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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: Fri, 04 Dec 2009 11:58:36 -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/04/t1259953146jwe1f4f5aesfpss.htm/, Retrieved Fri, 04 Dec 2009 19:59:11 +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/04/t1259953146jwe1f4f5aesfpss.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 «

14.9 18.6 19.1 18.8 18.2 18 19 20.7 21.2 20.7 19.6 18.6 18.7 23.8 24.9 24.8 23.8 22.3 21.7 20.7 19.7 18.4 17.4 17 18 23.8 25.5 25.6 23.7 22 21.3 20.7 20.4 20.3 20.4 19.8 19.5 23.1 23.5 23.5 22.9 21.9 21.5 20.5 20.2 19.4 19.2 18.8 18.8 22.6 23.3 23 21.4 19.9 18.8 18.6 18.4 18.6 19.9 19.2 18.4

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	611	0	62
Trend	19	1	2
Low-pass	13	1	2

Seasonal Decomposition by Loess - Time Series Components
t	Observed	Fitted	Seasonal	Trend	Remainder
1	14.9	16.0833782199729	-2.17917260877246	15.8957943887995	1.18337821997295
2	18.6	18.6924248730188	2.06946731768287	16.4381078092983	0.0924248730187855
3	19.1	18.3692112522954	2.85036751790743	16.9804212297972	-0.730788747704608
4	18.8	17.4449730688559	2.65009560440441	17.5049313267396	-1.35502693114406
5	18.2	16.9407351715805	1.4298234047374	18.0294414236821	-1.25926482841951
6	18	17.2948013746241	0.179085270079645	18.5261133552962	-0.705198625375889
7	19	19.228867540342	-0.251652827252362	19.0227852869104	0.228867540341984
8	20.7	22.4145922042113	-0.528140256457477	19.5135480522462	1.71459220421128
9	21.2	23.2403164077300	-0.844627225312054	20.004310817582	2.04031640773005
10	20.7	22.3216134160153	-1.40869537826754	20.4870819622522	1.62161341601533
11	19.6	19.8829103869749	-1.65276349389733	20.9698531069224	0.282910386974915
12	18.6	18.2619966420433	-2.31378734593564	21.2517907038923	-0.338003357956698
13	18.7	18.0454443079102	-2.17917260877246	21.5337283008623	-0.654555692089804
14	23.8	23.9422797729393	2.06946731768287	21.5882529093778	0.142279772939286
15	24.9	25.3068549641991	2.85036751790743	21.6427775178934	0.406854964199145
16	24.8	25.4081781803178	2.65009560440441	21.5417262152778	0.608178180317768
17	23.8	24.7295016826004	1.4298234047374	21.4406749126622	0.929501682600382
18	22.3	23.1172345840991	0.179085270079645	21.3036801458213	0.817234584099086
19	21.7	22.4849674482720	-0.251652827252362	21.1666853789803	0.784967448272038
20	20.7	20.846102110684	-0.528140256457477	21.0820381457735	0.146102110684016
21	19.7	19.2472363127455	-0.844627225312054	20.9973909125666	-0.452763687254539
22	18.4	17.2203463982370	-1.40869537826754	20.9883489800306	-1.17965360176305
23	17.4	15.4734564464028	-1.65276349389733	20.9793070474946	-1.92654355359725
24	17	15.2953876028983	-2.31378734593564	21.0183997430374	-1.70461239710173
25	18	17.1216801701923	-2.17917260877246	21.0574924385802	-0.878319829807705
26	23.8	24.3821277928127	2.06946731768287	21.1484048895044	0.58212779281271
27	25.5	26.9103151416639	2.85036751790743	21.2393173404287	1.41031514166389
28	25.6	27.1563757033793	2.65009560440441	21.3935286922163	1.55637570337933
29	23.7	24.4224365512588	1.4298234047374	21.5477400440038	0.722436551258767
30	22	22.1543150707330	0.179085270079645	21.6665996591874	0.154315070732974
31	21.3	21.0661935528814	-0.251652827252362	21.7854592743709	-0.233806447118567
32	20.7	20.1708749482594	-0.528140256457477	21.7572653081981	-0.529125051740593
33	20.4	19.9155558832868	-0.844627225312054	21.7290713420252	-0.484444116713156
34	20.3	20.3756449519973	-1.40869537826754	21.6330504262702	0.0756449519973366
35	20.4	20.9157339833821	-1.65276349389733	21.5370295105152	0.515733983382127
36	19.8	20.4199026247389	-2.31378734593564	21.4938847211967	0.619902624738923
37	19.5	19.7284326768942	-2.17917260877246	21.4507399318782	0.228432676894222
38	23.1	22.7041759182931	2.06946731768287	21.426356764024	-0.395824081706881
39	23.5	22.7476588859228	2.85036751790743	21.4019735961698	-0.752341114077218
40	23.5	23.0050409264346	2.65009560440441	21.3448634691610	-0.49495907356539
41	22.9	23.0824232531104	1.4298234047374	21.2877533421522	0.182423253110425
42	21.9	22.3938153670604	0.179085270079645	21.2270993628600	0.493815367060378
43	21.5	22.0852074436846	-0.251652827252362	21.1664453835678	0.585207443684588
44	20.5	20.4071914971068	-0.528140256457477	21.1209487593507	-0.092808502893206
45	20.2	20.1691750901785	-0.844627225312054	21.0754521351336	-0.0308249098215363
46	19.4	19.2127481933926	-1.40869537826754	20.9959471848750	-0.187251806607435
47	19.2	19.1363212592810	-1.65276349389733	20.9164422346164	-0.0636787407190234
48	18.8	19.1419524241542	-2.31378734593564	20.7718349217814	0.341952424154236
49	18.8	19.151944999826	-2.17917260877246	20.6272276089465	0.351944999825999
50	22.6	22.6621573076342	2.06946731768287	20.4683753746829	0.0621573076341981
51	23.3	23.4401093416732	2.85036751790743	20.3095231404194	0.140109341673163
52	23	23.1004797491053	2.65009560440441	20.2494246464903	0.100479749105283
53	21.4	21.1808504427014	1.4298234047374	20.1893261525612	-0.219149557298604
54	19.9	19.4120671109667	0.179085270079645	20.2088476189537	-0.487932889033345
55	18.8	17.6232837419062	-0.251652827252362	20.2283690853462	-1.17671625809383
56	18.6	17.4843739654162	-0.528140256457477	20.2437662910413	-1.11562603458380
57	18.4	17.3854637285757	-0.844627225312054	20.2591634967364	-1.01453627142433
58	18.6	18.3235520859379	-1.40869537826754	20.2851432923296	-0.276447914062082
59	19.9	21.1416404059745	-1.65276349389733	20.3111230879229	1.24164040597446
60	19.2	20.3543946168567	-2.31378734593564	20.3593927290789	1.15439461685671
61	18.4	18.5715102385375	-2.17917260877246	20.407662370235	0.171510238537454

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/14mww1259953114.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/14mww1259953114.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/22r2m1259953114.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/22r2m1259953114.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/3nseo1259953114.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/3nseo1259953114.ps (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/4kbws1259953114.png (open in new window)

http://www.freestatistics.org/blog/date/2009/Dec/04/t1259953146jwe1f4f5aesfpss/4kbws1259953114.ps (open in new window)

Parameters (Session):

par1 = 36 ; par2 = -1.8 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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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