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Paper statistiek - 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, 20 Dec 2010 13:18:44 +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/20/t1292851112mz0ldvl4icoh9rg.htm/, Retrieved Mon, 20 Dec 2010 14:18:38 +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/20/t1292851112mz0ldvl4icoh9rg.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 «

493 514 522 490 484 506 501 462 465 454 464 427 460 473 465 422 415 413 420 363 376 380 384 346 389 407 393 346 348 353 364 305 307 312 312 286 324 336 327 302 299 311 315 264 278 278 287 279 324 354 354 360 363 385 412 370 389 395 417 404

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	601	0	61
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	493	480.818230902225	9.0016299974883	496.180139100287	-12.1817690977750
2	514	504.680140347835	29.7643269514014	493.555532700764	-9.31985965216523
3	522	525.94205240748	27.1270212912793	490.930926301241	3.94205240747965
4	490	491.662097950526	0.301846850505906	488.036055198968	1.66209795052595
5	484	483.382129116384	-0.523313213078866	485.141184096695	-0.61787088361632
6	506	517.825780203495	12.1543793146486	482.019840481857	11.8257802034945
7	501	501.269423840608	21.8320792923732	478.898496867019	0.269423840608226
8	462	475.876649257514	-27.4751000466452	475.598450789131	13.8766492575139
9	465	474.683868008634	-16.9822727198782	472.298404711244	9.68386800863408
10	454	456.726657374498	-16.1842799895037	467.457622615006	2.72665737449779
11	464	472.56945654299	-7.18629706175729	462.616840518768	8.5694565429896
12	427	430.176734517691	-31.8300260244715	455.653291506781	3.17673451769059
13	460	462.308627507718	9.0016299974883	448.689742494794	2.30862750771757
14	473	475.182720107169	29.7643269514014	441.052952941429	2.18272010716925
15	465	469.456815320656	27.1270212912793	433.416163388064	4.45681532065618
16	422	417.478822971285	0.301846850505906	426.219330178209	-4.52117702871487
17	415	411.500816244725	-0.523313213078866	419.022496968353	-3.49918375527454
18	413	401.218936839048	12.1543793146486	412.626683846303	-11.7810631609519
19	420	411.937049983374	21.8320792923732	406.230870724253	-8.0629500166263
20	363	352.952128596696	-27.4751000466452	400.52297144995	-10.0478714033045
21	376	374.167200544232	-16.9822727198782	394.815072175646	-1.83279945576817
22	380	386.745184002375	-16.1842799895037	389.439095987128	6.74518400237542
23	384	391.123177263147	-7.18629706175729	384.06311979861	7.12317726314711
24	346	344.949862429613	-31.8300260244715	378.880163594859	-1.05013757038745
25	389	395.301162611404	9.0016299974883	373.697207391108	6.30116261140398
26	407	415.966416741832	29.7643269514014	368.269256306766	8.96641674183223
27	393	396.031673486296	27.1270212912793	362.841305222425	3.03167348629563
28	346	334.609198693265	0.301846850505906	357.088954456229	-11.390801306735
29	348	345.186709523046	-0.523313213078866	351.336603690033	-2.81329047695425
30	353	348.11330853846	12.1543793146486	345.732312146891	-4.88669146153973
31	364	366.039900103878	21.8320792923732	340.128020603749	2.03990010387764
32	305	302.498470097238	-27.4751000466452	334.976629949407	-2.50152990276194
33	307	301.157033424813	-16.9822727198782	329.825239295065	-5.84296657518701
34	312	314.790843368745	-16.1842799895037	325.393436620759	2.79084336874507
35	312	310.224663115305	-7.18629706175729	320.961633946452	-1.77533688469470
36	286	286.723896936261	-31.8300260244715	317.106129088210	0.723896936261156
37	324	325.747745772543	9.0016299974883	313.250624229969	1.74774577254311
38	336	332.307479169094	29.7643269514014	309.928193879505	-3.69252083090601
39	327	320.26721517968	27.1270212912793	306.605763529041	-6.73278482031992
40	302	299.570618966688	0.301846850505906	304.127534182807	-2.42938103331244
41	299	296.874008376506	-0.523313213078866	301.649304836572	-2.12599162349358
42	311	309.134005159677	12.1543793146486	300.711615525674	-1.86599484032257
43	315	308.393994492851	21.8320792923732	299.773926214775	-6.60600550714867
44	264	254.433114810935	-27.4751000466452	301.04198523571	-9.5668851890648
45	278	270.672228463234	-16.9822727198782	302.310044256645	-7.32777153676648
46	278	265.902654006528	-16.1842799895037	306.281625982976	-12.0973459934721
47	287	270.933089352450	-7.18629706175729	310.253207709307	-16.0669106475496
48	279	272.916242463392	-31.8300260244715	316.913783561079	-6.08375753660795
49	324	315.42401058966	9.0016299974883	323.574359412852	-8.5759894103403
50	354	345.765151955643	29.7643269514014	332.470521092956	-8.2348480443572
51	354	339.506295935661	27.1270212912793	341.366682773059	-14.4937040643388
52	360	367.892328276689	0.301846850505906	351.805824872805	7.89232827668883
53	363	364.278346240528	-0.523313213078866	362.244966972551	1.27834624052781
54	385	385.066107562783	12.1543793146486	372.779513122568	0.0661075627833725
55	412	418.853861435042	21.8320792923732	383.314059272585	6.85386143504178
56	370	373.520776035701	-27.4751000466452	393.954324010944	3.52077603570092
57	389	390.387683970575	-16.9822727198782	404.594588749304	1.38768397057459
58	395	390.921088565861	-16.1842799895037	415.263191423643	-4.07891143413906
59	417	415.254502963775	-7.18629706175729	425.931794097982	-1.74549703622461
60	404	403.243438185595	-31.8300260244715	436.586587838876	-0.756561814404563

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/16shf1292851121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/16shf1292851121.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/26shf1292851121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/26shf1292851121.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/3z1z01292851121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/3z1z01292851121.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/4z1z01292851121.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/20/t1292851112mz0ldvl4icoh9rg/4z1z01292851121.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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