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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: Thu, 03 Dec 2009 09:40:10 -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/03/t1259858468q8p98lhphr19h5y.htm/, Retrieved Thu, 03 Dec 2009 17:41:13 +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/03/t1259858468q8p98lhphr19h5y.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:

Dataseries X:

» Textbox « » Textfile « » CSV «

22 22 20 21 20 21 21 21 19 21 21 22 19 24 22 22 22 24 22 23 24 21 20 22 23 23 22 20 21 21 20 20 17 18 19 19 20 21 20 21 19 22 20 18 16 17 18 19 18 20 21 18 19 19 19 21 19 19 17 16 16 17 16 15 16 16 16 18 19 16 16 16

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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Seasonal Decomposition by Loess - Parameters
Component	Window	Degree	Jump
Seasonal	721	0	73
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	22	23.5446215786073	-0.179958467120170	20.6353368885129	1.54462157860729
2	22	21.9781668554750	1.36098354473269	20.6608495997923	-0.0218331445250257
3	20	18.9117121323421	0.401925556586096	20.6863623110718	-1.08828786765789
4	21	21.5252315700014	-0.247442376272705	20.7222108062713	0.525231570001392
5	20	19.4720841301929	-0.230143431663769	20.7580593014708	-0.527915869807067
6	21	20.3815719971259	0.818402728704188	20.8000252741699	-0.6184280028741
7	21	21.1243944095011	0.0336143436299316	20.841991246869	0.124394409501079
8	21	20.5138199863396	0.593397091427692	20.8927829222327	-0.486180013660423
9	19	17.569912282545	-0.513486880141483	20.9435745975965	-1.43008771745500
10	21	21.7233092515529	-0.788486748344325	21.0651774967915	0.723309251552866
11	21	21.7100398173959	-0.896820213382382	21.1867803959864	0.710039817395941
12	22	22.9889640682733	-0.351984666885551	21.3630205986122	0.988964068273347
13	19	16.6406976658822	-0.179958467120170	21.5392608012380	-2.35930233411779
14	24	24.9156198857781	1.36098354473269	21.7233965694892	0.915619885778113
15	22	21.6905421056735	0.401925556586096	21.9075323377404	-0.309457894326531
16	22	22.2178781052355	-0.247442376272705	22.0295642710372	0.21787810523546
17	22	22.0785472273297	-0.230143431663769	22.1515962043341	0.078547227329711
18	24	24.9584413175504	0.818402728704188	22.2231559537454	0.958441317550399
19	22	21.6716699532133	0.0336143436299316	22.2947157031568	-0.328330046786693
20	23	23.0939472090566	0.593397091427692	22.3126556995157	0.0939472090566191
21	24	26.1828911842669	-0.513486880141483	22.3305956958746	2.18289118426686
22	21	20.5507073513176	-0.788486748344325	22.2377793970268	-0.44929264868243
23	20	18.7518571152035	-0.896820213382382	22.1449630981789	-1.24814288479650
24	22	22.4024325377628	-0.351984666885551	21.9495521291227	0.402432537762838
25	23	24.4258173070536	-0.179958467120170	21.7541411600665	1.42581730705363
26	23	23.1727132367221	1.36098354473269	21.4663032185452	0.172713236722132
27	22	22.4196091663901	0.401925556586096	21.1784652770238	0.419609166390082
28	20	19.3773930358377	-0.247442376272705	20.8700493404350	-0.622606964162326
29	21	21.6685100278175	-0.230143431663769	20.5616334038462	0.668510027817526
30	21	20.8692016340899	0.818402728704188	20.3123956372059	-0.130798365910085
31	20	19.9032277858045	0.0336143436299316	20.0631578705655	-0.0967722141954752
32	20	19.5151203959771	0.593397091427692	19.8914825125952	-0.484879604022908
33	17	14.7936797255166	-0.513486880141483	19.7198071546249	-2.20632027448341
34	18	17.1274707810189	-0.788486748344325	19.6610159673254	-0.872529218981065
35	19	19.2945954333565	-0.896820213382382	19.6022247800259	0.294595433356491
