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LOESS Yuan

*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 13:22:06 +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/t12933696007bc2ylrtjmfmvc1.htm/, Retrieved Sun, 26 Dec 2010 14:20:04 +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/t12933696007bc2ylrtjmfmvc1.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 «

7,4271 7,7662 7,6289 7,5281 7,3831 7,2355 7,0617 7,1237 7,4533 7,5411 7,4978 7,3525 7,3862 7,311 7,2013 7,249 7,3321 7,59 7,9082 8,2123 8,0929 8,118 8,1206 8,2883 8,4281 8,7917 8,9168 8,9446 8,9786 9,5862 9,6533 9,4125 9,2195 9,2882 9,6774 9,6857 10,1688 10,4399 10,4675 10,149 9,9163 9,9268 10,0529 10,1622 10,083 10,1134 10,3423 10,7536 11,0967 10,8588 10,7719 10,9262 10,708 10,5062 10,0683 9,8954 9,9589 9,9177 9,7189 9,5273 9,5746 9,763 9,6117 9,6581 9,8361 10,2353 10,1285 10,1347 10,2141 10,0971 9,9651 10,1286 10,3356 10,1238 10,1326 10,2467 10,44 10,3689 10,2415 10,3899 10,3162 10,4533 10,6741 10,8957 10,7404 10,6568 10,5682 10,9833 11,0237 10,8462 10,7287 10,7809 10,2609 9,8252 9,1071 8,695 9,2205 9,0496 8,7406 8,921 9,011 9,3157 9,5786 9,6246 9,7485 9,9431 10,1152 10,1827 9,9777 9,7436 9,3462 9,2623 9,1505 8,5794 8,3245 8,6538 8,752 8,8104 9,2665 9,0895

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	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	7.4271	7.27153728809823	0.0786265539988212	7.50403615790295	-0.155562711901767
2	7.7662	7.96494274411558	0.0822453624857993	7.48521189339863	0.198742744115576
3	7.6289	7.83228808557461	-0.0408757144689129	7.4663876288943	0.203388085574608
4	7.5281	7.6113132649108	-0.00499209913591109	7.44987883422511	0.0832132649108033
5	7.3831	7.35908845507276	-0.0262584946286676	7.43337003955591	-0.0240115449272436
6	7.2355	7.04881986561961	0.00469814207787817	7.41748199230251	-0.186680134380389
7	7.0617	6.7716314617301	-0.0498254067792157	7.40159394504911	-0.290068538269897
8	7.1237	6.85701038599174	0.00815649503218206	7.38223311897608	-0.266689614008262
9	7.4533	7.57103931192951	-0.0273116048325628	7.36287229290305	0.117739311929515
10	7.5411	7.76429793730326	-0.0316960099752538	7.349598072672	0.223197937303262
11	7.4978	7.6584266110272	0.000849536531861234	7.33632385244094	0.160626611027202
12	7.3525	7.33866341711762	0.00638333069206466	7.35995325219032	-0.0138365828823828
13	7.3862	7.31019079406148	0.0786265539988212	7.3835826519397	-0.0760092059385213
14	7.311	7.1034980333605	0.0822453624857993	7.4362566041537	-0.207501966639502
15	7.2013	6.95454515810121	-0.0408757144689129	7.4889305563677	-0.246754841898793
16	7.249	6.94856662627712	-0.00499209913591109	7.55442547285879	-0.300433373722876
17	7.3321	7.0705381052788	-0.0262584946286676	7.61992038934987	-0.261561894721200
18	7.59	7.4685847707596	0.00469814207787817	7.70671708716252	-0.121415229240395
19	7.9082	8.07271162180405	-0.0498254067792157	7.79351378497517	0.164511621804047
20	8.2123	8.50571299603202	0.00815649503218206	7.9107305089358	0.293412996032017
21	8.0929	8.18516437193613	-0.0273116048325628	8.02794723289644	0.0922643719361282
22	8.118	8.10515420212657	-0.0316960099752538	8.16254180784869	-0.0128457978734353
23	8.1206	7.94321408066719	0.000849536531861234	8.29713638280095	-0.177385919332808
24	8.2883	8.13493793011022	0.00638333069206466	8.43527873919771	-0.153362069889779
25	8.4281	8.2041523504067	0.0786265539988212	8.57342109559448	-0.223947649593301
26	8.7917	8.801696905073	0.0822453624857993	8.69945773244121	0.00999690507299178
27	8.9168	9.04898134518097	-0.0408757144689129	8.82549436928794	0.132181345180975
28	8.9446	8.95019464506892	-0.00499209913591109	8.94399745406699	0.00559464506892304
29	8.9786	8.92095795578263	-0.0262584946286676	9.06250053884604	-0.0576420442173688
30	9.5862	9.98588292483493	0.00469814207787817	9.1818189330872	0.399682924834929
31	9.6533	10.0552880794509	-0.0498254067792157	9.30113732732835	0.401988079450867
32	9.4125	9.39501936951444	0.00815649503218206	9.42182413545338	-0.0174806304855615
