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LOESS Dollar

*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 13:01:50 +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/t1293368396iqgc172lsef40ug.htm/, Retrieved Sun, 26 Dec 2010 14:00:00 +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/t1293368396iqgc172lsef40ug.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 «

0,8973 0,9383 0,9217 0,9095 0,892 0,8742 0,8532 0,8607 0,9005 0,9111 0,9059 0,8883 0,8924 0,8833 0,87 0,8758 0,8858 0,917 0,9554 0,9922 0,9778 0,9808 0,9811 1,0014 1,0183 1,0622 1,0773 1,0807 1,0848 1,1582 1,1663 1,1372 1,1139 1,1222 1,1692 1,1702 1,2286 1,2613 1,2646 1,2262 1,1985 1,2007 1,2138 1,2266 1,2176 1,2218 1,249 1,2991 1,3408 1,3119 1,3014 1,3201 1,2938 1,2694 1,2165 1,2037 1,2292 1,2256 1,2015 1,1786 1,1856 1,2103 1,1938 1,202 1,2271 1,277 1,265 1,2684 1,2811 1,2727 1,2611 1,2881 1,3213 1,2999 1,3074 1,3242 1,3516 1,3511 1,3419 1,3716 1,3622 1,3896 1,4227 1,4684 1,457 1,4718 1,4748 1,5527 1,575 1,5557 1,5553 1,577 1,4975 1,4369 1,3322 1,2732 1,3449 1,3239 1,2785 1,305 1,319 1,365 1,4016 1,4088 1,4268 1,4562 1,4816 1,4914 1,4614 1,4272 1,3686 1,3569 1,3406 1,2565 1,2208 1,277 1,2894 1,3067 1,3898 1,3661