36	19	18.7361712189736	-0.351984666885551	19.615813447912	-0.263828781026426
37	20	20.5505563513221	-0.179958467120170	19.6294021157981	0.550556351322108
38	21	21.0359878154875	1.36098354473269	19.6030286397798	0.0359878154874949
39	20	20.0214192796523	0.401925556586096	19.5766551637616	0.0214192796523349
40	21	22.7642852271299	-0.247442376272705	19.4831571491428	1.76428522712986
41	19	18.8404842971397	-0.230143431663769	19.3896591345241	-0.159515702860340
42	22	23.918427746147	0.818402728704188	19.2631695251488	1.91842774614699
43	20	20.8297057405965	0.0336143436299316	19.1366799157735	0.829705740596545
44	18	16.3753075517735	0.593397091427692	19.0312953567988	-1.62469244822650
45	16	13.5875760823174	-0.513486880141483	18.9259107978241	-2.41242391768261
46	17	15.9578630157803	-0.788486748344325	18.8306237325640	-1.04213698421970
47	18	18.1614835460784	-0.896820213382382	18.7353366673040	0.161483546078419
48	19	19.64484520053	-0.351984666885551	18.7071394663555	0.64484520053
49	18	17.5010162017130	-0.179958467120170	18.6789422654071	-0.498983798286968
50	20	19.8620327393917	1.36098354473269	18.7769837158756	-0.137967260608271
51	21	22.7230492770699	0.401925556586096	18.8750251663440	1.72304927706988
52	18	17.2909418732722	-0.247442376272705	18.9565005030005	-0.709058126727808
53	19	19.1921675920068	-0.230143431663769	19.037975839657	0.192167592006772
54	19	18.2509292655982	0.818402728704188	18.9306680056976	-0.74907073440178
55	19	19.1430254846319	0.0336143436299316	18.8233601717382	0.143025484631885
56	21	22.8374651723261	0.593397091427692	18.5691377362462	1.83746517232615
57	19	20.1985715793873	-0.513486880141483	18.3149153007541	1.19857157938734
58	19	20.7907006580338	-0.788486748344325	17.9977860903105	1.79070065803379
59	17	17.2161633335155	-0.896820213382382	17.6806568798669	0.216163333515460
60	16	14.9862901848083	-0.351984666885551	17.3656944820772	-1.01370981519168
61	16	15.1292263828326	-0.179958467120170	17.0507320842875	-0.870773617167373
62	17	15.8179062919799	1.36098354473269	16.8211101632874	-1.18209370802010
63	16	15.0065862011266	0.401925556586096	16.5914882422873	-0.993413798873386
64	15	13.6364644627282	-0.247442376272705	16.6109779135445	-1.36353553727175
65	16	15.5996758468621	-0.230143431663769	16.6304675848016	-0.400324153137852
66	16	14.5435722057910	0.818402728704188	16.6380250655048	-1.45642779420898
67	16	15.3208031101621	0.0336143436299316	16.6455825462080	-0.67919688983789
68	18	18.7247838069152	0.593397091427692	16.6818191016571	0.72478380691522
69	19	21.7954312230353	-0.513486880141483	16.7180556571062	2.79543122303526
70	16	16.0019013722465	-0.788486748344325	16.7865853760978	0.00190137224649334
71	16	16.0417051182929	-0.896820213382382	16.8551150950894	0.041705118292942
72	16	15.4128994880585	-0.351984666885551	16.939085178827	-0.587100511941454

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/1epnd1259858408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/1epnd1259858408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/26mrq1259858408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/26mrq1259858408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/3pncx1259858408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/3pncx1259858408.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/4b5751259858408.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/03/t1259858468q8p98lhphr19h5y/4b5751259858408.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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