33	9.2195	8.92380066125415	-0.0273116048325628	9.5425109435784	-0.295699338745846
34	9.2882	8.96756992857378	-0.0316960099752538	9.64052608140147	-0.320630071426219
35	9.6774	9.6154092442436	0.000849536531861234	9.73854121922454	-0.0619907557563977
36	9.6857	9.5578000929349	0.00638333069206466	9.80721657637303	-0.127899907065091
37	10.1688	10.3830815124797	0.0786265539988212	9.87589193352152	0.214281512479662
38	10.4399	10.8626241217274	0.0822453624857993	9.93493051578683	0.422724121727368
39	10.4675	10.9819066164168	-0.0408757144689129	9.99396909805215	0.514406616416764
40	10.149	10.2511817127294	-0.00499209913591109	10.0518103864065	0.102181712729385
41	9.9163	9.74920681986776	-0.0262584946286676	10.1096516747609	-0.167093180132236
42	9.9268	9.68667923461403	0.00469814207787817	10.1622226233081	-0.240120765385971
43	10.0529	9.94083183492393	-0.0498254067792157	10.2147935718553	-0.112068165076069
44	10.1622	10.0471776364572	0.00815649503218206	10.2690658685106	-0.115022363542773
45	10.083	9.86997343966666	-0.0273116048325628	10.3233381651659	-0.213026560333336
46	10.1134	9.87201972052794	-0.0316960099752538	10.3864762894473	-0.241380279472061
47	10.3423	10.2341360497394	0.000849536531861234	10.4496144137287	-0.108163950260591
48	10.7536	11.0036084280527	0.00638333069206466	10.4972082412552	0.250008428052711
49	11.0967	11.5699713772195	0.0786265539988212	10.5448020687817	0.47327137721946
50	10.8588	11.0876088115944	0.0822453624857993	10.5477458259198	0.228808811594442
51	10.7719	11.0339861314111	-0.0408757144689129	10.5506895830578	0.262086131411113
52	10.9262	11.3528694226804	-0.00499209913591109	10.5045226764555	0.426669422680424
53	10.708	10.9839027247755	-0.0262584946286676	10.4583557698532	0.275902724775493
54	10.5062	10.6439446918504	0.00469814207787817	10.3637571660717	0.137744691850404
55	10.0683	9.91726684448896	-0.0498254067792157	10.2691585622903	-0.151033155511044
56	9.8954	9.62605166726387	0.00815649503218206	10.1565918377039	-0.269348332736131
57	9.9589	9.90108649171492	-0.0273116048325628	10.0440251131176	-0.0578135082850775
58	9.9177	9.91085980019882	-0.0316960099752538	9.95623620977643	-0.00684019980117512
59	9.7189	9.56850315703292	0.000849536531861234	9.86844730643522	-0.15039684296708
60	9.5273	9.21383310668766	0.00638333069206466	9.83438356262028	-0.313466893312343
61	9.5746	9.27025362719584	0.0786265539988212	9.80031981880534	-0.304346372804158
62	9.763	9.62977623905306	0.0822453624857993	9.81397839846114	-0.133223760946938
63	9.6117	9.43663873635198	-0.0408757144689129	9.82763697811694	-0.175061263648026
64	9.6581	9.45881060888475	-0.00499209913591109	9.86238149025116	-0.199289391115252
65	9.8361	9.80133249224328	-0.0262584946286676	9.89712600238539	-0.0347675077567189
66	10.2353	10.5225363229853	0.00469814207787817	9.94336553493685	0.287236322985271
67	10.1285	10.3172203392909	-0.0498254067792157	9.98960506748832	0.188720339290896
68	10.1347	10.2280513795349	0.00815649503218206	10.0331921254329	0.093351379534937
69	10.2141	10.3787324214551	-0.0273116048325628	10.0767791833774	0.164632421455121
70	10.0971	10.1152569912631	-0.0316960099752538	10.1106390187121	0.0181569912631048
71	9.9651	9.78485160942128	0.000849536531861234	10.1444988540469	-0.180248390578717
72	10.1286	10.0840215733385	0.00638333069206466	10.1667950959694	-0.0445784266615021
73	10.3356	10.4034821081092	0.0786265539988212	10.1890913378920	0.0678821081091598
74	10.1238	9.95554071031785	0.0822453624857993	10.2098139271964	-0.168259289682153
75	10.1326	10.0755391979682	-0.0408757144689129	10.2305365165007	-0.0570608020317742
76	10.2467	10.2340308164952	-0.00499209913591109	10.2643612826407	-0.0126691835048032
77	10.44	10.6080724458479	-0.0262584946286676	10.2981860487807	0.168072445847923
78	10.3689	10.3878307751401	0.00469814207787817	10.3452710827821	0.0189307751400634
79	10.2415	10.1404692899958	-0.0498254067792157	10.3923561167834	-0.101030710004157
80	10.3899	10.3332418151676	0.00815649503218206	10.4384016898003	-0.0566581848324397