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	1201	0	121
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	0.8973	0.87826707316982	0.00775203632752458	0.908580890502655	-0.0190329268301795
2	0.9383	0.962004182787066	0.00858966980454687	0.906006147408387	0.0237041827870664
3	0.9217	0.9479912771159	-0.00802268143001908	0.903431404314119	0.0262912771159005
4	0.9095	0.91979580081931	-0.00196406605448896	0.901168265235178	0.0102958008193107
5	0.892	0.888990325529938	-0.00389545168617577	0.898905126156238	-0.00300967447006228
6	0.8742	0.852782792587538	-0.00114275584256803	0.89675996325503	-0.0214172074124621
7	0.8532	0.819335284208058	-0.00755008456188078	0.894614800353822	-0.0338647157919415
8	0.8607	0.825927567785284	0.00339023601875575	0.89208219619596	-0.0347724322147160
9	0.9005	0.913179849079709	-0.00172944111780753	0.889549592038098	0.0126798490797091
10	0.9111	0.935880909782224	-0.00154295929125925	0.887862049509035	0.0247809097822242
11	0.9059	0.922691981538417	0.00293351148161116	0.886174506979972	0.0167919815384171
12	0.8883	0.88429797737463	0.00318200034728668	0.889120022278083	-0.00400202262536997
13	0.8924	0.88498242609628	0.00775203632752458	0.892065537576195	-0.00741757390371933
14	0.8833	0.8594847629171	0.00858966980454687	0.898525567278353	-0.0238152370828996
15	0.87	0.843037084449508	-0.00802268143001908	0.90498559698051	-0.0269629155504916
16	0.8758	0.840664612086668	-0.00196406605448896	0.912899453967821	-0.0351353879133325
17	0.8858	0.854682140731044	-0.00389545168617577	0.920813310955132	-0.0311178592689565
18	0.917	0.903949834554846	-0.00114275584256803	0.931192921287722	-0.0130501654451540
19	0.9554	0.976777552941569	-0.00755008456188078	0.941572531620312	0.0213775529415688
20	0.9922	1.02536581585112	0.00339023601875575	0.955643948130123	0.0331658158511213
21	0.9778	0.987614076477874	-0.00172944111780753	0.969715364639934	0.00981407647787358
22	0.9808	0.97715540473648	-0.00154295929125925	0.985987554554779	-0.00364459526351957
23	0.9811	0.957006744048765	0.00293351148161116	1.00225974446962	-0.0240932559512349
24	1.0014	0.980570966893974	0.00318200034728668	1.01904703275874	-0.0208290331060259
25	1.0183	0.99301364262462	0.00775203632752458	1.03583432104786	-0.0252863573753797
26	1.0622	1.06464850229789	0.00858966980454687	1.05116182789756	0.00244850229788907
27	1.0773	1.09613334668275	-0.00802268143001908	1.06648933474727	0.0188333466827459
28	1.0807	1.08255586169858	-0.00196406605448896	1.08080820435591	0.00185586169858087
29	1.0848	1.07836837772163	-0.00389545168617577	1.09512707396454	-0.00643162227836713
30	1.1582	1.20810873412947	-0.00114275584256803	1.10943402171310	0.0499087341294655
31	1.1663	1.21640911510022	-0.00755008456188078	1.12374096946166	0.0501091151002186
32	1.1372	1.13278255080149	0.00339023601875575	1.13822721317975	-0.00441744919850806
33	1.1139	1.07681598421996	-0.00172944111780753	1.15271345689784	-0.0370840157800354
34	1.1222	1.08136764237426	-0.00154295929125925	1.164575316917	-0.0408323576257406
35	1.1692	1.15902931158223	0.00293351148161116	1.17643717693616	-0.0101706884177684
36	1.1702	1.15237625048731	0.00318200034728668	1.18484174916540	-0.0178237495126898
37	1.2286	1.25620164227783	0.00775203632752458	1.19324632139465	0.0276016422778267
38	1.2613	1.31355734124438	0.00858966980454687	1.20045298895107	0.0522573412443839
39	1.2646	1.32956302492253	-0.00802268143001908	1.20765965650749	0.0649630249225288
40	1.2262	1.23975630970790	-0.00196406605448896	1.21460775634659	0.0135563097079032
41	1.1985	1.17933959550049	-0.00389545168617577	1.22155585618568	-0.0191604044995055
42	1.2007	1.17476967771972	-0.00114275584256803	1.22777307812285	-0.0259303222802774
43	1.2138	1.20115978450187	-0.00755008456188078	1.23399030006001	-0.0126402154981289
44	1.2266	1.20937176130681	0.00339023601875575	1.24043800267444	-0.0172282386931912
45	1.2176	1.19004373582895	-0.00172944111780753	1.24688570528886	-0.0275562641710536
46	1.2218	1.19063618535194	-0.00154295929125925	1.25450677393932	-0.0311638146480571
47	1.249	1.23293864592862	0.00293351148161116	1.26212784258977	-0.0160613540713828
48	1.2991	1.32694444069197	0.00318200034728668	1.26807355896074	0.0278444406919731
49	1.3408	1.39982868834077	0.00775203632752458	1.27401927533171	0.0590286883407667
50	1.3119	1.33989312941771	0.00858966980454687	1.27531720077774	0.0279931294177103
51	1.3014	1.33420755520624	-0.00802268143001908	1.27661512622378	0.0328075552062419
52	1.3201	1.36924607188081	-0.00196406605448896	1.27291799417368	0.0491460718808117
53	1.2938	1.32227458956260	-0.00389545168617577	1.26922086212358	0.0284745895625980
54	1.2694	1.27972304383652	-0.00114275584256803	1.26021971200605	0.0103230438365212
55	1.2165	1.18933152267336	-0.00755008456188078	1.25121856188852	-0.0271684773266354
56	1.2037	1.16361633519089	0.00339023601875575	1.24039342879035	-0.0400836648091101
57	1.2292	1.23056114542561	-0.00172944111780753	1.22956829569219	0.00136114542561483
58	1.2256	1.23062341665358	-0.00154295929125925	1.22211954263768	0.00502341665358341
59	1.2015	1.18539569893523	0.00293351148161116	1.21467078958316	-0.0161043010647699
60	1.1786	1.14027843354473	0.00318200034728668	1.21373956610799	-0.0383215664552727
61	1.1856	1.15063962103966	0.00775203632752458	1.21280834263281	-0.0349603789603383
62	1.2103	1.19489404652345	0.00858966980454687	1.21711628367200	-0.0154059534765498
63	1.1938	1.17419845671883	-0.00802268143001908	1.22142422471119	-0.0196015432811729
