Home » date » 2009 » Dec » 04 »

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: Fri, 04 Dec 2009 05:21:13 -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/t1259929407vbcwd9cn63kd9b8.htm/, Retrieved Fri, 04 Dec 2009 13:23:33 +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/t1259929407vbcwd9cn63kd9b8.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 «

19 18 19 19 22 23 20 14 14 14 15 11 17 16 20 24 23 20 21 19 23 23 23 23 27 26 17 24 26 24 27 27 26 24 23 23 24 17 21 19 22 22 18 16 14 12 14 16 8 3 0 5 1 1 3 6 7 8 14 14 13

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	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	19	16.5794726021753	1.03235054104375	20.388176856781	-2.42052739782475
2	18	17.9886985481575	-1.9169314554759	19.9282329073184	-0.0113014518424599
3	19	20.7625041635123	-2.23079312136806	19.4682889578557	1.76250416351234
4	19	18.3054067181281	0.660724143924287	19.0338691379476	-0.69459328187191
5	22	24.0483090239063	1.35224165805421	18.5994493180395	2.04830902390627
6	23	27.1994838743161	0.573790664277994	18.2267254614059	4.19948387431609
7	20	21.7506569828584	0.39534141236926	17.8540016047723	1.75065698285842
8	14	11.3164171196300	-0.857319827159091	17.5409027075291	-2.68358288036999
9	14	11.0821777540783	-0.309981564364153	17.2278038102858	-2.91782224592169
10	14	11.6123226040687	-0.694406986287024	17.0820843822183	-2.38767739593131
11	15	11.9424682005736	1.1211668452756	16.9363649541508	-3.05753179942642
12	11	3.96684807555007	0.873823516462943	17.159328407987	-7.03315192444993
13	17	15.5853575971331	1.03235054104375	17.3822918618232	-1.41464240286691
14	16	16.0153217418746	-1.9169314554759	17.9016097136013	0.0153217418745726
15	20	23.8098655559886	-2.23079312136806	18.4209275653795	3.80986555598856
16	24	28.1695431459581	0.660724143924287	19.1697327101176	4.16954314595814
17	23	24.7292204870902	1.35224165805421	19.9185378548556	1.72922048709015
18	20	18.7797288291388	0.573790664277994	20.6464805065832	-1.22027117086124
19	21	20.2302354293199	0.39534141236926	21.3744231583109	-0.769764570680117
20	19	17.0404348651263	-0.857319827159091	21.8168849620327	-1.95956513487366
21	23	24.0506347986095	-0.309981564364153	22.2593467657546	1.05063479860952
22	23	24.1978226689064	-0.694406986287024	22.4965843173806	1.19782266890643
23	23	22.1450112857179	1.1211668452756	22.7338218690065	-0.854988714282147
24	23	22.0772804574833	0.873823516462943	23.0488960260537	-0.922719542516653
25	27	29.6036792758554	1.03235054104375	23.3639701831009	2.60367927585537
26	26	30.1815384693696	-1.9169314554759	23.7353929861063	4.18153846936957
27	17	12.1239773322563	-2.23079312136806	24.1068157891118	-4.87602266774373
28	24	23.0460549716213	0.660724143924287	24.2932208844544	-0.953945028378676
29	26	26.1681323621488	1.35224165805421	24.479625979797	0.168132362148807
30	24	22.9984478087803	0.573790664277994	24.4277615269417	-1.00155219121974
31	27	29.2287615135442	0.39534141236926	24.3758970740865	2.22876151354423
32	27	30.7010085390211	-0.857319827159091	24.1563112881379	3.70100853902114
33	26	28.3732560621748	-0.309981564364153	23.9367255021894	2.37325606217477
34	24	25.0632564123993	-0.694406986287024	23.6311505738877	1.06325641239929
35	23	21.5532575091383	1.1211668452756	23.3255756455861	-1.44674249086167
36	23	22.3255098600014	0.873823516462943	22.8006666235356	-0.674490139998579
37	24	24.6918918574710	1.03235054104375	22.2757576014852	0.691891857471045
38	17	14.3977260030349	-1.9169314554759	21.5192054524410	-2.60227399696515
39	21	23.4681398179712	-2.23079312136806	20.7626533033969	2.46813981797116
40	19	17.4185426836807	0.660724143924287	19.9207331723951	-1.58145731631935
41	22	23.5689453005526	1.35224165805421	19.0788130413932	1.56894530055258
42	22	25.2877044618297	0.573790664277994	18.1385048738923	3.28770446182975
43	18	18.4064618812394	0.39534141236926	17.1981967063913	0.406461881239441
44	16	16.9138071487343	-0.857319827159091	15.9435126784248	0.913807148734259
45	14	13.6211529139058	-0.309981564364153	14.6888286504584	-0.378847086094213
46	12	11.5475051095578	-0.694406986287024	13.1469018767293	-0.452494890442246
47	14	15.2738580517242	1.1211668452756	11.6049751030002	1.27385805172423
48	16	21.0432565858975	0.873823516462943	10.0829198976396	5.04325658589749
49	8	6.40678476667728	1.03235054104375	8.56086469227896	-1.59321523332272
50	3	0.432365627144699	-1.9169314554759	7.4845658283312	-2.5676343728553
51	0	-4.17747384301538	-2.23079312136806	6.40826696438344	-4.17747384301538
52	5	3.07364791677477	0.660724143924287	6.26562793930094	-1.92635208322523
53	1	-5.47523057227266	1.35224165805421	6.12298891421845	-6.47523057227266
54	1	-5.1016158648699	0.573790664277994	6.52782520059191	-6.1016158648699
55	3	-1.32800289933463	0.39534141236926	6.93266148696538	-4.32800289933463
56	6	5.45729259748866	-0.857319827159091	7.40002722967043	-0.542707402511338
57	7	6.44258859198867	-0.309981564364153	7.86739297237548	-0.55741140801133
58	8	8.23080359847971	-0.694406986287024	8.46360338780731	0.230803598479714
59	14	17.8190193514853	1.1211668452756	9.05981380323914	3.81901935148526
60	14	17.3327782617739	0.873823516462943	9.7933982217632	3.33277826177386
61	13	14.440666818669	1.03235054104375	10.5269826402873	1.44066681866899

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/1js5m1259929271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/1js5m1259929271.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/2pho11259929271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/2pho11259929271.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/3cl7d1259929271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/3cl7d1259929271.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/4rrqx1259929271.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259929407vbcwd9cn63kd9b8/4rrqx1259929271.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ; par9 = 1 ;

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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

We may request personal information to be submitted to our servers in order to be able to:

personalize online software applications according to your needs
enforce strict security rules with respect to the data that you upload (e.g. statistical data)
manage user sessions of online applications
alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by