81	10.3162	10.1752643420154	-0.0273116048325628	10.4844472628171	-0.140935657984580
82	10.4533	10.4062516189094	-0.0316960099752538	10.5320443910659	-0.0470483810906437
83	10.6741	10.7677089441535	0.000849536531861234	10.5796415193147	0.0936089441534822
84	10.8957	11.1595806484230	0.00638333069206466	10.6254360208849	0.263880648423019
85	10.7404	10.730942923546	0.0786265539988212	10.6712305224552	-0.0094570764539963
86	10.6568	10.5393212199272	0.0822453624857993	10.692033417587	-0.117478780072803
87	10.5682	10.4644394017501	-0.0408757144689129	10.7128363127188	-0.103760598249922
88	10.9833	11.310312283311	-0.00499209913591109	10.6612798158249	0.327012283310992
89	11.0237	11.4639351756977	-0.0262584946286676	10.609723318931	0.44023517569766
90	10.8462	11.2053911830280	0.00469814207787817	10.4823106748941	0.359191183028013
91	10.7287	11.152327375922	-0.0498254067792157	10.3548980308572	0.423627375922006
92	10.7809	11.3661060539109	0.00815649503218206	10.1875374510569	0.585206053910911
93	10.2609	10.5289347335760	-0.0273116048325628	10.0201768712566	0.268034733575957
94	9.8252	9.8405577956229	-0.0316960099752538	9.84153821435236	0.0153577956228919
95	9.1071	8.55045090602002	0.000849536531861234	9.66289955744812	-0.556649093979981
96	8.695	7.86689400268922	0.00638333069206466	9.51672266661872	-0.828105997310784
97	9.2205	8.99182767021186	0.0786265539988212	9.37054577578932	-0.228672329788139
98	9.0496	8.71419079856122	0.0822453624857993	9.30276383895298	-0.335409201438779
99	8.7406	8.28709381235227	-0.0408757144689129	9.23498190211664	-0.453506187647728
100	8.921	8.5830793200624	-0.00499209913591109	9.26391277907352	-0.337920679937605
101	9.011	8.75541483859827	-0.0262584946286676	9.2928436560304	-0.255585161401726
102	9.3157	9.24498110000168	0.00469814207787817	9.38172075792044	-0.0707188999983188
103	9.5786	9.73642754696873	-0.0498254067792157	9.47059785981049	0.157827546968726
104	9.6246	9.69266093159368	0.00815649503218206	9.54838257337414	0.0680609315936813
105	9.7485	9.89814431789478	-0.0273116048325628	9.62616728693778	0.149644317894781
106	9.9431	10.2641476523792	-0.0316960099752538	9.65374835759606	0.321047652379189
107	10.1152	10.5482210352138	0.000849536531861234	9.68132942825435	0.433021035213793
108	10.1827	10.7249083376183	0.00638333069206466	9.63410833168963	0.542208337618307
109	9.9777	10.2898862108763	0.0786265539988212	9.58688723512491	0.312186210876268
110	9.7436	9.91792875111132	0.0822453624857993	9.48702588640288	0.174328751111322
111	9.3462	9.34611117678806	-0.0408757144689129	9.38716453768085	-8.88232119375942e-05
112	9.2623	9.23107697246837	-0.00499209913591109	9.29851512666754	-0.0312230275316328
113	9.1505	9.11739277897443	-0.0262584946286676	9.20986571565424	-0.0331072210255723
114	8.5794	8.02459245445172	0.00469814207787817	9.1295094034704	-0.554807545548284
115	8.3245	7.64967231549264	-0.0498254067792157	9.04915309128657	-0.674827684507358
116	8.6538	8.33128099238552	0.00815649503218206	8.9681625125823	-0.322519007614478
117	8.752	8.64413967095455	-0.0273116048325628	8.88717193387802	-0.107860329045453
118	8.8104	8.84054931712284	-0.0316960099752538	8.81194669285241	0.0301493171228433
119	9.2665	9.79542901164134	0.000849536531861234	8.7367214518268	0.528929011641335
120	9.0895	9.50363956657505	0.00638333069206466	8.66897710273289	0.414139566575049

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/1a5co1293369722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/1a5co1293369722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/22wtr1293369722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/22wtr1293369722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/32wtr1293369722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/32wtr1293369722.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/4v5ac1293369722.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/26/t12933696007bc2ylrtjmfmvc1/4v5ac1293369722.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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