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Decomposition by Loess

*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: Mon, 07 Dec 2009 15:45:54 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09.htm/, Retrieved Mon, 07 Dec 2009 23:46:51 +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/2009/Dec/07/t1260226006nw8iui5ip0hxw09.htm/},
    year = {2009},
}
@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 = {2009},
    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:

Decomposition by Loess

Dataseries X:

» Textbox « » Textfile « » CSV «

220206 220115 218444 214912 210705 209673 237041 242081 241878 242621 238545 240337 244752 244576 241572 240541 236089 236997 264579 270349 269645 267037 258113 262813 267413 267366 264777 258863 254844 254868 277267 285351 286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881 293299 288576

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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	941	0	95
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	220206	222139.361771694	2191.20667631383	216081.431551992	1933.36177169447
2	220115	221141.118750762	869.893614638668	218218.987634600	1026.11875076176
3	218444	219568.752050452	-3037.2957676599	220356.543717207	1124.75205045243
4	214912	213272.741670005	-5955.90431884818	222507.162648843	-1639.25832999524
5	210705	208627.353523921	-11875.1351044000	224657.781580479	-2077.64647607942
6	209673	206423.503035089	-13869.4003033098	226791.897268221	-3249.49696491141
7	237041	236866.276054402	8289.7109896351	228926.012955963	-174.723945598205
8	242081	241981.154345692	11142.3402486411	231038.505405666	-99.8456543075445
9	241878	241234.531610265	9370.47053436565	233150.997855370	-643.468389735441
10	242621	245823.553095302	4100.9752814866	235317.471623211	3202.55309530202
11	238545	241116.445825852	-1510.39121690493	237483.945391053	2571.44582585199
12	240337	240740.076238392	283.526112060651	239650.397649547	403.07623839227
13	244752	245495.943415645	2191.20667631383	241816.849908041	743.943415644928
14	244576	244304.627053904	869.893614638668	243977.479331458	-271.372946096235
15	241572	240043.187012786	-3037.2957676599	246138.108754874	-1528.81298721404
16	240541	238841.864752649	-5955.90431884818	248196.039566199	-1699.13524735058
17	236089	233799.164726876	-11875.1351044000	250253.970377524	-2289.83527312367
18	236997	235654.485714459	-13869.4003033098	252208.914588851	-1342.51428554137
19	264579	266704.430210186	8289.7109896351	254163.858800179	2125.43021018611
20	270349	273492.808590811	11142.3402486411	256062.851160548	3143.80859081139
21	269645	271957.685944718	9370.47053436565	257961.843520916	2312.68594471813
22	267037	270348.423685681	4100.9752814866	259624.601032832	3311.42368568148
23	258113	256449.032672157	-1510.39121690493	261287.358544748	-1663.96732784272
24	262813	262736.053032199	283.526112060651	262606.420855741	-76.9469678014284
25	267413	268709.310156952	2191.20667631383	263925.483166734	1296.31015695224
26	267366	268723.509181615	869.893614638668	265138.597203746	1357.50918161491
27	264777	266239.584526901	-3037.2957676599	266351.711240759	1462.58452690096
28	258863	255999.362516145	-5955.90431884818	267682.541802704	-2863.63748385548
29	254844	252549.762739752	-11875.1351044000	269013.372364648	-2294.23726024840
30	254868	253339.582135454	-13869.4003033098	270265.818167856	-1528.41786454635
31	277267	274726.025039301	8289.7109896351	271518.263971064	-2540.97496069915
32	285351	287006.897167738	11142.3402486411	272552.762583621	1655.89716773771
33	286602	290246.268269456	9370.47053436565	273587.261196178	3644.26826945611
34	283042	287470.726870883	4100.9752814866	274512.29784763	4428.72687088343
35	276687	279447.056717823	-1510.39121690493	275437.334499082	2760.0567178232
36	277915	279370.411270416	283.526112060651	276176.062617523	1455.41127041646
37	277128	275150.002587722	2191.20667631383	276914.790735964	-1977.99741227785
38	277103	275919.267932690	869.893614638668	277416.838452671	-1183.73206730967
39	275037	275192.409598282	-3037.2957676599	277918.886169378	155.409598281898
40	270150	267888.981861511	-5955.90431884818	278366.922457337	-2261.01813848934
41	267140	267340.176359103	-11875.1351044000	278814.958745297	200.176359103061
42	264993	264591.386467872	-13869.4003033098	279264.013835438	-401.613532127871
43	287259	286515.220084786	8289.7109896351	279713.068925578	-743.779915213585
44	291186	291170.384721549	11142.3402486411	280059.27502981	-15.6152784511214
45	292300	294824.048331593	9370.47053436565	280405.481134042	2524.04833159281
