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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: Thu, 03 Dec 2009 11:15:22 -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/03/t1259864252yzsx4097ucbgxs0.htm/, Retrieved Thu, 03 Dec 2009 19:17:37 +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/03/t1259864252yzsx4097ucbgxs0.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 7.1 7.2 7.1 6.9 7 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 8.1 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	611	0	62
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	8.39879041351494	-0.0371139635924531	7.83832355007751	0.298790413514941
2	7.7	7.82207879298828	-0.221989450113574	7.7999106571253	0.122078792988280
3	7.5	7.55617707684427	-0.317674841017347	7.76149776417308	0.0561770768442695
4	7.6	7.57245126837392	-0.101888837193282	7.72943756881936	-0.0275487316260774
5	7.8	7.66872560920646	0.233897017327904	7.69737737346564	-0.131274390793544
6	7.8	7.58166695836336	0.347861048757142	7.6704719928795	-0.218333041636645
7	7.8	7.69460829507833	0.261825092628304	7.64356661229337	-0.105391704921669
8	7.5	7.25452217234998	0.124636396911644	7.62084143073838	-0.245477827650022
9	7.5	7.49443621136643	-0.0925524605498187	7.59811624918339	-0.00556378863357487
10	7.1	6.88858905660276	-0.296129703128572	7.60754064652581	-0.211410943397238
11	7.5	7.30274190183907	0.0802930542926967	7.61696504386823	-0.197258098160926
12	7.5	7.32408309528293	0.0188371228413269	7.65707978187575	-0.175916904717073
13	7.6	7.53991944370919	-0.0371139635924531	7.69719451988326	-0.0600805562908091
14	7.7	7.88201863101455	-0.221989450113574	7.73997081909903	0.182018631014545
15	7.7	7.93492772270255	-0.317674841017347	7.7827471183148	0.234927722702549
16	7.9	8.11076165705711	-0.101888837193282	7.79112718013617	0.210761657057111
17	8.1	8.16659574071455	0.233897017327904	7.79950724195755	0.0665957407145497
18	8.2	8.30460947256587	0.347861048757142	7.74752947867698	0.104609472565873
19	8.2	8.44262319197527	0.261825092628304	7.69555171539642	0.242623191975272
20	8.2	8.66246158006728	0.124636396911644	7.61290202302108	0.462461580067277
21	7.9	8.36230012990409	-0.0925524605498187	7.53025233064573	0.462300129904084
22	7.3	7.45129036062526	-0.296129703128572	7.44483934250331	0.151290360625257
23	6.9	6.36028059134641	0.0802930542926967	7.3594263543609	-0.539719408653591
24	6.6	5.91435384938484	0.0188371228413269	7.26680902777384	-0.685646150615162
25	6.7	6.26292226240568	-0.0371139635924531	7.17419170118678	-0.437077737594322
26	6.9	6.93239184719101	-0.221989450113574	7.08959760292256	0.0323918471910121
27	7	7.312671336359	-0.317674841017347	7.00500350465835	0.312671336358996
28	7.1	7.34617664490531	-0.101888837193282	6.95571219228797	0.246176644905312
29	7.2	7.25968210275451	0.233897017327904	6.90642087991759	0.0596821027545102
30	7.1	6.97647847572306	0.347861048757142	6.87566047551979	-0.123521524276935
31	6.9	6.6932748362497	0.261825092628304	6.844900071122	-0.206725163750303
32	7	7.07650035578307	0.124636396911644	6.79886324730528	0.0765003557830735
33	6.8	6.93972603706125	-0.0925524605498187	6.75282642348857	0.139726037061252
34	6.4	6.38887781381601	-0.296129703128572	6.70725188931257	-0.0111221861839930
35	6.7	6.65802959057074	0.0802930542926967	6.66167735513657	-0.0419704094292621
36	6.6	6.55946061546232	0.0188371228413269	6.62170226169635	-0.0405393845376816
37	6.4	6.25538679533631	-0.0371139635924531	6.58172716825614	-0.144613204663688
38	6.3	6.29127126110243	-0.221989450113574	6.53071818901114	-0.00872873889756853
39	6.2	6.23796563125120	-0.317674841017347	6.47970920976614	0.037965631251204
40	6.5	6.64847237986478	-0.101888837193282	6.4534164573285	0.148472379864779
41	6.8	6.93897927778123	0.233897017327904	6.42712370489086	0.138979277781233
42	6.8	6.80815177998295	0.347861048757142	6.4439871712599	0.00815177998295358
43	6.4	6.07732426974275	0.261825092628304	6.46085063762894	-0.322675730257249
44	6.1	5.60144912148213	0.124636396911644	6.47391448160622	-0.498550878517865
45	5.8	5.20557413496632	-0.0925524605498187	6.4869783255835	-0.59442586503368
46	6.1	5.99688144065977	-0.296129703128572	6.4992482624688	-0.103118559340230
47	7.2	7.8081887463532	0.0802930542926967	6.5115181993541	0.608188746353196
48	7.3	8.00570265155849	0.0188371228413269	6.57546022560019	0.705702651558486
49	6.9	7.19771171174619	-0.0371139635924531	6.63940225184627	0.297711711746187
50	6.1	5.6774338568925	-0.221989450113574	6.74455559322107	-0.422566143107498
51	5.8	5.06796590642147	-0.317674841017347	6.84970893459588	-0.732034093578531
52	6.2	5.53849237410057	-0.101888837193282	6.96339646309271	-0.661507625899429
53	7.1	6.88901899108255	0.233897017327904	7.07708399158954	-0.210981008917448
54	7.7	7.85157332892625	0.347861048757142	7.20056562231661	0.151573328926246
55	7.9	8.21412765432802	0.261825092628304	7.32404725304368	0.314127654328017
56	7.7	7.82099318121975	0.124636396911644	7.45437042186861	0.120993181219746
57	7.4	7.30785886985628	-0.0925524605498187	7.58469359069354	-0.0921411301437214
58	7.5	7.57501258395088	-0.296129703128572	7.72111711917769	0.0750125839508815
59	8	8.06216629804546	0.0802930542926967	7.85754064766184	0.0621662980454607
60	8.1	8.18349238273097	0.0188371228413269	7.9976704944277	0.0834923827309684
61	8	7.89931362239889	-0.0371139635924531	8.13780034119356	-0.100686377601111

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/1fqfz1259864120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/1fqfz1259864120.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/2hbdw1259864120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/2hbdw1259864120.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/392rr1259864120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/392rr1259864120.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/4fnq01259864120.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259864252yzsx4097ucbgxs0/4fnq01259864120.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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