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*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, 19 Dec 2010 19:27:54 +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/19/t12927867323hfx2ix4541oait.htm/, Retrieved Sun, 19 Dec 2010 20:25:32 +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/19/t12927867323hfx2ix4541oait.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 «

8.7000 8.9000 8.9000 8.1000 8.0000 8.3000 8.5000 8.7000 8.6000 8.3000 7.9000 7.9000 8.1000 8.3000 8.1000 7.4000 7.3000 7.7000 8.0000 8.0000 7.7000 6.9000 6.6000 6.9000 7.5000 7.9000 7.7000 6.5000 6.1000 6.4000 6.8000 7.1000 7.3000 7.2000 7.0000 7.0000 7.0000 7.3000 7.5000 7.2000 7.7000 8.0000 7.9000 8.0000 8.0000 7.9000 7.9000 8.0000 8.1000 8.1000 8.2000 8.0000 8.3000 8.5000 8.6000 8.7000 8.7000 8.5000 8.4000 8.5000 8.7000 8.7000 8.6000 7.9000 8.1000 8.2000 8.5000 8.6000 8.5000 8.3000 8.2000 8.7000 9.3000 9.3000 8.8000 7.4000 7.2000 7.5000 8.3000 8.8000 8.9000 8.6000 8.4000 8.4000 8.4000 8.4000 8.3000 7.6000 7.6000 7.9000 8.0000 8.2000 8.3000 8.2000 8.1000 8.0000 7.8000 7.6000 7.5000 6.8000 6.9000 7.1000 7.3000 7.4000 7.6000 7.6000 7.5000 7.5000 6.8000 6.4000 6.2000 6.0000 6.3000 6.3000 6.1000 6.1000 6.3000

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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	1171	0	118
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	8.7	8.50226059733634	0.151179401603513	8.74656000106015	-0.197739402663663
2	8.9	8.88801549605772	0.225005457853007	8.68697904608928	-0.0119845039422852
3	8.9	9.03377047009582	0.138831438785768	8.6273980911184	0.133770470095824
4	8.1	8.16333840350676	-0.530324069798575	8.56698566629182	0.0633384035067568
5	8	7.94290621403236	-0.449479455497588	8.50657324146522	-0.0570937859676359
6	8.3	8.3401357190917	-0.186276429041907	8.4461407099502	0.0401357190917047
7	8.5	8.56736512108591	0.0469267004789071	8.38570817843518	0.0673651210859116
8	8.7	8.83894064368316	0.235729177246883	8.32533017906996	0.138940643683158
9	8.6	8.64051624159724	0.294531578698026	8.26495217970474	0.0405162415972367
10	8.3	8.31748860660206	0.0794790515869859	8.20303234181095	0.0174886066020630
11	7.9	7.72320107226537	-0.064313576182536	8.14111250391717	-0.176798927734629
12	7.9	7.65421613937726	0.0587107544686073	8.08707310615414	-0.245783860622745
13	8.1	8.01578689000538	0.151179401603513	8.03303370839111	-0.0842131099946242
14	8.3	8.4002558135419	0.225005457853007	7.97473872860509	0.100255813541904
15	8.1	8.14472481239516	0.138831438785768	7.91644374881907	0.0447248123951614
16	7.4	7.4939088021461	-0.530324069798575	7.83641526765247	0.093908802146105
17	7.3	7.29309266901172	-0.449479455497588	7.75638678648587	-0.00690733098828211
18	7.7	7.91532245289672	-0.186276429041907	7.67095397614519	0.215322452896715
19	8	8.36755213371658	0.0469267004789071	7.58552116580451	0.367552133716578
20	8	8.24638533796716	0.235729177246883	7.51788548478596	0.246385337967163
21	7.7	7.65521861753458	0.294531578698026	7.4502498037674	-0.0447813824654215
22	6.9	6.3411501260775	0.0794790515869859	7.37937082233552	-0.558849873922503
23	6.6	5.9558217352789	-0.064313576182536	7.30849184090364	-0.644178264721102
24	6.9	6.51548580885878	0.0587107544686073	7.22580343667261	-0.384514191141217
25	7.5	7.7057055659549	0.151179401603513	7.14311503244158	0.205705565954903
26	7.9	8.48740687135363	0.225005457853007	7.08758767079337	0.587406871353626
27	7.7	8.22910825206908	0.138831438785768	7.03206030914515	0.52910825206908
28	6.5	6.51058790129715	-0.530324069798575	7.01973616850143	0.0105879012971455
29	6.1	5.64206742763988	-0.449479455497588	7.0074120278577	-0.457932572360119
30	6.4	5.99253530671158	-0.186276429041907	6.99374112233033	-0.407464693288424
