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Workshop 9-7

*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 15:04:42 -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/t1259964363li0n02oynt2rhpw.htm/, Retrieved Fri, 04 Dec 2009 23:06:08 +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/t1259964363li0n02oynt2rhpw.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:

WS 9-7

Dataseries X:

» Textbox « » Textfile « » CSV «

5.7 6.1 6 5.9 5.8 5.7 5.6 5.4 5.4 5.5 5.6 5.7 5.9 6.1 6 5.8 5.8 5.7 5.5 5.3 5.2 5.2 5 5.1 5.1 5.2 4.9 4.8 4.5 4.5 4.4 4.4 4.2 4.1 3.9 3.8 3.9 4.2 4.1 3.8 3.6 3.7 3.5 3.4 3.1 3.1 3.1 3.2 3.3 3.5 3.6 3.5 3.3 3.2 3.1 3.2 3 3 3.1 3.4

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	5.7	5.64390068191752	0.0820312972922284	5.67406802079025	-0.0560993180824836
2	6.1	6.16026723946038	0.361679898295257	5.67805286224436	0.06026723946038
3	6	6.01663383621376	0.301328460087772	5.68203770369847	0.0166338362137592
4	5.9	5.9408111754613	0.172368480282047	5.68682034425665	0.0408111754613039
5	5.8	5.86498850163872	0.0434085135464493	5.69160298481483	0.0649885016387222
6	5.7	5.67097412301982	0.0320577024610755	5.6969681745191	-0.0290258769801781
7	5.6	5.57695982282192	-0.0792931870453021	5.70233336422338	-0.0230401771780766
8	5.4	5.22199642533729	-0.128642488921607	5.70664606358432	-0.178003574662709
9	5.4	5.34703306706318	-0.257991830008438	5.71095876294525	-0.0529669329368154
10	5.5	5.50839982213336	-0.220631963758278	5.71223214162492	0.00839982213335677
11	5.6	5.70976665562454	-0.223272175929134	5.71350552030459	0.109766655624544
12	5.7	5.77116395064941	-0.0830426668373444	5.71187871618793	0.0711639506494128
13	5.9	6.0077167906365	0.0820312972922284	5.71025191207127	0.107716790636498
14	6.1	6.13993889993326	0.361679898295257	5.69838120177149	0.0399388999332562
15	6	6.01216104844053	0.301328460087772	5.6865104914717	0.0121610484405288
16	5.8	5.77255845736976	0.172368480282047	5.6550730623482	-0.0274415426302435
17	5.8	5.93295585322886	0.0434085135464493	5.6236356332247	0.132955853228857
18	5.7	5.79683137990483	0.0320577024610755	5.57111091763409	0.096831379904831
19	5.5	5.56070698500181	-0.0792931870453021	5.5185862020435	0.060706985001806
20	5.3	5.28412094494497	-0.128642488921607	5.44452154397664	-0.0158790550550316
21	5.2	5.28753494409866	-0.257991830008438	5.37045688590978	0.0875349440986595
22	5.2	5.3432424477535	-0.220631963758278	5.27738951600478	0.143242447753495
23	5	5.03895002982935	-0.223272175929134	5.18432214609979	0.0389500298293477
24	5.1	5.19848205694164	-0.0830426668373444	5.08456060989571	0.098482056941637
25	5.1	5.13316962901614	0.0820312972922284	4.98479907369163	0.0331696290161432
26	5.2	5.14588071165869	0.361679898295257	4.89243939004605	-0.0541192883413109
27	4.9	4.69859183351175	0.301328460087772	4.80007970640048	-0.201408166488251
28	4.8	4.71634448775882	0.172368480282047	4.71128703195913	-0.0836555122411777
29	4.5	4.33409712893577	0.0434085135464493	4.62249435751778	-0.165902871064230
30	4.5	4.4343434523518	0.0320577024610755	4.53359884518713	-0.0656565476482012
31	4.4	4.43458985418883	-0.0792931870453021	4.44470333285647	0.0345898541888303
32	4.4	4.56724152065656	-0.128642488921607	4.36140096826505	0.167241520656559
33	4.2	4.37989322633482	-0.257991830008438	4.27809860367362	0.179893226334816
34	4.1	4.22208647767382	-0.220631963758278	4.19854548608446	0.122086477673821
35	3.9	3.90427980743384	-0.223272175929134	4.11899236849529	0.00427980743384104
36	3.8	3.64483051807001	-0.0830426668373444	4.03821214876733	-0.155169481929986
37	3.9	3.7605367736684	0.0820312972922284	3.95743192903937	-0.139463226331596
38	4.2	4.16245823014857	0.361679898295257	3.87586187155617	-0.0375417698514293
39	4.1	4.10437972583925	0.301328460087772	3.79429181407298	0.00437972583925106
40	3.8	3.70574838309000	0.172368480282047	3.72188313662795	-0.094251616909995
41	3.6	3.50711702727063	0.0434085135464493	3.64947445918292	-0.0928829727293672
42	3.7	3.77713902332322	0.0320577024610755	3.59080327421571	0.0771390233232174
43	3.5	3.54716109779681	-0.0792931870453021	3.5321320892485	0.0471610977968053
44	3.4	3.44492759474385	-0.128642488921607	3.48371489417775	0.0449275947438523
45	3.1	3.02269413090143	-0.257991830008438	3.43529769910701	-0.077305869098573
46	3.1	3.02356633163113	-0.220631963758278	3.39706563212714	-0.0764336683688667
47	3.1	3.06443861078185	-0.223272175929134	3.35883356514728	-0.0355613892181452
48	3.2	3.15409680902966	-0.0830426668373444	3.32894585780769	-0.0459031909703409
49	3.3	3.21891055223968	0.0820312972922284	3.29905815046809	-0.0810894477603203
50	3.5	3.35796895560346	0.361679898295257	3.28035114610129	-0.142031044396545
51	3.6	3.63702739817774	0.301328460087772	3.26164414173448	0.0370273981777443
52	3.5	3.56378065875596	0.172368480282047	3.26385086096199	0.0637806587559648
53	3.3	3.29053390626406	0.0434085135464493	3.26605758018949	-0.0094660937359401
54	3.2	3.09555585696474	0.0320577024610755	3.27238644057418	-0.104444143035258
55	3.1	3.00057788608643	-0.0792931870453021	3.27871530095887	-0.099422113913572
56	3.2	3.24257900534302	-0.128642488921607	3.28606348357859	0.0425790053430211
57	3	2.96458016381014	-0.257991830008438	3.29341166619830	-0.0354198361898592
58	3	2.91872153488000	-0.220631963758278	3.30191042887827	-0.0812784651199956
59	3.1	3.11286298437088	-0.223272175929134	3.31040919155825	0.0128629843708832
60	3.4	3.56296854014578	-0.0830426668373444	3.32007412669157	0.162968540145777

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/159z81259964280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/159z81259964280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/2ty3w1259964280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/2ty3w1259964280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/3nnkq1259964280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/3nnkq1259964280.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/4fmf11259964280.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259964363li0n02oynt2rhpw/4fmf11259964280.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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