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Workshp 9: Decomposition by Loess

*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: Wed, 02 Dec 2009 10:44:22 -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/02/t1259775931fpnu8hg3w3ij8pb.htm/, Retrieved Wed, 02 Dec 2009 18:45:36 +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/02/t1259775931fpnu8hg3w3ij8pb.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 «

8.1 7.7 7.5 7.6 7.8 7.8 7.8 7.5 7.5 7.1 7.5 7.5 7.6 7.7 7.7 7.9 8.1 8.2 8.2 8.2 7.9 7.3 6.9 6.6 6.7 6.9 7.0 7.1 7.2 7.1 6.9 7.0 6.8 6.4 6.7 6.6 6.4 6.3 6.2 6.5 6.8 6.8 6.4 6.1 5.8 6.1 7.2 7.3 6.9 6.1 5.8 6.2 7.1 7.7 7.9 7.7 7.4 7.5 8.0 8.1

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	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	8.1	8.39216057270666	-0.0291718879475741	7.83701131524091	0.292160572706662
2	7.7	7.82521439428966	-0.22399717032237	7.79878277603271	0.125214394289662
3	7.5	7.55826843806555	-0.31882267489005	7.7605542368245	0.0582684380655456
4	7.6	7.57413420218201	-0.102803263272707	7.7286690610907	-0.0258657978179864
5	7.8	7.67000012314051	0.233215991502604	7.69678388535688	-0.129999876859487
6	7.8	7.58194226402027	0.348006983221638	7.6700507527581	-0.218057735979730
7	7.8	7.69388439182984	0.262797988010859	7.6433176201593	-0.106115608170161
8	7.5	7.25387791665098	0.125402976995365	7.62071910635365	-0.246122083349017
9	7.5	7.49387161138435	-0.0919922039323482	7.598120592548	-0.00612838861565379
10	7.1	6.88935952260179	-0.296886407152134	7.60752688455035	-0.210640477398213
11	7.5	7.3048474338192	0.0782193896281048	7.61693317655269	-0.195152566180796
12	7.5	7.3268946515011	0.0160307741732048	7.6570745743257	-0.173105348498900
13	7.6	7.53195591584887	-0.0291718879475741	7.6972159720987	-0.0680440841511283
14	7.7	7.8840215752723	-0.22399717032237	7.73997559505008	0.184021575272292
15	7.7	7.9360874568886	-0.31882267489005	7.78273521800145	0.236087456888597
16	7.9	8.11167980251511	-0.102803263272707	7.7911234607576	0.211679802515111
17	8.1	8.16727230498366	0.233215991502604	7.79951170351374	0.067272304983657
18	8.2	8.30445289527314	0.348006983221638	7.74754012150522	0.104452895273143
19	8.2	8.44163347249244	0.262797988010859	7.6955685394967	0.24163347249244
20	8.2	8.6616835605139	0.125402976995365	7.61291346249073	0.461683560513908
21	7.9	8.3617338184476	-0.0919922039323482	7.53025838548475	0.461733818447595
22	7.3	7.45205997128563	-0.296886407152134	7.4448264358665	0.152059971285635
23	6.9	6.36238612412365	0.0782193896281048	7.35939448624824	-0.537613875876348
24	6.6	5.91716540642297	0.0160307741732048	7.26680381940382	-0.682834593577025
25	6.7	6.25495873538818	-0.0291718879475741	7.1742131525594	-0.445041264611825
26	6.9	6.93439479212987	-0.22399717032237	7.0896023781925	0.0343947921298744
27	7	7.31383107106446	-0.31882267489005	7.00499160382559	0.313831071064456
28	7.1	7.34709479024488	-0.102803263272707	6.95570847302783	0.247094790244879
29	7.2	7.26035866626733	0.233215991502604	6.90642534223006	0.0603586662673328
30	7.1	6.97632189747302	0.348006983221638	6.87567111930534	-0.123678102526981
31	6.9	6.69228511560852	0.262797988010859	6.84491689638062	-0.20771488439148
32	7	7.0757223355282	0.125402976995365	6.79887468747644	0.0757223355281988
33	6.8	6.9391597253601	-0.0919922039323482	6.75283247857225	0.139159725360098
34	6.4	6.38964742472681	-0.296886407152134	6.70723898242532	-0.0103525752731874
35	6.7	6.6601351240935	0.0782193896281048	6.66164548627839	-0.0398648759064972
36	6.6	6.56227217329595	0.0160307741732048	6.62169705253084	-0.0377278267040477
37	6.4	6.24742326916428	-0.0291718879475741	6.5817486187833	-0.152576730835720
38	6.3	6.29327420673292	-0.22399717032237	6.53072296358945	-0.00672579326707545
39	6.2	6.23912536649445	-0.31882267489005	6.4796973083956	0.0391253664944538
40	6.5	6.64939052511698	-0.102803263272707	6.45341273815573	0.149390525116978
41	6.8	6.93965584058153	0.233215991502604	6.42712816791586	0.139655840581533
42	6.8	6.8079952008713	0.348006983221638	6.44399781590706	0.00799520087129935
43	6.4	6.07633454809088	0.262797988010859	6.46086746389826	-0.323665451909119
44	6.1	5.60067110081069	0.125402976995365	6.47392592219395	-0.499328899189314
45	5.8	5.20500782344271	-0.0919922039323482	6.48698438048964	-0.594992176557288
46	6.1	5.99765105251483	-0.296886407152134	6.4992353546373	-0.102348947485171
47	7.2	7.81029428158692	0.0782193896281048	6.51148632878497	0.610294281586923
48	7.3	8.00851421159835	0.0160307741732048	6.57545501422844	0.708514211598355
49	6.9	7.18974818827567	-0.0291718879475741	6.63942369967191	0.289748188275666
50	6.1	5.67943680570701	-0.22399717032237	6.74456036461536	-0.420563194292987
51	5.8	5.06912564533124	-0.31882267489005	6.8496970295588	-0.730874354668757
52	6.2	5.53272045282779	-0.102803263272707	6.97008281044491	-0.667279547172207
53	7.1	6.87631541716637	0.233215991502604	7.09046859133102	-0.223684582833626
54	7.7	7.83965138452715	0.348006983221638	7.21234163225122	0.139651384527146
55	7.9	8.20298733881773	0.262797988010859	7.33421467317141	0.302987338817731
56	7.7	7.81126505241067	0.125402976995365	7.46333197059396	0.111265052410672
57	7.4	7.29954293591583	-0.0919922039323482	7.59244926801652	-0.100457064084168
58	7.5	7.5686845585445	-0.296886407152134	7.72820184860763	0.0686845585445051
59	8	8.05782618117315	0.0782193896281048	7.86395442919874	0.0578261811731533
60	8.1	8.1803119560173	0.0160307741732048	8.0036572698095	0.0803119560172956

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/1hphc1259775859.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/1hphc1259775859.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/2npf11259775859.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/2npf11259775859.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/30mzq1259775859.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/30mzq1259775859.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/4cpz01259775859.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/02/t1259775931fpnu8hg3w3ij8pb/4cpz01259775859.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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