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 14:19:18 -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/t125996162856qql0l39tosa89.htm/, Retrieved Fri, 04 Dec 2009 22:20:33 +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/t125996162856qql0l39tosa89.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 «

1.4 1 -0.8 -2.9 -0.7 -0.7 1.5 3 3.2 3.1 3.9 1 1.3 0.8 1.2 2.9 3.9 4.5 4.5 3.3 2 1.5 1 2.1 3 4 5.1 4.5 4.2 3.3 2.7 1.8 1.4 0.5 -0.4 0.8 0.7 1.9 2 1.1 0.9 0.4 0.7 2.1 2.8 3.9 3.5 2 2 1.5 2.5 3.1 2.7 2.8 2.5 3 3.2 2.8 2.4 2 1.8 1.1 -1.5 -3.7

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	641	0	65
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	1.4	3.12603629919863	-0.0062422588886947	-0.319794040309932	1.72603629919863
2	1	2.08655735077468	0.00591255538706756	-0.0924699061617446	1.08655735077468
3	-0.8	-1.43625604670859	-0.298598181277853	0.134854227986443	-0.63625604670859
4	-2.9	-5.30062053099167	-0.855413904200338	0.356034435192003	-2.40062053099166
5	-0.7	-2.08554340021248	0.108328757814914	0.577214642397563	-1.38554340021248
6	-0.7	-2.13194629029434	-0.0437619542908838	0.775708244585221	-1.43194629029434
7	1.5	1.76165112154424	0.264147031682881	0.97420184677288	0.26165112154424
8	3	4.27948101099796	0.549649086916032	1.17086990208601	1.27948101099796
9	3.2	4.5773105338339	0.455151508766955	1.36753795739914	1.37731053383390
10	3.1	4.24545250767873	0.294992175581996	1.65955531673928	1.14545250767873
11	3.9	5.8335948373583	0.0148324865622772	1.95157267607942	1.93359483735831
12	1	0.273475194677400	-0.48899689611326	2.21552170143586	-0.7265248053226
13	1.3	0.126771532096391	-0.0062422588886947	2.47947072679230	-1.17322846790361
14	0.8	-0.978769559437219	0.00591255538706756	2.57285700405015	-1.77876955943722
15	1.2	0.0323548999698546	-0.298598181277853	2.666243281308	-1.16764510003015
16	2.9	4.02051691199172	-0.855413904200338	2.63489699220862	1.12051691199172
17	3.9	5.08812053907585	0.108328757814914	2.60355070310923	1.18812053907585
18	4.5	6.42351488213942	-0.0437619542908838	2.62024707215146	1.92351488213942
19	4.5	6.09890952712343	0.264147031682881	2.63694344119369	1.59890952712343
20	3.3	3.29495392932495	0.549649086916032	2.75539698375902	-0.00504607067505347
21	2	0.67099796490869	0.455151508766955	2.87385052632435	-1.32900203509131
22	1.5	-0.269975787264094	0.294992175581996	2.9749836116821	-1.76997578726409
23	1	-1.09094918360212	0.0148324865622772	3.07611669703984	-2.09094918360212
24	2.1	1.58341773334659	-0.48899689611326	3.10557916276667	-0.516582266653407
25	3	2.8712006303952	-0.0062422588886947	3.13504162849349	-0.128799369604799
26	4	4.87711370991463	0.00591255538706756	3.11697373469830	0.877113709914628
27	5.1	7.39969234037474	-0.298598181277853	3.09890584090312	2.29969234037474
28	4.5	6.85446637078304	-0.855413904200338	3.00094753341729	2.35446637078304
29	4.2	5.38868201625361	0.108328757814914	2.90298922593147	1.18868201625361
30	3.3	3.95929058672703	-0.0437619542908838	2.68447136756385	0.659290586727034
31	2.7	2.66989945912089	0.264147031682881	2.46595350919623	-0.0301005408791064
32	1.8	0.86118425252812	0.549649086916032	2.18916666055585	-0.93881574747188
33	1.4	0.432468679317576	0.455151508766955	1.91237981191547	-0.967531320682424
34	0.5	-0.961824266630232	0.294992175581996	1.66683209104824	-1.46182426663023
35	-0.4	-2.23611685674328	0.0148324865622772	1.42128437018100	-1.83611685674328
36	0.8	0.81154130884303	-0.48899689611326	1.27745558727023	0.0115413088430294
37	0.7	0.272615454529238	-0.0062422588886947	1.13362680435946	-0.427384545470762
38	1.9	2.6431861603244	0.00591255538706756	1.15090128428853	0.743186160324398
39	2	3.13042241706024	-0.298598181277853	1.16817576421761	1.13042241706024
40	1.1	1.72482651258413	-0.855413904200338	1.33058739161620	0.624826512584134
41	0.9	0.198672223170289	0.108328757814914	1.49299901901480	-0.701327776829711
42	0.4	-0.801735937213794	-0.0437619542908838	1.64549789150468	-1.20173593721379
43	0.7	-0.66214379567744	0.264147031682881	1.79799676399456	-1.36214379567744
44	2.1	1.75716785181273	0.549649086916032	1.89318306127124	-0.342832148187275
45	2.8	3.15647913268512	0.455151508766955	1.98836935854793	0.356479132685118
46	3.9	5.3850059207251	0.294992175581996	2.12000190369291	1.48500592072510
47	3.5	4.73353306459984	0.0148324865622772	2.25163444883789	1.23353306459984
48	2	2.09078606254041	-0.48899689611326	2.39821083357285	0.090786062540412
49	2	1.46145504058089	-0.0062422588886947	2.54478721830781	-0.538544959419115
50	1.5	0.393175833988366	0.00591255538706756	2.60091161062457	-1.10682416601163
51	2.5	2.64156217833653	-0.298598181277853	2.65703600294132	0.141562178336530
52	3.1	4.41807734023935	-0.855413904200338	2.63733656396098	1.31807734023935
53	2.7	2.67403411720444	0.108328757814914	2.61763712498065	-0.02596588279556
54	2.8	3.05980038233924	-0.0437619542908838	2.58396157195164	0.259800382339240
55	2.5	2.18556694939448	0.264147031682881	2.55028601892264	-0.314433050605523
56	3	3.15250422976021	0.549649086916032	2.29784668332376	0.152504229760212
57	3.2	3.89944114350818	0.455151508766955	2.04540734772487	0.699441143508175
58	2.8	3.58073337409701	0.294992175581996	1.72427445032099	0.78073337409701
59	2.4	3.38202596052060	0.0148324865622772	1.40314155291712	0.982025960520605
60	2	3.41891028194955	-0.48899689611326	1.07008661416371	1.41891028194955
61	1.8	2.86921058347838	-0.0062422588886947	0.73703167541031	1.06921058347838
62	1.1	1.80983354212329	0.00591255538706756	0.38425390248964	0.709833542123293
63	-1.5	-2.73287794829112	-0.298598181277853	0.0314761295689689	-1.23287794829112
64	-3.7	-6.19891755895518	-0.855413904200338	-0.34566853684448	-2.49891755895518

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/109r41259961556.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/109r41259961556.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/2vo0w1259961556.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/2vo0w1259961556.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/3bjem1259961556.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/3bjem1259961556.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/47kfd1259961556.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t125996162856qql0l39tosa89/47kfd1259961556.ps (open in new window)

Parameters (Session):

par1 = multiplicative ; par2 = 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

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