Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2009 » Dec » 16 »

*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, 16 Dec 2009 10:53:53 -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/16/t1260986153ok37gjt95ropcav.htm/, Retrieved Wed, 16 Dec 2009 18:55:58 +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/16/t1260986153ok37gjt95ropcav.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 «

16,2 16,7 18,4 16 16,5 18,2 16,8 17,3 18 19,6 23,3 23,7 20,3 22,8 24,3 21,5 23,5 22,2 20,9 22,2 19,5 21,1 22 19,2 17,8 19,2 19,9 19,6 18,1 20,4 18,1 18,6 17,6 19,4 19,3 18,6 16,9 16,4 19 18,7 17,1 21,5 17,8 18,1 19 18,9 16,8 18,1 15,7 15,1 18,3 16,5 16,9 18,4 16,4 15,7 16,9 16,6 16,7 16,6

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	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	16.2	17.7529106330725	-1.24079060096212	15.8878799678896	1.55291063307252
2	16.7	17.7338339430023	-0.645628693858412	16.3117947508561	1.03383394300231
3	18.4	18.8347584684581	1.22953199771934	16.7357095338226	0.43475846845806
4	16	15.1430664977010	-0.329726188549798	17.1866596908488	-0.856933502299022
5	16.5	15.7713757163297	-0.408985564204701	17.6376098478750	-0.728624283670342
6	18.2	16.9820673004599	1.31801344441013	18.0999192551300	-1.21793269954011
7	16.8	15.8527594204671	-0.814988082852054	18.5622286623849	-0.94724057953286
8	17.3	15.9804923499207	-0.403556778697102	19.0230644287764	-1.31950765007928
9	18	17.0682266648122	-0.552126859980067	19.4839001951678	-0.931773335187778
10	19.6	18.8057202089458	0.388887421522159	20.0053923695320	-0.794279791054205
11	23.3	25.1632152561489	0.90990019995485	20.5268845438962	1.86321525614891
12	23.7	25.8671667873304	0.549470230541295	20.9833629821283	2.16716678733043
13	20.3	20.4009491806018	-1.24079060096212	21.4398414203603	0.100949180601813
14	22.8	24.5372319934486	-0.645628693858412	21.7083967004098	1.73723199344863
15	24.3	25.3935160218214	1.22953199771934	21.9769519804593	1.09351602182139
16	21.5	21.3389218422696	-0.329726188549798	21.9908043462802	-0.161078157730358
17	23.5	25.4043288521037	-0.408985564204701	22.0046567121010	1.90432885210365
18	22.2	21.2964962129089	1.31801344441013	21.7854903426809	-0.903503787091076
19	20.9	21.0486641095912	-0.814988082852054	21.5663239732608	0.148664109591206
20	22.2	23.54268613486	-0.403556778697102	21.2608706438371	1.34268613486002
21	19.5	18.5967095455667	-0.552126859980067	20.9554173144133	-0.90329045443325
22	21.1	21.1630507658102	0.388887421522159	20.6480618126676	0.0630507658102388
23	22	22.7493934891233	0.90990019995485	20.3407063109219	0.74939348912326
24	19.2	17.7758535492377	0.549470230541295	20.074676220221	-1.42414645076228
25	17.8	17.0321444714420	-1.24079060096212	19.8086461295201	-0.76785552855797
26	19.2	19.4528892494031	-0.645628693858412	19.5927394444553	0.252889249403150
27	19.9	19.1936352428902	1.22953199771934	19.3768327593904	-0.706364757109771
28	19.6	20.307575931795	-0.329726188549798	19.2221502567548	0.707575931794977
29	18.1	17.5415178100855	-0.408985564204701	19.0674677541192	-0.558482189914514
30	20.4	20.5361872764974	1.31801344441013	18.9457992790924	0.136187276497431
31	18.1	18.1908572787864	-0.814988082852054	18.8241308040657	0.0908572787863946
32	18.6	18.8998222648226	-0.403556778697102	18.7037345138745	0.299822264822637
33	17.6	17.1687886362968	-0.552126859980067	18.5833382236833	-0.431211363703202
34	19.4	19.9203716058627	0.388887421522159	18.4907409726152	0.520371605862675
35	19.3	19.2919560784981	0.90990019995485	18.3981437215471	-0.00804392150191191
36	18.6	18.2788271890347	0.549470230541295	18.371702580424	-0.321172810965301
37	16.9	16.6955291616612	-1.24079060096212	18.3452614393010	-0.204470838338835
38	16.4	15.0851952227374	-0.645628693858412	18.360433471121	-1.31480477726258
39	19	18.3948624993396	1.22953199771934	18.3756055029410	-0.605137500660366
40	18.7	19.3622526741488	-0.329726188549798	18.3674735144010	0.662252674148828
41	17.1	16.2496440383438	-0.408985564204701	18.3593415258609	-0.850355961656213
42	21.5	23.3843935371597	1.31801344441013	18.2975930184302	1.88439353715971
43	17.8	18.1791435718526	-0.814988082852054	18.2358445109994	0.379143571852644
44	18.1	18.4829281561925	-0.403556778697102	18.1206286225046	0.382928156192513
45	19	20.5467141259703	-0.552126859980067	18.0054127340098	1.5467141259703
46	18.9	19.5630156458498	0.388887421522159	17.8480969326281	0.663015645849786
47	16.8	14.9993186687988	0.90990019995485	17.6907811312463	-1.80068133120119
48	18.1	18.1367504079296	0.549470230541295	17.5137793615292	0.0367504079295529
49	15.7	15.3040130091502	-1.24079060096212	17.3367775918120	-0.395986990849849
50	15.1	13.6632164232756	-0.645628693858412	17.1824122705828	-1.43678357672439
51	18.3	18.3424210529270	1.22953199771934	17.0280469493536	0.0424210529270255
52	16.5	16.3949103896600	-0.329726188549798	16.9348157988898	-0.105089610339974
53	16.9	17.3674009157788	-0.408985564204701	16.8415846484259	0.467400915778793
54	18.4	18.7314983770573	1.31801344441013	16.7504881785325	0.331498377057336
55	16.4	16.9555963742129	-0.814988082852054	16.6593917086392	0.55559637421289
56	15.7	15.2285527172126	-0.403556778697102	16.5750040614845	-0.471447282787384
57	16.9	17.8615104456503	-0.552126859980067	16.4906164143298	0.961510445650262
58	16.6	16.4044061707598	0.388887421522159	16.406706407718	-0.195593829240174
59	16.7	16.1673033989389	0.90990019995485	16.3227964011062	-0.532696601061078
60	16.6	16.4149638779918	0.549470230541295	16.2355658914669	-0.185036122008185

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/1oczm1260986031.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/1oczm1260986031.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/22cn31260986031.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/22cn31260986031.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/3e2c21260986031.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/3e2c21260986031.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/4w9tm1260986031.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/16/t1260986153ok37gjt95ropcav/4w9tm1260986031.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

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