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WS9

*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 13:13:58 -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/t1259957728qjpjtnvw1vmjp2x.htm/, Retrieved Fri, 04 Dec 2009 21:15:34 +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/t1259957728qjpjtnvw1vmjp2x.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 «

14,3 14,2 15,9 15,3 15,5 15,1 15 12,1 15,8 16,9 15,1 13,7 14,8 14,7 16 15,4 15 15,5 15,1 11,7 16,3 16,7 15 14,9 14,6 15,3 17,9 16,4 15,4 17,9 15,9 13,9 17,8 17,9 17,4 16,7 16 16,6 19,1 17,8 17,2 18,6 16,3 15,1 19,2 17,7 19,1 18 17,5 17,8 21,1 17,2 19,4 19,8 17,6 16,2 19,5 19,9 20 17,3

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	1 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	14.3	14.5055286346968	-0.769919697682463	14.8643910629857	0.205528634696785
2	14.2	14.0742534074969	-0.554651214080902	14.8803978065840	-0.125746592503061
3	15.9	15.2429785070513	1.66061694276646	14.8964045501822	-0.657021492948704
4	15.3	15.6591152640235	0.0306876059942150	14.9101971299823	0.359115264023481
5	15.5	16.0152535763458	0.0607567138718357	14.9239897097824	0.515253576345803
6	15.1	14.3700384024409	0.893087764214257	14.9368738333448	-0.729961597559077
7	15	15.6048244048515	-0.554582361758829	14.9497579569073	0.604824404851549
8	12.1	12.0238279496140	-2.78797194115725	14.9641439915433	-0.076172050386024
9	15.8	15.5428311676223	1.07863880619848	14.9785300261793	-0.257168832377735
10	16.9	17.6990932274996	1.11384166522624	14.9870651072742	0.799093227499586
11	15.1	14.6553545031669	0.549045308464032	14.9956001883691	-0.444645496833129
12	13.7	13.1263659992336	-0.71954950149192	14.9931835022583	-0.573634000766360
13	14.8	15.379152881535	-0.769919697682463	14.9907668161475	0.579152881535
14	14.7	14.9618341393319	-0.554651214080902	14.9928170747490	0.261834139331885
15	16	15.3445157238830	1.66061694276646	14.9948673333506	-0.655484276117027
16	15.4	15.7648184329994	0.0306876059942150	15.0044939610064	0.364818432999428
17	15	14.9251226974660	0.0607567138718357	15.0141205886621	-0.074877302533979
18	15.5	15.0648152738607	0.893087764214257	15.0420969619251	-0.435184726139331
19	15.1	15.6845090265708	-0.554582361758829	15.070073335188	0.584509026570819
20	11.7	11.057059163064	-2.78797194115725	15.1309127780932	-0.64294083693599
21	16.3	16.3296089728031	1.07863880619848	15.1917522209985	0.0296089728030591
22	16.7	16.9985694382563	1.11384166522624	15.2875888965175	0.298569438256269
23	15	14.0675291194994	0.549045308464032	15.3834255720365	-0.932470880500558
24	14.9	15.0158368808434	-0.71954950149192	15.5037126206485	0.115836880843409
25	14.6	14.3459200284220	-0.769919697682463	15.6239996692605	-0.254079971578037
26	15.3	15.3914385685573	-0.554651214080902	15.7632126455236	0.09143856855726
27	17.9	18.2369574354468	1.66061694276646	15.9024256217868	0.336957435446752
28	16.4	16.718647174543	0.0306876059942150	16.0506652194628	0.318647174542992
29	15.4	14.5403384689894	0.0607567138718357	16.1989048171388	-0.859661531010632
30	17.9	18.5700078900127	0.893087764214257	16.3369043457731	0.670007890012666
31	15.9	15.8796784873515	-0.554582361758829	16.4749038744074	-0.0203215126485254
32	13.9	13.9948576595404	-2.78797194115725	16.5931142816169	0.0948576595403772
33	17.8	17.8100365049751	1.07863880619848	16.7113246888264	0.0100365049751403
34	17.9	17.8669180579048	1.11384166522624	16.8192402768690	-0.0330819420951904
35	17.4	17.3237988266244	0.549045308464032	16.9271558649115	-0.0762011733755585
36	16.7	17.1024268257636	-0.71954950149192	17.0171226757283	0.402426825763591
37	16	15.6628302111373	-0.769919697682463	17.1070894865451	-0.337169788862663
38	16.6	16.5738896773568	-0.554651214080902	17.1807615367241	-0.0261103226432411
39	19.1	19.2849494703304	1.66061694276646	17.2544335869032	0.184949470330380
40	17.8	18.2384053052512	0.0306876059942150	17.3309070887546	0.438405305251163
41	17.2	16.9318626955221	0.0607567138718357	17.4073805906061	-0.268137304477925
42	18.6	18.8035140235161	0.893087764214257	17.5033982122696	0.203514023516099
43	16.3	15.5551665278256	-0.554582361758829	17.5994158339332	-0.744833472174367
44	15.1	15.2799706817059	-2.78797194115725	17.7080012594514	0.179970681705861
45	19.2	19.5047745088319	1.07863880619848	17.8165866849696	0.304774508831944
46	17.7	16.3636973845136	1.11384166522624	17.9224609502602	-1.33630261548641
47	19.1	19.6226194759852	0.549045308464032	18.0283352155508	0.522619475985195
48	18	18.5820931040295	-0.71954950149192	18.1374563974624	0.582093104029497
49	17.5	17.5233421183084	-0.769919697682463	18.2465775793741	0.0233421183083991
50	17.8	17.8122028066369	-0.554651214080902	18.3424484074441	0.0122028066368500
51	21.1	22.1010638217195	1.66061694276646	18.4383192355140	1.00106382171951
52	17.2	15.8789358059494	0.0306876059942150	18.4903765880564	-1.32106419405059
53	19.4	20.1968093455295	0.0607567138718357	18.5424339405987	0.796809345529454
54	19.8	20.1252235540461	0.893087764214257	18.5816886817397	0.325223554046065
55	17.6	17.1336389388782	-0.554582361758829	18.6209434228806	-0.466361061121816
56	16.2	16.5329445808413	-2.78797194115725	18.6550273603159	0.332944580841321
57	19.5	19.2322498960503	1.07863880619848	18.6891112977512	-0.267750103949677
58	19.9	19.9664074808011	1.11384166522624	18.7197508539726	0.066407480801125
59	20	20.7005642813419	0.549045308464032	18.7503904101941	0.700564281341894
60	17.3	16.5407693465616	-0.71954950149192	18.7787801549303	-0.759230653438419

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/1l8bf1259957636.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/1l8bf1259957636.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/2duos1259957636.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/2duos1259957636.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/3qjhg1259957636.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/3qjhg1259957636.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/4f43k1259957636.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259957728qjpjtnvw1vmjp2x/4f43k1259957636.ps (open in new window)

Parameters (Session):

par1 = 0.2 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

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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