Blog & Share Statistical Computations at FreeStatistics.org

Home » date » 2010 » Dec » 26 »

*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: Sun, 26 Dec 2010 21:23:25 +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/26/t1293398560kenvk4npgy0iw81.htm/, Retrieved Sun, 26 Dec 2010 22:22:45 +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/26/t1293398560kenvk4npgy0iw81.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 «

24 29 29 25 16 18 13 22 15 20 19 18 13 17 17 13 14 13 17 17 15 9 10 9 14 18 18 12 16 12 19 13 12 13 11 10 16 12 6 8 6 8 8 9 13 8 11 8 10 15 12 13 12 15 13 13 16 14 12 15 14 19 16 16 11 13 12 11 6 9 6 15 17 13 12 13 10 14 13 10 11 12 7 11 9 13 12 5 13 11 8 8 8 8 0 3 0 -1 -1 -4 1 -1 0 -1 6 0 -3 -3 4 1 0 -4 -2 3 2 5 6 6 3 4 7 5 6 1 3 6 0 3 4 7 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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	1311	0	132
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	24	22.0523470839929	0.840369300930925	25.1072836150762	-1.94765291600712
2	29	31.5701939800138	2.20555902047047	24.2242469995157	2.57019398001385
3	29	33.5425881519472	1.11620146409760	23.3412103839552	4.54258815194724
4	25	28.8694788550773	-1.38165105416281	22.5121721990855	3.86947885507729
5	16	11.3781893906424	-1.06132340485826	21.6831340142159	-4.62181060935761
6	18	14.9747934490082	0.15059111969638	20.8746154312954	-3.02520655099176
7	13	6.29866849866082	-0.364765347035717	20.0660968483749	-6.70133150133918
8	22	24.5612470895888	0.228100451218178	19.210652459193	2.56124708958881
9	15	11.0965480014072	0.548243928581726	18.3552080700111	-3.90345199859284
10	20	22.2003100109309	0.159867649668498	17.6398223394006	2.20031001093086
11	19	22.9404354860675	-1.86487209485763	16.9244366087902	3.94043548606748
12	18	19.9393771220751	-0.576320559842185	16.6369434377671	1.93937712207510
13	13	8.81018043232506	0.840369300930925	16.349450266744	-4.18981956767494
14	17	15.7242072831905	2.20555902047047	16.0702336963390	-1.27579271680950
15	17	17.0927814099683	1.11620146409760	15.7910171259341	0.0927814099683495
16	13	12.053103935675	-1.38165105416281	15.3285471184878	-0.94689606432499
17	14	14.1952462938167	-1.06132340485826	14.8660771110415	0.195246293816716
18	13	11.4072364785557	0.15059111969638	14.4421724017480	-1.59276352144435
19	17	20.3464976545813	-0.364765347035717	14.0182676924544	3.34649765458133
20	17	19.887071561262	0.228100451218178	13.8848279875198	2.88707156126201
21	15	15.7003677888330	0.548243928581726	13.7513882825852	0.700367788833045
22	9	4.1024867022614	0.159867649668498	13.7376456480701	-4.8975132977386
23	10	8.14096908130265	-1.86487209485763	13.7239030135550	-1.85903091869735
24	9	4.82116216267775	-0.576320559842185	13.7551583971644	-4.17883783732225
25	14	13.3732169182952	0.840369300930925	13.7864137807739	-0.626783081704817
26	18	19.9627316093343	2.20555902047047	13.8317093701952	1.96273160933428
27	18	21.0067935762858	1.11620146409760	13.8770049596166	3.00679357628580
28	12	11.4109712676107	-1.38165105416281	13.9706797865521	-0.58902873238933
29	16	18.9969687913706	-1.06132340485826	14.0643546134877	2.99696879137059
30	12	9.82478436563946	0.15059111969638	14.0246245146642	-2.17521563436054
31	19	24.3798709311951	-0.364765347035717	13.9848944158407	5.37987093119506
32	13	12.1706205887349	0.228100451218178	13.6012789600469	-0.829379411265082
33	12	10.2340925671651	0.548243928581726	13.2176635042531	-1.76590743283487
34	13	13.2405024423805	0.159867649668498	12.599629907951	0.240502442380496
35	11	11.8832757832088	-1.86487209485763	11.9815963116489	0.88327578320877
36	10	9.22084157086565	-0.576320559842185	11.3554789889765	-0.77915842913435
37	16	20.4302690327649	0.840369300930925	10.7293616663042	4.43026903276486
38	12	11.5051293298394	2.20555902047047	10.2893116496901	-0.494870670160557
