 11.3 9.7 2.9 0.1 2.5 6.7 10.3 11.2 17.4 20.5 17 14.2 10.6 6.1

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	561	0	57
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	9.3	7.27787551221526	0.0206500189642453	11.3014744688205	-2.02212448778474
2	14.2	13.8229943766453	3.05375084093265	11.5232547824221	-0.377005623354743
3	17.3	16.9881162911357	5.86684861284062	11.7450350960237	-0.311883708864309
4	23	25.6391023899078	8.42280575612615	11.938091853966	2.63910238990784
5	16.3	13.9900833196333	6.4787680684584	12.1311486119083	-2.30991668036671
6	18.4	20.1947915050885	4.30685145264669	12.2983570422648	1.79479150508853
7	14.2	15.4994976197142	0.434936907664548	12.4655654726212	1.29949761971421
8	9.1	8.84112869650511	-3.24515996496951	12.6040312684644	-0.258871303494887
9	5.9	6.29236914128705	-7.2348662055946	12.7424970643076	0.392369141287048
10	7.2	9.24471900437253	-7.52797701598902	12.6832580116165	2.04471900437253
11	6.8	7.37206906519959	-6.396088024125	12.6240189589254	0.57206906519959
12	8	7.81805337693192	-4.18052050067075	12.3624671237388	-0.181946623068075
13	14.3	16.4784346924835	0.0206500189642453	12.1009152885522	2.17843469248351
14	14.6	14.3114031059102	3.05375084093265	11.8348460531572	-0.28859689408981
15	17.5	17.5643745693973	5.86684861284062	11.5687768177621	0.0643745693973088
16	17.2	14.5745593233213	8.42280575612615	11.4026349205526	-2.62544067667874
17	17.2	16.6847389081985	6.4787680684584	11.2364930233431	-0.515261091801497
18	14.1	12.7594727321467	4.30685145264669	11.1336758152066	-1.34052726785329
19	10.4	9.33420448526537	0.434936907664548	11.0308586070701	-1.06579551473463
20	6.8	5.84079317473804	-3.24515996496951	11.0043667902315	-0.959206825261957
21	4.1	4.45699123220176	-7.2348662055946	10.9778749733928	0.356991232201755
22	6.5	9.51763148669913	-7.52797701598902	11.0103455292899	3.01763148669913
23	6.1	7.55327193893807	-6.396088024125	11.0428160851869	1.45327193893807
24	6.3	5.74605472505955	-4.18052050067075	11.0344657756112	-0.55394527494045
25	9.3	7.55323451500028	0.0206500189642453	11.0261154660355	-1.74676548499972
26	16.4	18.838333939098	3.05375084093265	10.9079152199694	2.43833393909797
27	16.1	15.5434364132561	5.86684861284062	10.7897149739033	-0.556563586743907
28	18	16.9786196581408	8.42280575612615	10.598574585733	-1.02138034185915
29	17.6	18.3137977339789	6.4787680684584	10.4074341975627	0.713797733978899
30	14	13.3642631472466	4.30685145264669	10.3288854001067	-0.635736852753443
31	10.5	10.3147264896847	0.434936907664548	10.2503366026508	-0.185273510315341
32	6.9	6.76913710495947	-3.24515996496951	10.27602286001	-0.130862895040531
33	2.8	2.53315708822532	-7.2348662055946	10.3017091173693	-0.266842911774685
34	0.7	-1.46205745039481	-7.52797701598902	10.3900344663838	-2.16205745039481
35	3.6	3.11772820872663	-6.396088024125	10.4783598153984	-0.482271791273369
36	6.7	6.96228908572192	-4.18052050067075	10.6182314149488	0.262289085721925
37	12.5	14.2212469665365	0.0206500189642453	10.7581030144993	1.72124696653647
38	14.4	14.8575247164862	3.05375084093265	10.8887244425812	0.457524716486168
39	16.5	16.1138055164963	5.86684861284062	11.0193458706631	-0.386194483503695
40	18.7	17.9590283877051	8.42280575612615	11.0181658561687	-0.740971612294889
41	19.4	21.3042460898672	6.4787680684584	11.0169858416744	1.90424608986721
42	15.8	16.3939873001345	4.30685145264669	10.8991612472188	0.593987300134513
43	11.3	11.3837264395723	0.434936907664548	10.7813366527632	0.0837264395722528
44	9.7	11.9919239800575	-3.24515996496951	10.653235984912	2.29192398005752
45	2.9	2.50973088853383	-7.2348662055946	10.5251353170608	-0.39026911146617
46	0.1	-2.72100995822563	-7.52797701598902	10.4489869742146	-2.82100995822563
47	2.5	1.02324939275649	-6.396088024125	10.3728386313685	-1.47675060724351
48	6.7	7.24593107457508	-4.18052050067075	10.3345894260957	0.545931074575078
49	10.3	10.2830097602129	0.0206500189642453	10.2963402208228	-0.0169902397870842
50	11.2	9.10086323633162	3.05375084093265	10.2453859227357	-2.09913676366837
51	17.4	18.7387197625108	5.86684861284062	10.1944316246486	1.33871976251077
52	20.5	22.4136462725701	8.42280575612615	10.1635479713038	1.91364627257008
53	17	17.3885676135827	6.4787680684584	10.1326643179589	0.388567613582685
54	14.2	13.9760947874313	4.30685145264669	10.117053759922	-0.223905212568681
55	10.6	10.6636198904504	0.434936907664548	10.1014432018851	0.0636198904503988
56	6.1	5.35565354904449	-3.24515996496951	10.089506415925	-0.744346450955506

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/1rfe61293556100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/1rfe61293556100.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/2rfe61293556100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/2rfe61293556100.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/3k7d91293556100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/3k7d91293556100.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/4k7d91293556100.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/28/t1293555980vitmktculffpcbd/4k7d91293556100.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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