64	1.202	1.17802585745309	-0.00196406605448896	1.2279382086014	-0.0239741425469111
65	1.2271	1.22364325919457	-0.00389545168617577	1.23445219249161	-0.00345674080543268
66	1.277	1.31224957731953	-0.00114275584256803	1.24289317852304	0.0352495773195254
67	1.265	1.28621592000740	-0.00755008456188078	1.25133416455448	0.0212159200074040
68	1.2684	1.27313625702654	0.00339023601875575	1.26027350695471	0.00473625702653813
69	1.2811	1.29471659176287	-0.00172944111780753	1.26921284935494	0.0136165917628717
70	1.2727	1.26925875140074	-0.00154295929125925	1.27768420789052	-0.00344124859925921
71	1.2611	1.23311092209229	0.00293351148161116	1.2861555664261	-0.0279890779077121
72	1.2881	1.27907586735009	0.00318200034728668	1.29394213230263	-0.00902413264991497
73	1.3213	1.33311926549332	0.00775203632752458	1.30172869817916	0.0118192654933198
74	1.2999	1.28123419723393	0.00858966980454687	1.30997613296152	-0.0186658027660653
75	1.3074	1.30459911368614	-0.00802268143001908	1.31822356774388	-0.00280088631386244
76	1.3242	1.32190944190828	-0.00196406605448896	1.32845462414621	-0.00229055809171674
77	1.3516	1.36840977113765	-0.00389545168617577	1.33868568054853	0.0168097711376456
78	1.3511	1.35213297902282	-0.00114275584256803	1.35120977681975	0.00103297902281874
79	1.3419	1.32761621147091	-0.00755008456188078	1.36373387309097	-0.0142837885290874
80	1.3716	1.36200105283017	0.00339023601875575	1.37780871115108	-0.0095989471698339
81	1.3622	1.33424589190662	-0.00172944111780753	1.39188354921119	-0.0279541080933805
82	1.3896	1.37216434584800	-0.00154295929125925	1.40857861344326	-0.0174356541520031
83	1.4227	1.41719281084305	0.00293351148161116	1.42527367767534	-0.00550718915694737
84	1.4684	1.48999671807565	0.00318200034728668	1.44362128157706	0.0215967180756518
85	1.457	1.44427907819369	0.00775203632752458	1.46196888547879	-0.0127209218063109
86	1.4718	1.45741309553354	0.00858966980454687	1.47759723466191	-0.0143869044664597
87	1.4748	1.46439709758498	-0.00802268143001908	1.49322558384504	-0.0104029024150198
88	1.5527	1.60943270876027	-0.00196406605448896	1.49793135729422	0.056732708760268
89	1.575	1.65125832094277	-0.00389545168617577	1.50263713074340	0.0762583209427734
90	1.5557	1.61827839442782	-0.00114275584256803	1.49426436141475	0.0625783944278173
91	1.5553	1.63225849247578	-0.00755008456188078	1.4858915920861	0.0769584924757811
92	1.577	1.68195289961315	0.00339023601875575	1.46865686436810	0.104952899613146
93	1.4975	1.54530730446771	-0.00172944111780753	1.45142213665010	0.0478073044677112
94	1.4369	1.44568092984733	-0.00154295929125925	1.42966202944393	0.00878092984732537
95	1.3322	1.25356456628062	0.00293351148161116	1.40790192223777	-0.0786354337193829
96	1.2732	1.15452551166664	0.00318200034728668	1.38869248798607	-0.118674488333357
97	1.3449	1.31256490993811	0.00775203632752458	1.36948305373437	-0.0323350900618937
98	1.3239	1.27889276600416	0.00858966980454687	1.36031756419130	-0.0450072339958449
99	1.2785	1.21387060678179	-0.00802268143001908	1.35115207464823	-0.064629393218208
100	1.305	1.25639510072518	-0.00196406605448896	1.35556896532931	-0.0486048992748245
101	1.319	1.28190959567578	-0.00389545168617577	1.3599858560104	-0.0370904043242237
102	1.365	1.35807883132040	-0.00114275584256803	1.37306392452217	-0.00692116867959713
103	1.4016	1.42460809152795	-0.00755008456188078	1.38614199303393	0.02300809152795
104	1.4088	1.41656378382043	0.00339023601875575	1.39764598016081	0.00776378382043186
105	1.4268	1.44617947383011	-0.00172944111780753	1.40914996728769	0.0193794738301132
106	1.4562	1.50058960115251	-0.00154295929125925	1.41335335813874	0.0443896011525149
107	1.4816	1.54270973952859	0.00293351148161116	1.41755674898979	0.0611097395285944
108	1.4914	1.56869515090550	0.00318200034728668	1.41092284874721	0.0772951509055015
109	1.4614	1.51075901516785	0.00775203632752458	1.40428894850463	0.049359015167846
110	1.4272	1.45549971681793	0.00858966980454687	1.39031061337752	0.0282997168179329
111	1.3686	1.36889040317961	-0.00802268143001908	1.37633227825041	0.000290403179607823
112	1.3569	1.35052462391047	-0.00196406605448896	1.36523944214402	-0.00637537608953442
113	1.3406	1.33094884564854	-0.00389545168617577	1.35414660603764	-0.00965115435145991
114	1.2565	1.16956625543929	-0.00114275584256803	1.34457650040328	-0.086933744560713
115	1.2208	1.11414368979295	-0.00755008456188078	1.33500639476893	-0.106656310207045
116	1.277	1.22523140205776	0.00339023601875575	1.32537836192348	-0.0517685979422375
117	1.2894	1.26477911203977	-0.00172944111780753	1.31575032907804	-0.0246208879602297
118	1.3067	1.30786948655402	-0.00154295929125925	1.30707347273724	0.00116948655401528
119	1.3898	1.47826987212194	0.00293351148161116	1.29839661639645	0.0884698721219381
120	1.3661	1.43806070684212	0.00318200034728668	1.29095729281059	0.0719607068421186

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/1he341293368506.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/1he341293368506.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/2r5k71293368506.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/2r5k71293368506.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/3r5k71293368506.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/3r5k71293368506.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/42xja1293368506.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293368396iqgc172lsef40ug/42xja1293368506.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

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