31	6.8	6.57300308271814	0.0469267004789071	6.98007021680296	-0.226996917281864
32	7.1	6.99514298562754	0.235729177246883	6.96912783712558	-0.104857014372461
33	7.3	7.34728296385377	0.294531578698026	6.9581854574482	0.0472829638537737
34	7.2	7.30979392718783	0.0794790515869859	7.01072702122518	0.109793927187832
35	7	7.00104499118037	-0.064313576182536	7.06326858500216	0.00104499118037182
36	7	6.77616179028032	0.0587107544686073	7.16512745525107	-0.223838209719680
37	7	6.5818342728965	0.151179401603513	7.26698632549998	-0.418165727103494
38	7.3	7.01568131663052	0.225005457853007	7.35931322551647	-0.284318683369476
39	7.5	7.40952843568127	0.138831438785768	7.45164012553296	-0.090471564318726
40	7.2	7.39832457951408	-0.530324069798575	7.5319994902845	0.198324579514082
41	7.7	8.23712060046156	-0.449479455497588	7.61235885503603	0.537120600461559
42	8	8.49660702882084	-0.186276429041907	7.68966940022107	0.496607028820836
43	7.9	7.98609335411498	0.0469267004789071	7.76697994540611	0.0860933541149791
44	8	7.93796558286939	0.235729177246883	7.82630523988373	-0.0620344171306098
45	8	7.81983788694063	0.294531578698026	7.88563053436134	-0.180162113059366
46	7.9	7.7879866313387	0.0794790515869859	7.93253431707431	-0.112013368661296
47	7.9	7.88487547639526	-0.064313576182536	7.97943809978728	-0.0151245236047446
48	8	7.90557169005654	0.0587107544686073	8.03571755547485	-0.0944283099434555
49	8.1	7.95682358723407	0.151179401603513	8.09199701116242	-0.143176412765929
50	8.1	7.817138907791	0.225005457853007	8.157855634356	-0.282861092209007
51	8.2	8.03745430366465	0.138831438785768	8.22371425754958	-0.162545696335352
52	8	8.24909673960108	-0.530324069798575	8.2812273301975	0.249096739601079
53	8.3	8.71073905265218	-0.449479455497588	8.3387404028454	0.410739052652181
54	8.5	8.80132427182254	-0.186276429041907	8.38495215721936	0.301324271822542
55	8.6	8.72190938792777	0.0469267004789071	8.43116391159332	0.121909387927770
56	8.7	8.70502071178774	0.235729177246883	8.45925011096538	0.00502071178773811
57	8.7	8.61813211096454	0.294531578698026	8.48733631033743	-0.0818678890354594
58	8.5	8.43240494320994	0.0794790515869859	8.48811600520308	-0.067595056790065
59	8.4	8.37541787611381	-0.064313576182536	8.48889570006873	-0.0245821238861890
60	8.5	8.46367194383027	0.0587107544686073	8.47761730170112	-0.0363280561697277
61	8.7	8.78248169506297	0.151179401603513	8.46633890333351	0.0824816950629739
62	8.7	8.71891620347183	0.225005457853007	8.45607833867517	0.0189162034718269
63	8.6	8.61535078719741	0.138831438785768	8.44581777401682	0.0153507871974128
64	7.9	7.89626808765296	-0.530324069798575	8.43405598214562	-0.00373191234704073
65	8.1	8.22718526522317	-0.449479455497588	8.42229419027441	0.127185265223174
66	8.2	8.15697751872669	-0.186276429041907	8.42929891031521	-0.043022481273308
67	8.5	8.51676966916508	0.0469267004789071	8.43630363035601	0.0167696691650789
68	8.6	8.50601643264785	0.235729177246883	8.45825439010527	-0.0939835673521543
69	8.5	8.22526327144745	0.294531578698026	8.48020514985453	-0.274736728552554
70	8.3	8.04761035776178	0.0794790515869859	8.47291059065123	-0.252389642238217
71	8.2	7.9986975447346	-0.064313576182536	8.46561603144793	-0.201302455265399
72	8.7	8.9056748607756	0.0587107544686073	8.43561438475579	0.205674860775604
73	9.3	10.0432078603328	0.151179401603513	8.40561273806364	0.743207860332847
74	9.3	9.97994353449932	0.225005457853007	8.39505100764768	0.679943534499317
75	8.8	9.07667928398252	0.138831438785768	8.38448927723171	0.276679283982521
76	7.4	6.94807974932132	-0.530324069798575	8.38224432047725	-0.451920250678677
77	7.2	6.4694800917748	-0.449479455497588	8.3799993637228	-0.730519908225206
78	7.5	6.83155448414625	-0.186276429041907	8.35472194489565	-0.668445515853746