46	288186	291535.832847547	4100.9752814866	280735.191870967	3349.83284754661
47	281477	283399.488609013	-1510.39121690493	281064.902607892	1922.48860901286
48	282656	283666.749455714	283.526112060651	281361.724432225	1010.74945571402
49	280190	276530.247067128	2191.20667631383	281658.546256559	-3659.75293287239
50	280408	278258.575972374	869.893614638668	281687.530412988	-2149.42402762617
51	276836	274992.781198243	-3037.2957676599	281716.514569416	-1843.21880175656
52	275216	275136.022952009	-5955.90431884818	281251.881366840	-79.9770479913568
53	274352	279791.886940137	-11875.1351044000	280787.248164263	5439.88694013742
54	271311	276667.925553243	-13869.4003033098	279823.474750067	5356.9255532432
55	289802	292454.587674494	8289.7109896351	278859.701335871	2652.58767449425
56	290726	292978.768489573	11142.3402486411	277330.891261786	2252.76848957269
57	292300	299427.448277933	9370.47053436565	275802.081187702	7127.44827793259
58	278506	279266.744397849	4100.9752814866	273644.280320665	760.744397848903
59	269826	269675.911763278	-1510.39121690493	271486.479453627	-150.088236722338
60	265861	262589.549254871	283.526112060651	268848.924633069	-3271.45074512943
61	269034	269665.423511176	2191.20667631383	266211.369812510	631.423511175846
62	264176	263972.477460978	869.893614638668	263509.628924383	-203.522539021971
63	255198	252625.407731404	-3037.2957676599	260807.888036256	-2572.59226859643
64	253353	254275.785358376	-5955.90431884818	258386.118960472	922.785358376248
65	246057	248024.785219712	-11875.1351044000	255964.349884688	1967.78521971244
66	235372	230564.608926460	-13869.4003033098	254048.791376850	-4807.39107353968
67	258556	256689.056141353	8289.7109896351	252133.232869012	-1866.94385864664
68	260993	260293.200353081	11142.3402486411	250550.459398278	-699.799646918953
69	254663	250987.84353809	9370.47053436565	248967.685927544	-3675.15646190979
70	250643	249547.652634694	4100.9752814866	247637.372083819	-1095.34736530599
71	243422	242047.332976810	-1510.39121690493	246307.058240095	-1374.66702318969
72	247105	248678.472671898	283.526112060651	245248.001216041	1573.47267189820
73	248541	250701.849131698	2191.20667631383	244188.944191988	2160.84913169846
74	245039	245847.746373508	869.893614638668	243360.360011854	808.746373507602
75	237080	234665.51993594	-3037.2957676599	242531.775831720	-2414.48006405987
76	237085	237995.34924079	-5955.90431884818	242130.555078058	910.34924078986
77	225554	221253.800780003	-11875.1351044000	241729.334324397	-4300.19921999692
78	226839	225261.183643550	-13869.4003033098	242286.216659759	-1577.81635644956
79	247934	244735.190015243	8289.7109896351	242843.098995122	-3198.80998475698
80	248333	240741.848019879	11142.3402486411	244781.81173148	-7591.15198012133
81	246969	237847.004997796	9370.47053436565	246720.524467839	-9121.9950022042
82	245098	236169.237181142	4100.9752814866	249925.787537372	-8928.76281885823
83	246263	240905.34061	-1510.39121690493	253131.050606905	-5357.65938999978
84	255765	254139.886223203	283.526112060651	257106.587664737	-1625.11377679720
85	264319	265364.668601118	2191.20667631383	261082.124722568	1045.66860111777
86	268347	271022.067466503	869.893614638668	264802.038918858	2675.06746650289
87	273046	280607.342652511	-3037.2957676599	268521.953115149	7561.34265251138
88	273963	281783.664476132	-5955.90431884818	272098.239842716	7820.66447613225
89	267430	271060.608534117	-11875.1351044000	275674.526570283	3630.60853411665
90	271993	278642.794515026	-13869.4003033098	279212.605788283	6649.79451502638
91	292710	294379.604004081	8289.7109896351	282750.685006284	1669.60400408134
92	295881	294454.696643892	11142.3402486411	286164.963107467	-1426.30335610779
93	293299	287648.288256984	9370.47053436565	289579.24120865	-5650.7117430155
94	288576	280190.556144213	4100.9752814866	292860.468574301	-8385.44385578745

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/1gveu1260225950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/1gveu1260225950.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/281r51260225950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/281r51260225950.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/32l8u1260225950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/32l8u1260225950.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/431r91260225950.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/07/t1260226006nw8iui5ip0hxw09/431r91260225950.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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