39	6	1.03453690282644	1.11620146409760	9.84926163307596	-4.96546309717356
40	8	7.76466067885004	-1.38165105416281	9.61699037531277	-0.235339321149963
41	6	3.67660428730868	-1.06132340485826	9.38471911754958	-2.32339571269132
42	8	6.56430930496204	0.15059111969638	9.28509957534158	-1.43569069503796
43	8	7.17928531390214	-0.364765347035717	9.18548003313358	-0.820714686097864
44	9	8.42848446598966	0.228100451218178	9.34341508279216	-0.571515534010338
45	13	15.9504059389675	0.548243928581726	9.50135013245074	2.95040593896753
46	8	5.91773923402581	0.159867649668498	9.9223931163057	-2.08226076597419
47	11	13.5214359946970	-1.86487209485763	10.3434361001607	2.52143599469698
48	8	5.77372283002227	-0.576320559842185	10.8025977298199	-2.22627716997773
49	10	7.8978713395899	0.840369300930925	11.2617593594792	-2.10212866041010
50	15	16.1306287569068	2.20555902047047	11.6638122226227	1.13062875690683
51	12	10.8179334501362	1.11620146409760	12.0658650857662	-1.18206654986383
52	13	14.9463797994544	-1.38165105416281	12.4352712547084	1.94637979945444
53	12	12.2566459812078	-1.06132340485826	12.8046774236505	0.256645981207766
54	15	16.6847888683009	0.15059111969638	13.1646200120027	1.68478886830092
55	13	12.8402027466808	-0.364765347035717	13.5245626003549	-0.159797253319194
56	13	11.9466025348275	0.228100451218178	13.8252970139544	-1.05339746517255
57	16	17.3257246438644	0.548243928581726	14.1260314275538	1.32572464386445
58	14	13.5553829184523	0.159867649668498	14.2847494318792	-0.444617081547706
59	12	11.4214046586530	-1.86487209485763	14.4434674362046	-0.578595341346954
60	15	16.1627168699102	-0.576320559842185	14.4136036899320	1.16271686991023
61	14	12.7758907554098	0.840369300930925	14.3837399436593	-1.22410924459025
62	19	21.7055231024131	2.20555902047047	14.0889178771164	2.70552310241309
63	16	17.0897027253289	1.11620146409760	13.7940958105735	1.08970272532885
64	16	20.0547177613867	-1.38165105416281	13.3269332927761	4.05471776138667
65	11	10.2015526298795	-1.06132340485826	12.8597707749787	-0.798447370120465
66	13	13.3363589311080	0.15059111969638	12.5130499491957	0.336358931107956
67	12	12.1984362236231	-0.364765347035717	12.1663291234126	0.198436223623110
68	11	9.84944500990827	0.228100451218178	11.9224545388736	-1.15055499009173
69	6	-0.226823882916229	0.548243928581726	11.6785799543345	-6.22682388291623
70	9	6.2916439988843	0.159867649668498	11.5484883514472	-2.7083560011157
71	6	2.44647534629774	-1.86487209485763	11.4183967485599	-3.55352465370226
72	15	19.0699828717998	-0.576320559842185	11.5063376880424	4.06998287179977
73	17	21.5653520715441	0.840369300930925	11.5942786275249	4.56535207154414
74	13	12.0093913608027	2.20555902047047	11.7850496187269	-0.990608639197323
75	12	10.9079779259736	1.11620146409760	11.9758206099288	-1.09202207402636
76	13	15.3440391989245	-1.38165105416281	12.0376118552384	2.34403919892445
77	10	8.96192030431031	-1.06132340485826	12.0994031005479	-1.03807969568969
78	14	15.9563773345053	0.15059111969638	11.8930315457983	1.95637733450528
79	13	14.678105355987	-0.364765347035717	11.6866599910487	1.67810535598699
80	10	8.35832194694586	0.228100451218178	11.4135776018360	-1.64167805305414
81	11	10.3112608587951	0.548243928581726	11.1404952126232	-0.688739141204918
82	12	12.9180871161313	0.159867649668498	10.9220452342002	0.918087116131304
83	7	5.16127683908043	-1.86487209485763	10.7035952557772	-1.83872316091957
84	11	12.0673947883771	-0.576320559842185	10.5089257714651	1.06739478837708
85	9	6.84537441191606	0.840369300930925	10.3142562871530	-2.15462558808394
86	13	13.6924385704528	2.20555902047047	10.1020024090768	0.692438570452763
87	12	12.9940500049019	1.11620146409760	9.88974853100051	0.994050004901887
88	5	1.84731807802191	-1.38165105416281	9.5343329761409	-3.15268192197809
89	13	17.8824059835770	-1.06132340485826	9.17891742128128	4.88240598357698