79	8.3	8.22362877345258	0.0469267004789071	8.32944452606851	-0.076371226547419
80	8.8	9.06108025695262	0.235729177246883	8.3031905658005	0.261080256952622
81	8.9	9.2285318157695	0.294531578698026	8.27693660553248	0.328531815769495
82	8.6	8.841240205791	0.0794790515869859	8.279280742622	0.241240205791007
83	8.4	8.582688696471	-0.064313576182536	8.28162487971153	0.182688696471006
84	8.4	8.46474290524565	0.0587107544686073	8.27654634028574	0.0647429052456499
85	8.4	8.37735279753653	0.151179401603513	8.27146780085995	-0.0226472024634656
86	8.4	8.34066399677984	0.225005457853007	8.23433054536715	-0.0593360032201602
87	8.3	8.26397527133988	0.138831438785768	8.19719328987435	-0.0360247286601201
88	7.6	7.57171324096232	-0.530324069798575	8.15861082883625	-0.0282867590376785
89	7.6	7.52945108769944	-0.449479455497588	8.12002836779815	-0.0705489123005627
90	7.9	7.9017118469381	-0.186276429041907	8.08456458210381	0.00171184693809501
91	8	7.90397250311162	0.0469267004789071	8.04910079640948	-0.0960274968883832
92	8.2	8.16529735303537	0.235729177246883	7.99897346971775	-0.0347026469646341
93	8.3	8.35662227827595	0.294531578698026	7.94884614302603	0.0566222782759489
94	8.2	8.43551104503783	0.0794790515869859	7.88500990337518	0.235511045037829
95	8.1	8.4431399124582	-0.064313576182536	7.82117366372434	0.343139912458195
96	8	8.18924219943735	0.0587107544686073	7.75204704609404	0.189242199437351
97	7.8	7.76590016993275	0.151179401603513	7.68292042846374	-0.0340998300672544
98	7.6	7.36231312051659	0.225005457853007	7.6126814216304	-0.237686879483414
99	7.5	7.31872614641716	0.138831438785768	7.54244241479707	-0.181273853582842
100	6.8	6.645628001655	-0.530324069798575	7.48469606814358	-0.154371998345004
101	6.9	6.8225297340075	-0.449479455497588	7.42694972149008	-0.0774702659924955
102	7.1	7.01010743885044	-0.186276429041907	7.37616899019147	-0.0898925611495631
103	7.3	7.22768504062824	0.0469267004789071	7.32538825889286	-0.0723149593717647
104	7.4	7.30842078418436	0.235729177246883	7.25585003856876	-0.0915792158156403
105	7.6	7.71915660305731	0.294531578698026	7.18631181824466	0.119156603057315
106	7.6	8.01512750447172	0.0794790515869859	7.10539344394129	0.415127504471721
107	7.5	8.03983850654461	-0.064313576182536	7.02447506963792	0.539838506544611
108	7.5	8.01152510983279	0.0587107544686073	6.9297641356986	0.51152510983279
109	6.8	6.6137673966372	0.151179401603513	6.83505320175928	-0.186232603362796
110	6.4	5.85267467372677	0.225005457853007	6.72231986842023	-0.547325326273233
111	6.2	5.65158202613306	0.138831438785768	6.60958653508117	-0.54841797386694
112	6	6.03845310611077	-0.530324069798575	6.4918709636878	0.0384531061107722
113	6.3	6.67532406320316	-0.449479455497588	6.37415539229443	0.375324063203156
114	6.3	6.52975833040326	-0.186276429041907	6.25651809863864	0.229758330403264
115	6.1	6.01419249453824	0.0469267004789071	6.13888080498285	-0.0858075054617613
116	6.1	5.94212481718623	0.235729177246883	6.02214600556689	-0.157875182813775
117	6.3	6.40005721515104	0.294531578698026	5.90541120615093	0.100057215151042

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/1puj21292786869.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/1puj21292786869.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/2puj21292786869.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/2puj21292786869.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/30lin1292786869.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/30lin1292786869.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/40lin1292786869.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927867323hfx2ix4541oait/40lin1292786869.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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