Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 07 »

*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, 07 Dec 2010 09:50:59 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk.htm/, Retrieved Tue, 07 Dec 2010 10:51:43 +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/2010/Dec/07/t12917154988i1aviammp0hukk.htm/},
    year = {2010},
}
@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 = {2010},
    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 «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	3 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	721	0	73
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	46	36.4219352653799	-1.06327449224725	56.6413392268674	-9.57806473462015
2	62	67.6930864217614	0.0994992650936819	56.2074143131449	5.69308642176144
3	66	63.4642247719535	12.7622858286241	55.7734893994223	-2.53577522804649
4	59	64.3254419639629	-1.64060804315987	55.315166079197	5.32544196396289
5	58	63.3533214485102	-2.21016420748182	54.8568427589716	5.35332144851019
6	61	59.8570228399605	7.74803404288557	54.3949431171540	-1.14297716003952
7	41	41.1940625712892	-13.1271060466254	53.9330434753363	0.194062571289166
8	27	22.2720342413456	-21.6800365776477	53.408002336302	-4.72796575865438
9	58	57.5166778481113	5.6003609546209	52.8829611972678	-0.483322151888707
10	70	76.0689190070463	11.7094427070518	52.2216382859018	6.06891900704635
11	49	49.2878276758584	-2.84814305039416	51.5603153745358	0.287827675858360
12	59	61.8693205390778	4.64971233884341	51.4809671220788	2.86932053907781
13	44	37.6616556226255	-1.06327449224725	51.4016188696218	-6.33834437737452
14	36	20.2923432920945	0.0994992650936819	51.6081574428118	-15.7076567079055
15	72	79.423018155374	12.7622858286241	51.8146960160018	7.42301815537401
16	45	39.880002307446	-1.64060804315987	51.7606057357139	-5.11999769255398
17	56	62.503648752056	-2.21016420748182	51.7065154554259	6.50364875205597
18	54	48.4577991365265	7.74803404288557	51.794166820588	-5.54220086347354
19	53	67.2452878608754	-13.1271060466254	51.8818181857501	14.2452878608753
20	35	39.3126183512332	-21.6800365776477	52.3674182264145	4.31261835123318
21	61	63.5466207783002	5.6003609546209	52.8530182670789	2.54662077830024
22	52	39.2521682773744	11.7094427070518	53.0383890155737	-12.7478317226256
23	47	43.6243832863255	-2.84814305039416	53.2237597640686	-3.37561671367447
24	51	44.2774550111896	4.64971233884341	53.072832649967	-6.72254498881042
25	52	52.1413689563819	-1.06327449224725	52.9219055358654	0.141368956381854
26	63	73.1432092674779	0.0994992650936819	52.7572914674285	10.1432092674779
27	74	82.6450367723843	12.7622858286241	52.5926773989915	8.64503677238433
28	45	39.1806383240464	-1.64060804315987	52.4599697191135	-5.81936167595359
29	51	51.8829021682464	-2.21016420748182	52.3272620392354	0.882902168246417
30	64	68.3917069773624	7.74803404288557	51.860258979752	4.39170697736241
31	36	33.7338501263568	-13.1271060466254	51.3932559202687	-2.26614987364321
32	30	30.9447079403866	-21.6800365776477	50.7353286372611	0.944707940386564
33	55	54.3222376911256	5.6003609546209	50.0774013542535	-0.677762308874428
34	64	66.6265755325199	11.7094427070518	49.6639817604283	2.62657553251985
35	39	31.5975808837911	-2.84814305039416	49.2505621666031	-7.40241911620891
36	40	26.4005892996235	4.64971233884341	48.9496983615331	-13.5994107003765
37	63	78.414439935784	-1.06327449224725	48.6488345564632	15.4144399357841
38	45	41.5675097874044	0.0994992650936819	48.3329909475019	-3.43249021259558
39	59	57.2205668328352	12.7622858286241	48.0171473385406	-1.77943316716475
40	55	63.6981659156896	-1.64060804315987	47.9424421274702	8.69816591568964
41	40	34.3424272910820	-2.21016420748182	47.8677369163999	-5.65757270891804
42	64	71.9010884776593	7.74803404288557	48.3508774794552	7.90108847765928
43	27	18.293088004115	-13.1271060466254	48.8340180425105	-8.70691199588502
44	28	28.3713481005724	-21.6800365776477	49.3086884770753	0.371348100572405
45	45	34.6162801337391	5.6003609546209	49.78335891164	-10.3837198662609
46	57	52.1660662920335	11.7094427070518	50.1244910009147	-4.83393370796654
47	45	42.3825199602048	-2.84814305039416	50.4656230901894	-2.61748003979520
48	69	82.652666042068	4.64971233884341	50.6976216190886	13.6526660420680
49	60	70.1336543442595	-1.06327449224725	50.9296201479878	10.1336543442595
50	56	60.728421006318	0.0994992650936819	51.1720797285883	4.72842100631803
51	58	51.8231748621871	12.7622858286241	51.4145393091888	-6.17682513781293
52	50	49.9848409745743	-1.64060804315987	51.6557670685856	-0.0151590254257457
53	51	52.3131693794994	-2.21016420748182	51.8969948279825	1.31316937949936
54	53	46.5549140799125	7.74803404288557	51.6970518772019	-6.44508592008748
55	37	35.6299971202041	-13.1271060466254	51.4971089264214	-1.37000287979594
56	22	14.5811344327679	-21.6800365776477	51.0989021448797	-7.41886556723205
57	55	53.6989436820411	5.6003609546209	50.700695363338	-1.30105631795894
58	70	77.8184527562157	11.7094427070518	50.4721045367324	7.81845275621574
59	62	76.6046293402674	-2.84814305039416	50.2435137101268	14.6046293402674
60	58	61.0097818229296	4.64971233884341	50.340505838227	3.00978182292960
61	39	28.6257765259201	-1.06327449224725	50.4374979663272	-10.3742234740799
62	49	46.9813591915328	0.0994992650936819	50.9191415433735	-2.01864080846720
63	58	51.836929050956	12.7622858286241	51.4007851204198	-6.16307094904398
64	47	43.3006707792362	-1.64060804315987	52.3399372639237	-3.69932922076383
65	42	32.9310748000542	-2.21016420748182	53.2790894074276	-9.06892519994576
66	62	62.0819742703485	7.74803404288557	54.1699916867659	0.0819742703485105
67	39	36.0662120805212	-13.1271060466254	55.0608939661043	-2.93378791947883
68	40	45.6010195404533	-21.6800365776477	56.0790170371943	5.60101954045332
69	72	81.3024989370947	5.6003609546209	57.0971401082844	9.3024989370947
70	70	70.0437115666013	11.7094427070518	58.2468457263468	0.043711566601317
71	54	51.4515917059849	-2.84814305039416	59.3965513444093	-2.54840829401512
72	65	64.7433691464514	4.64971233884341	60.6069185147052	-0.256630853548621

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/1fswg1291715456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/1fswg1291715456.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/2qjvj1291715456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/2qjvj1291715456.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/3qjvj1291715456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/3qjvj1291715456.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/40svm1291715456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/07/t12917154988i1aviammp0hukk/40svm1291715456.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 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