90	11	13.3115690914744	0.15059111969638	8.53783978882917	2.31156909147445
91	8	8.46800319065864	-0.364765347035717	7.89676215637707	0.468003190658642
92	8	8.83938923074823	0.228100451218178	6.93251031803359	0.839389230748233
93	8	9.48349759172817	0.548243928581726	5.9682584796901	1.48349759172817
94	8	10.9441034190456	0.159867649668498	4.89602893128588	2.94410341904562
95	0	-1.95892728802402	-1.86487209485763	3.82379938288166	-1.95892728802402
96	3	3.70806663296536	-0.576320559842185	2.86825392687683	0.708066632965358
97	0	-2.75307777180292	0.840369300930925	1.912708470872	-2.75307777180292
98	-1	-5.48363789299196	2.20555902047047	1.27807887252149	-4.48363789299196
99	-1	-3.75965073826858	1.11620146409760	0.64344927417098	-2.75965073826858
100	-4	-6.91300488780998	-1.38165105416281	0.294655941972783	-2.91300488780998
101	1	3.11546079508367	-1.06132340485826	-0.0541373902254153	2.11546079508367
102	-1	-2.04160489341302	0.15059111969638	-0.108986226283359	-1.04160489341302
103	0	0.52860040937702	-0.364765347035717	-0.163835062341303	0.52860040937702
104	-1	-2.14055932568515	0.228100451218178	-0.0875411255330258	-1.14055932568515
105	6	11.4630032601430	0.548243928581726	-0.0112471887247481	5.46300326014302
106	0	-0.162301795975297	0.159867649668498	0.00243414630679873	-0.162301795975297
107	-3	-4.15124338648071	-1.86487209485763	0.0161154813383456	-1.15124338648071
108	-3	-5.475965492561	-0.576320559842185	0.052286052403185	-2.475965492561
109	4	7.07117407560105	0.840369300930925	0.0884566234680244	3.07117407560105
110	1	-0.527424679845944	2.20555902047047	0.321865659375471	-1.52742467984594
111	0	-1.67147615938052	1.11620146409760	0.555274695282918	-1.67147615938052
112	-4	-7.58852350756102	-1.38165105416281	0.970174561723824	-3.58852350756102
113	-2	-4.32375102330647	-1.06132340485826	1.38507442816473	-2.32375102330647
114	3	3.93928638323596	0.15059111969638	1.91012249706766	0.93928638323596
115	2	1.92959478106513	-0.364765347035717	2.43517056597059	-0.0704052189348734
116	5	6.85546527119971	0.228100451218178	2.91643427758211	1.85546527119971
117	6	8.05405808222464	0.548243928581726	3.39769798919363	2.05405808222464
118	6	8.06474334035414	0.159867649668498	3.77538900997736	2.06474334035414
119	3	3.71179206409654	-1.86487209485763	4.15308003076109	0.71179206409654
120	4	4.32081791813428	-0.576320559842185	4.25550264170791	0.320817918134277
121	7	8.80170544641435	0.840369300930925	4.35792525265472	1.80170544641435
122	5	3.51675501146904	2.20555902047047	4.27768596806049	-1.48324498853096
123	6	6.68635185243615	1.11620146409760	4.19744668346625	0.686351852436152
124	1	-0.87316402548323	-1.38165105416281	4.25481507964604	-1.87316402548323
125	3	2.74913992903243	-1.06132340485826	4.31218347582582	-0.250860070967565
126	6	7.46184587288986	0.15059111969638	4.38756300741376	1.46184587288986
127	0	-4.09817719196599	-0.364765347035717	4.4629425390017	-4.09817719196599
128	3	1.22733261207864	0.228100451218178	4.54456693670318	-1.77266738792136
129	4	2.82556473701362	0.548243928581726	4.62619133440466	-1.17443526298638
130	7	9.10608541281595	0.159867649668498	4.73404693751555	2.10608541281595
131	6	9.02296955423119	-1.86487209485763	4.84190254062645	3.02296955423119

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/1jdj71293398601.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/1jdj71293398601.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/2u4is1293398601.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/2u4is1293398601.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/3u4is1293398601.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/3u4is1293398601.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/45dzv1293398601.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293398560kenvk4npgy0iw81/45dzv1293398601.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