Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2009 » Dec » 01 »

*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: Tue, 01 Dec 2009 14:17:55 -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/01/t1259702330mz0vzk54k47i28x.htm/, Retrieved Tue, 01 Dec 2009 22:18:55 +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/01/t1259702330mz0vzk54k47i28x.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 «

111.4 87.4 96.8 114.1 110.3 103.9 101.6 94.6 95.9 104.7 102.8 98.1 113.9 80.9 95.7 113.2 105.9 108.8 102.3 99 100.7 115.5 100.7 109.9 114.6 85.4 100.5 114.8 116.5 112.9 102 106 105.3 118.8 106.1 109.3 117.2 92.5 104.2 112.5 122.4 113.3 100 110.7 112.8 109.8 117.3 109.1 115.9 96 99.8 116.8 115.7 99.4 94.3 91 93.2 103.1 94.1 91.8 102.7

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	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	111.4	109.963346045378	9.16838097747883	103.668272977143	-1.43665395462226
2	87.4	88.6036736845629	-17.1719323623381	103.368258677775	1.20367368456289
3	96.8	96.5973291255034	-6.06557350391051	103.068244378407	-0.202670874496548
4	114.1	116.457517548846	8.9572235623914	102.785258888763	2.35751754884552
5	110.3	109.117702239616	8.98002436126518	102.502273399119	-1.18229776038429
6	103.9	102.953194741660	2.60386789529949	102.242937363040	-0.94680525833968
7	101.6	106.108694559546	-4.89229588650733	101.983601326961	4.50869455954602
8	94.6	91.9733611951045	-4.50979903122016	101.736437836116	-2.62663880489546
9	95.9	93.3380328820775	-3.0273072273474	101.48927434527	-2.56196711792253
10	104.7	102.08940220981	6.01711529445967	101.293482495730	-2.61059779019
11	102.8	104.420773067899	0.0815362859103597	101.097690646191	1.62077306789890
12	98.1	95.1446975631707	-0.141240972135107	101.196543408964	-2.9553024368293
13	113.9	117.336222850783	9.16838097747883	101.295396171738	3.43622285078314
14	80.9	77.3261746459533	-17.1719323623381	101.645757716385	-3.57382535404668
15	95.7	95.469454242879	-6.06557350391051	101.996119261032	-0.230545757121092
16	113.2	114.966939786945	8.9572235623914	102.475836650664	1.76693978694486
17	105.9	99.864421598439	8.98002436126518	102.955554040296	-6.03557840156105
18	108.8	111.594547759381	2.60386789529949	103.401584345320	2.79454775938096
19	102.3	105.644681236164	-4.89229588650733	103.847614650343	3.34468123616413
20	99	98.2724303495114	-4.50979903122016	104.237368681709	-0.727569650488562
21	100.7	99.8001845142732	-3.0273072273474	104.627122713074	-0.899815485726847
22	115.5	120.001104451738	6.01711529445967	104.981780253802	4.50110445173834
23	100.7	95.98202591956	0.0815362859103597	105.336437794530	-4.71797408044007
24	109.9	114.270358847045	-0.141240972135107	105.670882125091	4.3703588470446
25	114.6	114.026292566870	9.16838097747883	106.005326455651	-0.573707433130139
26	85.4	81.6242328066046	-17.1719323623381	106.347699555734	-3.77576719339542
27	100.5	100.375500848095	-6.06557350391051	106.690072655816	-0.124499151905312
28	114.8	113.593824176599	8.9572235623914	107.04895226101	-1.20617582340141
29	116.5	116.612143772531	8.98002436126518	107.407831866204	0.112143772530601
30	112.9	115.465950029336	2.60386789529949	107.730182075364	2.56595002933602
31	102	100.839763601983	-4.89229588650733	108.052532284525	-1.16023639801746
32	106	108.184936219764	-4.50979903122016	108.324862811456	2.18493621976414
33	105.3	105.030113888960	-3.0273072273474	108.597193338387	-0.269886111039852
34	118.8	122.82197826745	6.01711529445967	108.760906438091	4.02197826744982
35	106.1	103.193844176296	0.0815362859103597	108.924619537794	-2.90615582370411
36	109.3	109.743296250230	-0.141240972135107	108.997944721905	0.443296250230148
37	117.2	116.160349116505	9.16838097747883	109.071269906016	-1.03965088349501
38	92.5	92.9536029288053	-17.1719323623381	109.218329433533	0.453602928805338
39	104.2	105.100184542861	-6.06557350391051	109.365388961049	0.900184542861098
40	112.5	106.469024896160	8.9572235623914	109.573751541448	-6.03097510383954
41	122.4	126.037861516888	8.98002436126518	109.782114121847	3.63786151688795
42	113.3	114.017973067506	2.60386789529949	109.978159037195	0.717973067505511
43	100	94.7180919339642	-4.89229588650733	110.174203952543	-5.28190806603577
44	110.7	115.669011815345	-4.50979903122016	110.240787215875	4.96901181534471
45	112.8	118.319936748140	-3.0273072273474	110.307370479208	5.5199367481396
46	109.8	103.465832535862	6.01711529445967	110.117052169678	-6.33416746413765
47	117.3	124.591729853941	0.0815362859103597	109.926733860148	7.29172985394149
48	109.1	109.138300545420	-0.141240972135107	109.202940426715	0.038300545420384
49	115.9	114.152472029240	9.16838097747883	108.479146993281	-1.74752797076010
50	96	101.895817470474	-17.1719323623381	107.276114891864	5.89581747047399
51	99.8	99.5924907134635	-6.06557350391051	106.073082790447	-0.207509286536492
52	116.8	120.037153163822	8.9572235623914	104.605623273787	3.23715316382173
53	115.7	119.281811881608	8.98002436126518	103.138163757127	3.58181188160809
54	99.4	94.5397019732192	2.60386789529949	101.656430131481	-4.86029802678078
55	94.3	93.3175993806715	-4.89229588650733	100.174696505836	-0.982400619328544
56	91	87.8460931492642	-4.50979903122016	98.663705881956	-3.15390685073575
57	93.2	92.2745919692715	-3.0273072273474	97.152715258076	-0.925408030728548
58	103.1	104.550830325112	6.01711529445967	95.6320543804288	1.45083032511151
59	94.1	94.007070211308	0.0815362859103597	94.1113935027817	-0.0929297886920466
60	91.8	91.1365193366132	-0.141240972135107	92.6047216355219	-0.663480663386778
61	102.7	105.133569254259	9.16838097747883	91.0980497682621	2.43356925425908

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/140ek1259702273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/140ek1259702273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/242ru1259702273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/242ru1259702273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/3ta6t1259702273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/3ta6t1259702273.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/4v6sr1259702273.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259702330mz0vzk54k47i28x/4v6sr1259702273.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